texonom/texonom-md · Datasets at Hugging Face

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Bayes Theorem	null	null	null	null	null	null	## Bayes's rule 사후확률을 사전확률과 likelihood를 이용하여 계산하는 방법 확률적 사고방식을 표현하는 공식일 뿐 [Conditional probability](https://texonom.com/conditional-probability-89f109f0347b4a68b7f31e27dcd0794d), [Joint Probability](https://texonom.com/joint-probability-ddefdc8d4f8d4b3eb3d8dafb5706b8e5), [Marginalization](https://texonom.com/marginalization-de8a54419bb842ba8bbb0ecb951caae7) 정의로 유도되는 한 형태 관측되기 전과 후에 모델의 파라미터에 대한 확률 분포가 어떻게 변하는지에 따라 차이 그래서 자동차 열기 예시가 베이즈 확률을 잘 설명해주는 사례 prior probability과 새로운 증거evidence에 따른 업데이트된 믿음의 정도를 계산하는 공식 사후확률을 계산하기 위해 조건부확률을 사용 likelihood is probability that fits evidence among target prior $$posterior = \frac{prior * marginal \; likelihood}{data \; prior}$$ $$P(A\|B) := \frac{P(B\|A)P(A)}{P(B)} = P(B\|A)P(A) (if B \ne P(A))$$ ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F61a64894-440b-46b9-8a3f-b0b5776bb8e2%2FUntitled.png?table=block&id=2fae2c26-69f7-4006-938d-f5dbc13ac16a&cache=v2) We can chain $\alpha, \beta$ is [Hyperparameter](https://texonom.com/hyperparameter-ef7e34566add4e98b673d4cef59fca90) used to determine prior and $P(D\|\theta )$ not $P(D\|\theta, \alpha, \beta)$ is the reason that 하이퍼파라미터 알파와 베타가 사전확률 분포를 결정하는 데 사용되지만, 데이터 D와 모델 파라미터 theta 간의 관계에는 영향을 미치지 않는다 $$P(\theta\|D, \alpha, \beta) = \frac{P(\theta\|\alpha, \beta)P(D\|\theta)}{P(D\|\alpha, \beta)}$$ ### Bayes Theorem Notion \|Title\| \|:-:\| \|[Posterior](https://texonom.com/posterior-87e0f5df288140c7ba475b0629bdda05)\| \|[Prior Probability](https://texonom.com/prior-probability-34585174a5cd42bbae9094138713932b)\| \|[Odds](https://texonom.com/odds-fc52380a1eb842c8b76a1089ae85311c)\| \|[Bayes Factor](https://texonom.com/bayes-factor-d73be6d93c004384b454957f98e13aad)\| \|[Likelihood](https://texonom.com/likelihood-7a4315f7502440cfbb93b4a469cfe55b)\| \|[Evidence](https://texonom.com/evidence-80ff49d6ff4f44d8a0a212a75012908f)\| ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F05ba0e17-74d6-44c3-94aa-e5cf0c9544bf%2FScreenshot_20191226-002240_YouTube.jpg?table=block&id=dd6553b3-8d59-4ac7-a73b-8caf44072aea&cache=v2) ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F2933798d-3a5d-47d8-8801-5320e1fa3a03%2FScreenshot_20191226-002138_YouTube.jpg?table=block&id=46afb5bb-de49-4736-a73b-64b05d94c285&cache=v2) > [Bayes theorem, the geometry of changing beliefs](https://www.youtube.com/watch?v=HZGCoVF3YvM)	e512b6c0308f4270aaae9ae53060ccab
Markov Chain	Bayesian Statistics Notion	Apr 3, 2022	Alan Jo	Alan Jo	Sep 10, 2023	[Gradient Descent](https://texonom.com/gradient-descent-c1342b13182f4fb6959023a75b5e2ff8)	### 여러 State를 갖는 Chain 형태의 구조 특정 시점의 상태 확률은 단지 그 이전 상태에만 의존한다는 것이 핵심 Markov assumption 을 따르는 이산 시간 확률 과정 마코프 가정은 러시아 수학자 마코프가 1913년경에 러시아어 문헌에 나오는 글자들의 순서에 관한 모델을 구축하기 위해 제안된 개념 [Stationary distribution](https://texonom.com/stationary-distribution-33dad1d30cb44491be6156020969c62c) > [[Machine learning] Markov Chain, Gibbs Sampling, 마르코프 체인, 깁스 샘플링 (day2 / 201010)](https://huidea.tistory.com/128) > [Markov Chain Monte Carlo Without all the Bullshit](https://jeremykun.com/2015/04/06/markov-chain-monte-carlo-without-all-the-bullshit/) > [Markov Chain & Stationary Distribution](https://kim-hjun.medium.com/markov-chain-stationary-distribution-5198941234f6)	497b662ec8cd4bba84c4d947067d717f
Metropolis Algorithm	Bayesian Statistics Notion	Apr 3, 2022	Alan Jo	Alan Jo	Jun 2, 2022		### Metropolis–Hastings algorithm > [Metropolis-Hastings algorithm - Wikipedia](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm)	5af42c3e93a64159a2016705eb71ef4c
Continuous Joint Probability Distribution	Bayesian Statistics Usages	Feb 3, 2020	Alan Jo	Alan Jo	Apr 3, 2022		> [베이지언 러닝 5 - 연속형 결합확률분포(Continuous Joint Probability Distribution)](https://www.youtube.com/watch?v=yPU93luXiLw)	82734d0b70f04ebabef90d2e1395c980
MCMC	Bayesian Statistics Usages	Apr 3, 2022	Alan Jo	Alan Jo	Apr 3, 2022	[Markov Chain](https://texonom.com/markovchain-497b662ec8cd4bba84c4d947067d717f) [Monte Carlo Method](https://texonom.com/monte-carlo-method-9e3e9708b973488eb0f6f3e5c66c852e) [Metropolis Algorithm](https://texonom.com/metropolis-algorithm-5af42c3e93a64159a2016705eb71ef4c)	## Markov chain Monte Carlo 통계적인 특성을 이용해 무수히 뭔가를 많이 시도해본다는 의미로 Monte Carlo라는 이름 통계학의 특성 상 무한히 많은 [Simulation](https://texonom.com/simulation-e039940aa59f4efc8f6b4cefbe1d2673)을 거쳐야만 진짜 정답이 뭔지 알 수 있지만, 그렇게 하기가 현실적으로 어렵기 때문에 Finite 시도만으로 정답을 추정하자 첫 샘플을 랜덤하게 선정한 뒤, 첫 샘플에 의해 그 다음번 샘플이 추천되는 방식의 시도 반복 여기서 추천되는 방식이 각자 다르고 Markov chain에서 Monte Carlo는 Metropolis Algorithm 이용 ### MCMC Notion \|Title\| \|:-:\| > [Markov Chain Monte Carlo](https://angeloyeo.github.io/2020/09/17/MCMC.html) > [Untitled](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo)	80063d374ddd4a3381edc04748063826
Bias	null	null	null	null	null	null	### Can be come from intrinsic not due to the lack of data rather caused by that the family of models fundamentally cannot approximate the ground truth not data	ba063cd622a54deb8a677e8fb87dfdc8
Bias-Variance Trade-off	Probability theory Notion	May 9, 2023	Alan Jo	Alan Jo	May 11, 2023	[Bias](https://texonom.com/bias-ba063cd622a54deb8a677e8fb87dfdc8) [Variance](https://texonom.com/variance-08c1eccc7dc84957afbb815ad6b41280)	### Determine model complexity because this is perspective of model If a model is too simple and has very few parameters, then it may have large bias and small variance > It may typically suffer from underfitting If a model is too complex and has very many parameters, then it may suffer from largevariance but small bias and thus overfitting ### Theoretical background mean squared error or risk = bias^2 + variance ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F5d0f7ab4-d570-46ed-ab0b-eb1cf7ed8f1a%2FUntitled.png?table=block&id=29775cf4-8846-485a-b15d-974242966e62&cache=v2)	753e9b8d891f4f6e9e3e595024ac546e
Correlation	null	null	null	null	null	null	$$-1 \leq corr(X, Y) = \frac{cov(X, Y)}{\sigma_X\sigma_Y} \leq 1$$ ### Difference with [Convolution](https://texonom.com/convolution-54def9d34de64e199ea46393675af2ce) is flip $$(f \ast g) (x, y) = \int f(i,j) I(x+i, y+j)$$ ### Correlations \|Title\| \|:-:\| \|[Pearson correlation coefficient](https://texonom.com/pearson-correlation-coefficient-7a5a92a34f8944efb0d2c28dce89f913)\| > [Correlation](https://en.wikipedia.org/wiki/Correlation)	d75ea902ec294bf19e1180b6bfd22137
Covariance	null	null	null	null	null	null	### a measure of correlation $$cov(X, Y) = E[(x - E[X])(Y - E[Y])] \newline = E[XY] - E[X]E[Y]$$ - positively correlated - uncorrelated - negatively correlated	f3b864d48bf14625a4415c8f0500e688
Deviation	Probability theory Notion	Mar 16, 2023	Alan Jo	Alan Jo	Jun 6, 2023		## 편차 ### Deviations \|Title\| \|:-:\| \|[Standard Deviation](https://texonom.com/standard-deviation-792bf99f68174ae38bb95a0721831fe8)\|	6637194ca1b046ac9b681c550e6b853b
Expectation value	Probability theory Notion	Mar 9, 2023	Alan Jo	Alan Jo	Jun 5, 2023	[Expectation](https://texonom.com/expectation-e1e2f11d2f864805a5cb8a673bbfb774)	$$E[X] = \Sigma_x{xP(X= x)} = \int{xf(x)dx}$$ ### k-th moment of X defined as the expected value of x raised to the power of k $$E[X^k] =\Sigma_xx^kP(X = x)$$ ### If only X, Y is independence, $E[XY] = E[X]E[Y]$ $E[X]=0$ does not means $E[X^2] = 0$	3e14abcd31734ddea3fa0d1c92e3d63f
Mean	Probability theory Notion	Mar 7, 2023	Alan Jo	Alan Jo	Mar 7, 2023		### Mean Usages \|Title\| \|:-:\| \|[Sample Mean](https://texonom.com/sample-mean-3e3c5fd01f72460aacfd4c11c94e781b)\|	1ea2a9d53da24baab2bc057d4d781e41
Probability	Probability theory Notion	Apr 1, 2021	Alan Jo	Alan Jo	Mar 7, 2023		### Probability Notion \|Title\| \|:-:\| \|[Probability Space](https://texonom.com/probability-space-3fd335842e494992b50cc2c3a2b38c8b)\| \|[Continuous Probability](https://texonom.com/continuous-probability-858f49fcb68f43eaa7d2be67e6abca45)\| \|[Joint Distribution](https://texonom.com/joint-distribution-939ae5cbac404e9eb369afb843f9ba75)\| ### Probability Properties \|Title\| \|:-:\| \|[Conditional probability](https://texonom.com/conditional-probability-89f109f0347b4a68b7f31e27dcd0794d)\| \|[Marginalization](https://texonom.com/marginalization-de8a54419bb842ba8bbb0ecb951caae7)\| \|[Joint Probability](https://texonom.com/joint-probability-ddefdc8d4f8d4b3eb3d8dafb5706b8e5)\| \|[Marginal Probability](https://texonom.com/marginal-probability-ee22b391f7f44fab8b821400cf67e63d)\| \|[Probability Independence](https://texonom.com/probability-independence-0be53b596155414ab2819b0cd525d50d)\|	6b1e766c2c6442c7a599b558453300e4
Probability distribution	null	null	null	null	null	null	> [Probability distribution - Wikipedia](https://en.wikipedia.org/wiki/Probability_distribution)	2d33768bdc43438794829b004dd37804
Random Variable	Probability theory Notion	Mar 7, 2023	Alan Jo	Alan Jo	Jun 11, 2023		### Random Variable Notion \|Title\| \|:-:\| \|[Random Vector](https://texonom.com/random-vector-7e1c3cbc223d4f939e5dd65bb0da384f)\| \|[Indicator random variable](https://texonom.com/indicator-random-variable-cac27017b7ba4e0db0242d305884e37d)\| \|[Random number](https://texonom.com/random-number-23cec3dc46b74275a70c50875d9708cc)\|	0bc19e0582784ec3a6e0de5b91296212
Variance	null	null	null	null	null	null	### spurious Pattern Comes from randomness of dataset Variance captures how the random nature of the finite dataset not family of model i.e. the sensitivity of the model to the randomness in the dataset $$Var(X) = E[(X - E[X])^2] \newline= E[X^2] - 2E[X]E[X] + E[X]^2 \newline = E[X^2] - E[X]^2$$ $$Var(X) = Cov(X, X)$$ ### Variance Usages \|Title\| \|:-:\| \|[ANOVA](https://texonom.com/anova-aad04dffd648401c8c44525003c6f083)\| \|[law of total variance](https://texonom.com/law-of-total-variance-481cd44bdfde4e069f7f5f6913e17eb8)\|	08c1eccc7dc84957afbb815ad6b41280
Pearson correlation coefficient	Correlations	May 2, 2023	Alan Jo	Alan Jo	May 2, 2023		## PCC - the correlation coefficient - Pearson product-moment correlation coefficient - PPMCC - bivariate correlation - Pearson's r ### Property - ranges from −1 to 1 ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fa7d2bc58-3aff-44a8-ae44-317b75bb027d%2FUntitled.png?table=block&id=e9168a5e-cb8a-4836-b5e2-391646d396b2&cache=v2) > [Pearson correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient)	7a5a92a34f8944efb0d2c28dce89f913
Standard Deviation	null	null	null	null	null	null	### SD	792bf99f68174ae38bb95a0721831fe8
Sample Mean	Mean Usages	Mar 7, 2023	Alan Jo	Alan Jo	Mar 7, 2023		### Sample Mean Notion \|Title\| \|:-:\| \|[The law of Large number](https://texonom.com/the-law-of-large-number-a2eeb851d5e242bea80d7a122e4f8e78)\|	3e3c5fd01f72460aacfd4c11c94e781b
The law of Large number	null	null	null	null	null	null	## Laplace Theorem 모집단에서 무작위로 뽑은 표본의 평균이 큰수로 갈수록 전체 모집단의 평균으로 근사한다 [de Moivre - Laplace Theorem](https://texonom.com/de-moivre--laplace-theorem-67212a2c48ee4220ad4bd709ea2982dd)	a2eeb851d5e242bea80d7a122e4f8e78
Continuous Probability	Probability Notion	Mar 7, 2023	Alan Jo	Alan Jo	Mar 7, 2023		single point is always zero need integral ### Continuous Probability Notion \|Title\| \|:-:\| \|[Probability Density Function](https://texonom.com/probability-density-function-8c4790cbb52e485586d767f4f499da49)\| \|[Cumulative Distribution Function](https://texonom.com/cumulative-distribution-function-379072b12ae0492abdb3178913c1a5a9)\|	858f49fcb68f43eaa7d2be67e6abca45
Joint Distribution	Probability Notion	Mar 15, 2023	Alan Jo	Alan Jo	Mar 15, 2023		It describes the likelihood of occurrence of two or more random variables	939ae5cbac404e9eb369afb843f9ba75
Probability Space	Probability Notion	Mar 7, 2023	Alan Jo	Alan Jo	Mar 27, 2023		### defined by triplet - sample space $\Omega$ set of all possible outcomes - $\sigma$- Field F (set of subset with sample space for the probability case) $F \subset 2^{\Omega}$ - Probability P : F → [0, 1] ### event E is subset of Omega > [Probability spaces and random variables](https://www.youtube.com/watch?v=DqGUwoz4d4M)	3fd335842e494992b50cc2c3a2b38c8b
Cumulative Distribution Function	Continuous Probability Notion	Mar 7, 2023	Alan Jo	Alan Jo	Mar 7, 2023		### CDF	379072b12ae0492abdb3178913c1a5a9
Probability Density Function	Continuous Probability Notion	Mar 7, 2023	Alan Jo	Alan Jo	Mar 7, 2023		### PDF can be greater than 1 at a particular point	8c4790cbb52e485586d767f4f499da49
Conditional probability	null	null	null	null	null	null	### Pipe \| is typically read as ‘given that’ however can also indicate Conditional Probability $$P(A\|B) = P(A, B) / P(B)$$ 최적값을 구하려고 하는 게 항상 조건에 간다 ### Semicolon ; is grand kind of comma > [What does a semicolon denote in the context of probability and statistics?](https://math.stackexchange.com/questions/2559085/what-does-a-semicolon-denote-in-the-context-of-probability-and-statistics) > [What do vertical bars mean in statistical distributions?](https://stats.stackexchange.com/questions/110194/what-do-vertical-bars-mean-in-statistical-distributions)	89f109f0347b4a68b7f31e27dcd0794d
Joint Probability	null	null	null	null	null	null		ddefdc8d4f8d4b3eb3d8dafb5706b8e5
Marginal Probability	null	null	null	null	null	null	### 다른 확률 변수의 값을 무시한 부분 집합 속의 확률 변수의 분포 calculated by summing or integrating the joint probability distribution function over all possible values of the variables probability distribution of a single variable without taking into account the values of other variables 그 부분 집합에 속한 확률 변수들의 확률분포 위의 부분 집합에 속한 확률 변수들을 Marginal Variable	ee22b391f7f44fab8b821400cf67e63d
Marginalization	null	null	null	null	null	null	## Law of total Probability 조건부 확률로부터 조건이 붙지 않은 확률을 계산할 때 $P(A) = \Sigma{P(A, B_i)} = \Sigma{P(A\|B_i)}P(B_i)$ After that we can decide independence	de8a54419bb842ba8bbb0ecb951caae7
Probability Independence	null	null	null	null	null	null	### Difference Between mutual independent and pairwise independent 서로서로 동시에 영향 안준다고 합쳐졌을 때 영향 없는 것은 아님 $P(A, B) = P(A)P(B)$ [Conditionally Independent](https://texonom.com/conditionally-independent-8fe069550d0b4a28b031eed8293a7392)	0be53b596155414ab2819b0cd525d50d
Conditionally Independent	Probability Independence	null	null	null	null	null	A is conditionally independent of B given C if, $$P(A\|B, C) = P(A\|C)$$ A, B are conditionally independent given C if, $$P(A, B\|C) = P(A\|C) \cdot P(B\|C)$$	8fe069550d0b4a28b031eed8293a7392
Random Vector	Random Variable Notion	Mar 9, 2023	Alan Jo	Alan Jo	Mar 9, 2023			7e1c3cbc223d4f939e5dd65bb0da384f
chi Square	Probability theory Usages	Jan 23, 2022	Alan Jo	Alan Jo	Apr 3, 2022		### 합을 이용해서 오차 또는 편차를 정의 자유도는 몇개의 표준정규분포 변수를 더한건가 1. 각 표준정규분포 샘플 하나 추출 2. 제곱합한 값의 위치 분포 우리가 얻은 데이터들은 모델의 출력값을 중심으로 하는 정규분포에서 랜덤하게 샘플링되어 얻은 값이라고 보고 error를 정규분포로 설계한다는 점 ### chi Square Notion \|Title\| \|:-:\| \|[chi Square Distribution](https://texonom.com/chi-square-distribution-014792b9b4f849f38edcbe52e9d8deb1)\| \|[chi Square Test](https://texonom.com/chi-square-test-a34793e6d05e432f968f1249c09b505b)\| \|[Pearson's chi-squared statistics](https://texonom.com/pearsons-chi-squared-statistics-954324a08d9e4a8494a62493a56ea3e7)\| > [카이제곱 분포와 검정](https://www.youtube.com/watch?v=_GrdeYtYLO4) > [카이제곱 분포와 검정](https://angeloyeo.github.io/2021/12/13/chi_square.html)	697c74917a0b4a9c83b1856d89bde6af
The Goodhart's Law	Probability theory Usages	May 31, 2021	Alan Jo	Alan Jo	May 2, 2023	[Gamification](https://texonom.com/gamification-ffc99e95fb57466fbcf5e13ee4ebbed6) [Overfitting](https://texonom.com/overfitting-24c3b183372845e8999ad7f7a0ba5035)	### 측정값이 목표가 되면 더 이상 좋은 측정값이 아니다 관측된 통계적 규칙성은 그것을 조종할 목적으로 개입할 경우 사라져버리는 경향 특정 수치를 만족시키기 위해 시스템을 "게임화"함으로써 국소적으로만 최적화하는 경향 영국의 경제학자 Charles Goodhart의 이름을 따서 명명	ccece645e5e3484381fe0721d6ba2cd8
chi Square Distribution	chi Square Notion	Jan 23, 2022	Alan Jo	Alan Jo	Jan 23, 2022			014792b9b4f849f38edcbe52e9d8deb1
chi Square Test	chi Square Notion	Jan 23, 2022	Alan Jo	Alan Jo	Jan 23, 2022		오차를 검증하려는 것에서 우연히 발생한 것인지 숨겨진 의미가 있는지 판별가능 [Goodness of fit Test](https://texonom.com/goodness-of-fit-test-6c9fc48cd54c47d0accec760b8e1beb3) [Cross Tabulation Analysis](https://texonom.com/cross-tabulation-analysis-379ac6e0176146ecbfcc09fb487696ab)	a34793e6d05e432f968f1249c09b505b
Pearson's chi-squared statistics	chi Square Notion	Jan 23, 2022	Alan Jo	Alan Jo	Jan 23, 2022		세트 간 관측 된 차이가 우연히 발생했을 가능성을 평가 카이 제곱 분포를 참조하여 결과를 평가하는 통계 절차 인 여러 카이 제곱 검정 중 가장 널리 사용 편차의 제곱을 기댓값으로 나눠 정규화 표준편차로 나누지 못하는 이유는 통계량 증명 과정에서 있다 > [카이제곱 분포와 검정](https://www.youtube.com/watch?v=_GrdeYtYLO4)	954324a08d9e4a8494a62493a56ea3e7
Cross Tabulation Analysis	chi Square Test	null	null	null	null	null	교차분석 범주형 변수가 여러 개인 경우 적용 여러 번주형 변수의 범주간 차이가 기댓값에서 유의미하게 벗어나는지	379ac6e0176146ecbfcc09fb487696ab
Goodness of fit Test	chi Square Test	null	null	null	null	null	적합도 검정 범주형 변수(독립)가 하나이고 이론적으로 기대되는 빈도의 분포(frequency distribution)와 관찰한 빈도의 분포를 비교하기 위해	6c9fc48cd54c47d0accec760b8e1beb3
Autoregressive	null	null	null	null	null	null	시간에 따라 변하는 특정 프로세스를 설명 출력 변수가 자신의 이전 값과 확률적 항에 선형적으로 의존함을 의미	93cf5710b4b54730a7e7efcc6e0fc642
Bayesian	null	null	null	null	null	null	## Subjectivism, epistemic, logical probability Bayesian school 확률의 신뢰도로 해석하고 그에 기반한다 발생 가능성에 대해 알고 있을때, 이를 직접적으로 이용하여 계산 ## Relative probability	abfa2017bb054f3a9dfcbc9a6c1042f6
BP	Statistics Terms	Mar 27, 2022	Alan Jo	Alan Jo	Jun 6, 2023		### BPS ### Basic Point 0.01%	512f1e376cbc4448adec9a1f5acb66a6
Degrees of Freedom	Statistics Terms	Jan 22, 2022	Alan Jo	Alan Jo	Jun 6, 2023		### 자유도 독립적으로 달라질 수있는 시스템의 매개 변수의 수 평면의 한 점은 변환에 대해 두 개의 자유도를 갖는다 number of values in the final calculation of a [statistic](https://en.wikipedia.org/wiki/Statistic) that are free to vary 통계적 제한을 받지 않고 자유롭게 변화를 줄수 있는 독립 원소의 수 > [Degrees of freedom (statistics) - Wikipedia](https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)) > [통계의 자유도(degree of freedom : df)](https://wiserloner.tistory.com/1013)	35beaefd93fd46d58172097155eedab9
Frequentist	null	null	null	null	null	null	### Frequentism, Classical Probability, Frequentist school no [Posterior](https://texonom.com/posterior-87e0f5df288140c7ba475b0629bdda05) [Prior Probability](https://texonom.com/prior-probability-34585174a5cd42bbae9094138713932b) 확률의 빈도로 해석 관찰된 데이터와 관찰되지 않은 데이터들에 의한 우도에 의존 계산량이 적다	c7636520ad8d4ae3ba69b8c24f516ab1
Mean	Statistics Terms	May 2, 2023	Alan Jo	Alan Jo	Jun 6, 2023		## Average ### Averages \|Title\| \|:-:\| \|[Arithmetic Average](https://texonom.com/arithmetic-average-86fa34b8da344ec38c89ceff73b67a60)\| \|[Geometric Average](https://texonom.com/geometric-average-8dcca049c6a94778815ec6b114d89125)\|	e903056370974e0082893cb8ea8952dd
p-value	Statistics Terms	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023	[t-value](https://texonom.com/t-value-4f1e6fb2b0034235910718dd48de8096)	### 우리가 얻은 검정 통계량보다 크거나 같은 값을 얻을 수 있을 확률 계산하는 검정 통계량들은 거의 대부분이 [Null Hypothesis](https://texonom.com/null-hypothesis-ce9a2477f77f48b09553e7a0c47da050) 을 가정하고 얻게되는 값 다시 말해 두 표본 평균의 차이를 검증한다고 할 때, 두 표본 집단의 모집단은 같다는 가정을 전제 두 표본 집단의 특징값의 평균이 통계적으로 유의한 차이가 있는지 검증 p-value는 이 [t-value](https://texonom.com/t-value-4f1e6fb2b0034235910718dd48de8096) 에 관한 확률 보통은 5% 기준을 많이 사용한다. 그래서 p-value가 5%보다 작으면 유의한 차이가 있다고 얘기 효과의 크기(effect size)와 표본의 크기(n 수)의 정보를 한꺼번에 담고있다 즉 실제로 한 모집단에서 두 표본 집단이 나왔음에도 n의 차이로 p-value는 0.05보다 낮을 수 있다 그러므로 p-value를 맹신하지 말아야 한다 > [p-value의 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/03/29/p_value.html)	73c98ef557494f86a7ae0c1dba8f81df
Percent	Statistics Terms	Mar 27, 2022	Alan Jo	Alan Jo	Jun 6, 2023		> [당신이 미처 몰랐던 확률 개념](https://youtube.com/watch?v=Exjc8D8drP0&feature=shares)	f4c541ab49fe4ffb92ec673995898108
Robust	Statistics Terms	Jun 28, 2021	Alan Jo	Alan Jo	Jun 6, 2023		이상값에 영향을 적게 받는 통계량을 로버스트한 통계량 > [로버스트(robust) 하다?](https://m.blog.naver.com/vnf3751/220827101273)	062dfadfcdd64fff9b828cca5442a684
Statistical parameter	Statistics Terms	Jun 6, 2023	Alan Jo	Alan Jo	Jun 25, 2023		### Parameter 전체 집단의 모든 데이터를 알지 못하더라도 수학적으로 그 분포를 기술할 수 있는 특성값들을 알 수만 있다면 그걸 모수라고 함 - [Expectation value](https://texonom.com/expectation-value-3e14abcd31734ddea3fa0d1c92e3d63f) - [Variance](https://texonom.com/variance-08c1eccc7dc84957afbb815ad6b41280) - [Standard Deviation](https://texonom.com/standard-deviation-792bf99f68174ae38bb95a0721831fe8) ### Statistical parameter Notion \|Title\| \|:-:\| \|[Confidence interval](https://texonom.com/confidence-interval-68004b3ce6204c808b5994a38464c4a2)\| \|[Confidence Level](https://texonom.com/confidence-level-046400554651433cac5f5dec69f542f0)\| \|[Effect Size](https://texonom.com/effect-size-14b3f7443cfb49fd94ccb2604bc16434)\| > [표본과 표준 오차의 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/02/12/standard_error.html)	0e888c61f6cd48b7a2df1217087f07d1
Statistical Population	Statistics Terms	Jun 6, 2023	Alan Jo	Alan Jo	Jun 25, 2023		### **모집단** 관심 대상의 전체 집합 [Statistical parameter](https://texonom.com/statistical-parameter-0e888c61f6cd48b7a2df1217087f07d1) > [표본과 표준 오차의 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/02/12/standard_error.html)	f2a529ec04b646b1af86335b788a2030
Test statistic	Statistics Terms	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023		## 검정 통계량 통계적 가설의 진위 여부를 검정하기 위해 표본으로 부터 계산하는 통계량 즉 표본 통계량을 2차 가공한 것 ### Test statistics \|Title\| \|:-:\| \|[t-value](https://texonom.com/t-value-4f1e6fb2b0034235910718dd48de8096)\| \|[f test](https://texonom.com/f-test-60ca3e84894c4929b6b1dbecb61f3385)\| > [Test statistic](https://en.wikipedia.org/wiki/Test_statistic)	11746f80eefb4309b516bc06160718d6
Arithmetic Average	Averages	May 2, 2023	Alan Jo	Alan Jo	May 2, 2023	null		86fa34b8da344ec38c89ceff73b67a60
Geometric Average	Averages	May 2, 2023	Alan Jo	Alan Jo	May 2, 2023	null	$$(\Pi a_i)^{1/n}$$ [compounding effect](https://texonom.com/compounding-effect-4c3ebe3d22a0458b8518c5a87bc1130d) compounding effect 반영가	8dcca049c6a94778815ec6b114d89125
compounding effect	Geometric Average	null	null	null	null	null		4c3ebe3d22a0458b8518c5a87bc1130d
Confidence interval	Statistical parameter Notion	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023		> [Confidence interval](https://en.wikipedia.org/wiki/Confidence_interval)	68004b3ce6204c808b5994a38464c4a2
Confidence Level	Statistical parameter Notion	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023			046400554651433cac5f5dec69f542f0
Effect Size	Statistical parameter Notion	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023		### Effect Size Types \|Title\| \|:-:\| \|[Cohen's D](https://texonom.com/cohens-d-e406e8e0848d457188a631df615b8755)\| > [Effect size](https://en.wikipedia.org/wiki/Effect_size)	14b3f7443cfb49fd94ccb2604bc16434
Cohen's D	Effect Size Types	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023	null		e406e8e0848d457188a631df615b8755
f test	Test statistics	Jul 13, 2023	Alan Jo	Alan Jo	Jul 13, 2023	[F Distribution](https://texonom.com/f-distribution-491a1836300446499b51b79e388b9e80)		60ca3e84894c4929b6b1dbecb61f3385
t-value	Test statistics	Jun 6, 2023	Alan Jo	Alan Jo	Jun 6, 2023		### Paired t-test ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F1160b548-031e-4a43-95a2-da68ce36e9f2%2FUntitled.png?table=block&id=7844eb5b-76de-4561-8d12-53cfa355abea&cache=v2) > [t-value의 의미와 스튜던트의 T 테스트 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/02/13/Students_t_test.html)	4f1e6fb2b0034235910718dd48de8096
Statistical Inference	null	null	null	null	null	null	![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F3a8a3f1e-02ef-49ad-b017-39b7a61e6fe2%2FUntitled.png?table=block&id=9209f048-47cd-486c-b54b-8cc2cf432859&cache=v2) > [Statistical inference - Wikipedia](https://en.wikipedia.org/wiki/Statistical_inference) > [통계적 추론 - Big Picture](https://angeloyeo.github.io/2020/02/11/big_picture_stats_infer.html)	168ef97c06d24b44bb49653d70516e73
Statistics Tool	Statistics Usages	Oct 6, 2021	Alan Jo	Alan Jo	Apr 3, 2022		### Statistics Tools \|Title\| \|:-:\| \|[statsmodels](https://texonom.com/statsmodels-96fb7be66a01419cbd417f6342f384d6)\| \|[numpy](https://texonom.com/numpy-8a514dfb88ef49c19959f85d43b2fafc)\| \|[Pandas](https://texonom.com/pandas-c7aa68bdc16545418519cf18e791c346)\| \|[scikit-learn](https://texonom.com/scikit-learn-e37a30b2d2ac4edea30825c8be0c7ddf)\| \|[StatsForecast](https://texonom.com/statsforecast-17a112dd5c554673be0b654758ba92fb)\|	cd8ad9a0f6be46b4979d8e302c6dbd52
numpy	Statistics Tools	Sep 24, 2020	Alan Jo	Alan Jo	Aug 19, 2023		### numpy Usages \|Title\| \|:-:\| \|[numpy subsampling](https://texonom.com/numpy-subsampling-567f9cfa79d5415ea17b357c71d59ebc)\| \|[numpy.sqrt](https://texonom.com/numpysqrt-9a01904b3df24cce877c513b3a133f1d)\| \|[numpy.pad](https://texonom.com/numpypad-3ec51ac35c954b6294a5b37099655261)\| \|[numpy.ones](https://texonom.com/numpyones-121a1bfaa2274e06b0b2d521057af876)\| \|[numpy.zeros_like](https://texonom.com/numpyzeroslike-caa460eb53c44c84821e77344ee7d29b)\| \|[numpy.sum](https://texonom.com/numpysum-63171863a2064059825bd42833f31aad)\| \|[numpy.dstack](https://texonom.com/numpydstack-261094d453194bb6aff5526b4bb11c5a)\| \|[np.conj](https://texonom.com/npconj-b8fa8274980447deb35dc20ff7a2c2fe)\| \|[numpy.arrange](https://texonom.com/numpyarrange-5abc5c6dd50b4af5be9c5d9e86557037)\| \|[numpy.reshape](https://texonom.com/numpyreshape-d9797e899197489981b55c67849e710f)\| \|[numpy.full()](https://texonom.com/numpyfull-8e57ff0d90854ab6a7747ca384e4a6fa)\| \|[numpy.empty()](https://texonom.com/numpyempty-3a55645bdeee4266920c3e415d9525fc)\| \|[numpy.memmap](https://texonom.com/numpymemmap-a26cd2ad2e4f49338d8d5d1d5cdd1d31)\| ### numpy Notion \|Title\| \|:-:\| \|[numpy Boolean Indexing](https://texonom.com/numpy-boolean-indexing-55e814616d504e4cb921d506f8110713)\| \|[numpy broadcasting semantic](https://texonom.com/numpy-broadcasting-semantic-9ac806088cbe4a869f6e5676f4e91b2d)\| > [NumPy documentation — NumPy v1.24 Manual](https://numpy.org/doc/stable/index.html)	8a514dfb88ef49c19959f85d43b2fafc
Pandas	Statistics Tools	Nov 5, 2019	Alan Jo	Seong-lae Cho	May 1, 2023		append 도 그냥 return 만 하고 자동 업데이트 안해서 좀 뻘짓했다.. pandas 자체 성격이 그런듯 ### Pandas Notion \|Title\| \|:-:\| \|[Pandas Class](https://texonom.com/pandas-class-54f6fe2fea2b4faf82041da11e8d33dc)\| ### pandas Usages \|Title\| \|:-:\| \|[polars](https://texonom.com/polars-2df74bdc72e44bbfa0b2e0e816f8651e)\| \|[](https://texonom.com/95f186e7c7174acba2d8b0e1c3729e6c)\| \|[pandas AI](https://texonom.com/pandas-ai-46da363d6b444fe7955bab2f60085f2c)\| > [Python\| Pandas dataframe.append() - GeeksforGeeks](https://www.geeksforgeeks.org/python-pandas-dataframe-append/)	c7aa68bdc16545418519cf18e791c346
scikit-learn	Statistics Tools	Oct 16, 2021	Alan Jo	Alan Jo	May 24, 2023		### scikit-learn Usages \|Title\| \|:-:\| \|[scikit-llm](https://texonom.com/scikit-llm-5f9754697e81460eaa6aab50031f2088)\|	e37a30b2d2ac4edea30825c8be0c7ddf
StatsForecast	Statistics Tools	Aug 21, 2022	Alan Jo	Alan Jo	Aug 21, 2022	[Numba](https://texonom.com/numba-92b190dc95ab40308495541afc11a0d1)	[statsforecast](https://github.com/Nixtla/statsforecast)	17a112dd5c554673be0b654758ba92fb
statsmodels	Statistics Tools	Oct 6, 2021	Alan Jo	Alan Jo	Oct 6, 2021		### statsmodels Usage \|Title\| \|:-:\| > [Introduction - statsmodels](https://www.statsmodels.org/stable/index.html) > [Untitled](https://notebook.community/zzsza/Datascience_School/13.%20Scikit-Learn%2C%20Statsmodel/05.%20statsmodels%20%ED%8C%A8%ED%82%A4%EC%A7%80%20%EC%86%8C%EA%B0%9C)	96fb7be66a01419cbd417f6342f384d6
numpy Boolean Indexing	numpy Notion	Sep 24, 2020	Alan Jo	Alan Jo	Aug 19, 2023		```typea[b > 0] = b[b > 0]```	55e814616d504e4cb921d506f8110713
numpy broadcasting semantic	numpy Notion	May 25, 2023	Alan Jo	Alan Jo	Aug 19, 2023		data copy 없이 ### In-place semantics broadcasting에 따라 in-place tensor의 모양이 변경되지 않는다 ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F72309b61-e4f1-4d08-8fc0-3f50b44b0042%2FUntitled.png?table=block&id=e43379de-3b70-4a33-a85b-aa58e7de5036&cache=v2) 1차원은 broadcasting되는데 2차원부터 안되니까 1차원만 되는 이유 차원 없다면 뒤부터 둔다 ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F8a1d486d-e229-46ad-981d-c4c094f05088%2FUntitled.png?table=block&id=47c2b71b-8bc5-4684-9744-0e24448f0750&cache=v2) 즉 위 첫 케이스에서 3을 중간에 둘 수 없다 ### Backwards compatibility > [How does pytorch broadcasting work?](https://stackoverflow.com/questions/51371070/how-does-pytorch-broadcasting-work) > [pytorch broadcasting](https://velog.io/@optjyy/pytorch-broad-casting)	9ac806088cbe4a869f6e5676f4e91b2d
np.conj	numpy Usages	Apr 14, 2023	Alan Jo	Alan Jo	Apr 26, 2023		### np.conjugate Return the complex conjugate	b8fa8274980447deb35dc20ff7a2c2fe
numpy subsampling	numpy Usages	Oct 20, 2020	Alan Jo	Alan Jo	Apr 13, 2023		```type[start::jump]``` or random > [subsampling every nth entry in a numpy array](https://stackoverflow.com/questions/25876640/subsampling-every-nth-entry-in-a-numpy-array)	567f9cfa79d5415ea17b357c71d59ebc
numpy.arrange	numpy Usages	Apr 19, 2023	Alan Jo	Alan Jo	Apr 19, 2023		like range function > [(파이썬) numpy.arange](https://codepractice.tistory.com/88)	5abc5c6dd50b4af5be9c5d9e86557037
numpy.dstack	numpy Usages	Apr 13, 2023	Alan Jo	Alan Jo	Apr 13, 2023			261094d453194bb6aff5526b4bb11c5a
numpy.empty()	numpy Usages	May 29, 2023	Alan Jo	Alan Jo	May 29, 2023			3a55645bdeee4266920c3e415d9525fc
numpy.full()	numpy Usages	May 29, 2023	Alan Jo	Alan Jo	May 29, 2023			8e57ff0d90854ab6a7747ca384e4a6fa
numpy.ones	numpy Usages	Apr 13, 2023	Alan Jo	Alan Jo	Apr 13, 2023		create array which has all components 1	121a1bfaa2274e06b0b2d521057af876
numpy.pad	numpy Usages	Oct 20, 2020	Alan Jo	Alan Jo	Apr 13, 2023	[Matrix Padding](https://texonom.com/matrix-padding-0f44aaaee9d54bb3a6960130541ac90a)	### Padding ```typenumpy.pad```	3ec51ac35c954b6294a5b37099655261
numpy.reshape	numpy Usages	Apr 19, 2023	Alan Jo	Alan Jo	Apr 19, 2023			d9797e899197489981b55c67849e710f
numpy.sqrt	numpy Usages	Sep 24, 2020	Alan Jo	Alan Jo	Apr 13, 2023		> [numpy.sqrt - NumPy v1.19 Manual](https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html)	9a01904b3df24cce877c513b3a133f1d
numpy.sum	numpy Usages	Apr 13, 2023	Alan Jo	Alan Jo	Apr 13, 2023			63171863a2064059825bd42833f31aad
numpy.zeros_like	numpy Usages	Apr 13, 2023	Alan Jo	Alan Jo	Apr 13, 2023			caa460eb53c44c84821e77344ee7d29b
Pandas Class	Pandas Notion	Nov 5, 2019	Alan Jo	Seong-lae Cho	Jun 2, 2023		### Pandas Classes \|Title\| \|:-:\| \|[Pandas DataFrame](https://texonom.com/pandas-dataframe-ade738f428f542b0a5e884467b841290)\| \|[Pandas Series](https://texonom.com/pandas-series-6dc9909d3e98499896b66ffc41542fbb)\|	54f6fe2fea2b4faf82041da11e8d33dc
Pandas DataFrame	Pandas Classes	Nov 5, 2019	Alan Jo	Seong-lae Cho	Jun 2, 2023		```typepd.DataFrame(data)``` list of dictionary can be converted directly ### Add same value column ```typedf['Name'] = 'abc'``` ### Pandas DataFrame Usages \|Title\| \|:-:\| \|[Dataframe to list of dict](https://texonom.com/dataframe-to-list-of-dict-04751c84aabb4a41a7444b0fbff4fe2d)\| \|[lance rs](https://texonom.com/lance-rs-d2dc40c991944ef2b1e0e35392d809cf)\| \|[Draft py](https://texonom.com/draft-py-077240b76a714c99b317025991bfc2f3)\| > [Untitled](https://stackoverflow.com/questions/29517072/add-column-to-dataframe-with-default-value) > [Convert list of dictionaries to a pandas DataFrame](https://stackoverflow.com/questions/20638006/convert-list-of-dictionaries-to-a-pandas-dataframe)	ade738f428f542b0a5e884467b841290
Pandas Series	Pandas Classes	Nov 5, 2019	Alan Jo	Seong-lae Cho	Jun 2, 2023		1차원	6dc9909d3e98499896b66ffc41542fbb
Dataframe to list of dict	Pandas DataFrame Usages	Sep 10, 2020	Alan Jo	Alan Jo	Jun 2, 2023		```typedf.to_dict('records'):``` > [Pandas DataFrame to List of Dictionaries](https://stackoverflow.com/questions/29815129/pandas-dataframe-to-list-of-dictionaries)	04751c84aabb4a41a7444b0fbff4fe2d
Draft py	Pandas DataFrame Usages	Jun 11, 2023	Alan Jo	Alan Jo	Jun 11, 2023		[Daft](https://github.com/Eventual-Inc/Daft)	077240b76a714c99b317025991bfc2f3
lance rs	Pandas DataFrame Usages	Jun 2, 2023	Alan Jo	Alan Jo	Jun 2, 2023	[lance](https://github.com/lancedb/lance)		d2dc40c991944ef2b1e0e35392d809cf
[pygwalker](https://github.com/Kanaries/pygwalker)	pandas Usages	Jul 15, 2022	Alan Jo	Alan Jo	May 1, 2023			95f186e7c7174acba2d8b0e1c3729e6c
pandas AI	pandas Usages	May 1, 2023	Alan Jo	Alan Jo	May 1, 2023		[pandas-ai](https://github.com/gventuri/pandas-ai)	46da363d6b444fe7955bab2f60085f2c
polars	pandas Usages	Jul 15, 2022	Alan Jo	Alan Jo	May 1, 2023		rust. and py	2df74bdc72e44bbfa0b2e0e816f8651e
scikit-llm	scikit-learn Usages	May 24, 2023	Alan Jo	Alan Jo	May 24, 2023	‣		5f9754697e81460eaa6aab50031f2088
Algebra	null	null	null	null	null	null	### Algebra Areas \|Title\| \|:-:\| \|[Linear Algebra](https://texonom.com/linear-algebra-a5879da463c442d89c51891d124f97ac)\| \|[Lie Algebra](https://texonom.com/lie-algebra-77e6ab22461948778fff08818171cdae)\| \|[Universal algebra](https://texonom.com/universal-algebra-8f94ab573ea2438b84deac618daafeda)\| \|[Algebraic Structure](https://texonom.com/algebraic-structure-4fb610f539064ec18d3edf2b310b7759)\|	e7024eed5b654acbaae54725ccc6b15f
Arithmetic	Math fields	Dec 17, 2021	Alan Jo	Alan Jo	Jun 6, 2023	[Number Theory](https://texonom.com/number-theory-0bf9f82f550d43d382ba1c67ebb7dae2)	### 숫자가 들어가는 순간 어느정도의 이산성이 주입된다 산술은 수학의 가장 역사 깊은 분야로, 수의 개념이나 수에 대하여 간단한 계산을 하는 방법, 그 성질이나 계산의 법칙 등의 이론적인 방법을 다루는 학문 특히 정수, 유리수, 실수, 복소수를 사용하여 계산하는 방법 ### Arithmetic Notion \|Title\| \|:-:\| \|[Number Theory](https://texonom.com/number-theory-0bf9f82f550d43d382ba1c67ebb7dae2)\| \|[Fixed-point arithmetic](https://texonom.com/fixed-point-arithmetic-c46e0722c58c4e2fbc1d2f7027bf6fbe)\| \|[Arithmetic Precision](https://texonom.com/arithmetic-precision-baffc5389f06430eb20806e985685c9b)\| \|[Elementary arithmetic](https://texonom.com/elementary-arithmetic-57a9f00b3f30433299816f32b4d49fbd)\| \|[Exponentiation](https://texonom.com/exponentiation-760c53a791ee4d6696e819b079afe066)\|	0c758b320acb4e919df40892427248d0
Calculus	null	null	null	null	null	null	### 인간에게 연속적인 것을 직관적으로 이해시킨 방법론 ### Calculus Notion \|Title\| \|:-:\| \|[Derivation](https://texonom.com/derivation-79d0547aee0d45ce93cdae0f26bc3ce6)\| \|[Integral](https://texonom.com/integral-ed91b8e9d33d49bfa6a32e93f7bfdfca)\| \|[Inflection point](https://texonom.com/inflection-point-6448287d912942cea85ee85a981505d6)\| \|[Vector Calculus](https://texonom.com/vector-calculus-77976c6127ad49c9a6611e16a40f337f)\| \|[Explicit Function](https://texonom.com/explicit-function-df8104e2876c42e9b112f6308718e3bc)\| \|[Implicit Function](https://texonom.com/implicit-function-1e383ff61a8b4831abca72e4c37649bd)\| \|[Local extremum point](https://texonom.com/local-extremum-point-f7a7579a29474436b2a8670a28fed921)\| \|[Convex Point](https://texonom.com/convex-point-160b14cc61114a8a9be9797578e11c7a)\| \|[Concave Point](https://texonom.com/concave-point-c3f6835eb9ef4378830d3b916da3f074)\| ### Calculus Examples \|Title\| \|:-:\| \|[The Tower Function](https://texonom.com/the-tower-function-7a63cab2617a402782fbf88c9055d43c)\|	8e37e7dac61e435da6a6970da7296f73
Chaos Theory	null	null	null	null	null	null	조그만 변화로 크게 변화 ### Chaos Theory Notion \|Title\| \|:-:\| \|[Lorenz Attractor](https://texonom.com/lorenz-attractor-b3249a819200420797f82e204cc9d58c)\| \|[Butterfly Effect](https://texonom.com/butterfly-effect-62e1b65850da4b3ab2d429292473f8a1)\| \|[Complex System](https://texonom.com/complex-system-b2457d8f6fcc4fe2abffd71828908a1f)\|	2fbd6b2c5e474a63b6f07a90803b8f9d
Discrete Math	null	null	null	null	null	null	### Discrete Math Topics \|Title\| \|:-:\| \|[Pigeonhole principle](https://texonom.com/pigeonhole-principle-998c7a67c04e43d28b132eaa02d5f0d8)\| \|[Order Theory](https://texonom.com/order-theory-8c7e8fb9638f41b19b6829d686fc6f9b)\| \|[Combinatorics](https://texonom.com/combinatorics-887b47c6bb1c46388a8387d89bd304cf)\|	6cd7d73a0fe94fd981f0d59b2c906714
Ergodic theory	Math fields	Apr 3, 2022	Alan Jo	Alan Jo	Apr 5, 2022		### Ergodic theory Notion \|Title\| \|:-:\| \|[Poincare Recurrence Theorem](https://texonom.com/poincare-recurrence-theorem-1aca4c4a3d2446c1892de56b1071953c)\| \|[Dynamical System](https://texonom.com/dynamical-system-a4e33185067b49b28e8f62454028f7b1)\| > [Ergodic theory - Wikipedia](https://en.wikipedia.org/wiki/Ergodic_theory)	ead101eaed774cacbd95b2497b8837c6
Foundations of Mathematics	Math fields	Jun 19, 2022	Alan Jo	Alan Jo	May 13, 2023	[Mathematical Logic](https://texonom.com/mathematical-logic-dc5a5765623c4cef9f76a78cca288960) [Set Theory](https://texonom.com/set-theory-a74b3919af5e4e6e885862f6f76103f9)	### Foundations of Mathematics Notion \|Title\| \|:-:\| \|[Gödel’s incompleteness theorem](https://texonom.com/gdels-incompleteness-theorem-820d082fd9bf424f8125dda3bf9e859b)\| \|[Langlands program](https://texonom.com/langlands-program-629d720ec59b4bf4a42c0b066675b220)\| \|[Set Theory](https://texonom.com/set-theory-a74b3919af5e4e6e885862f6f76103f9)\| \|[Type Theory](https://texonom.com/type-theory-a6967220456b47498b951f11598381f7)\| \|[Category Theory](https://texonom.com/category-theory-1b6594b7d4ce4c128ec2f9aed95d9f3c)\| > [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://www.youtube.com/watch?v=oippSXvxUlw&t=590s)	62157cb1d60a461cace32359d099137f
Measure Theory	null	null	null	null	null	null	### Measure Theory Notion \|Title\| \|:-:\| \|[Lebesgue Theorem](https://texonom.com/lebesgue-theorem-50dd4d0d814244799c6b43126d669c5d)\| \|[Null Set](https://texonom.com/null-set-1f83671ec46848a4b8232daad30419bd)\| \|[Measure Zero](https://texonom.com/measure-zero-84f55b9439c743f390eb69ddbd5f4a5b)\| > [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://youtu.be/oippSXvxUlw) > [당신이 미처 몰랐던 확률 개념](https://youtube.com/watch?v=Exjc8D8drP0&feature=shares)	4fb6210801ea4d7abcb937cd068ba461
Number Theory	Arithmetic Notion	Nov 5, 2019	Alan Jo	Seong-lae Cho	Sep 3, 2023	[Arithmetic](https://texonom.com/arithmetic-0c758b320acb4e919df40892427248d0) [Harmonic Analysis](https://texonom.com/harmonic-analysis-e1e54ebeffd0407088bebab57acbfd53)	### Number Theory Notion \|Title\| \|:-:\| \|[Infinite](https://texonom.com/infinite-f4d16a6949084f6c9c9763e78492486b)\| \|[Number System](https://texonom.com/number-system-4bfd6d8ac2e34aef9e0c847ccd7c1378)\| \|[Factorial](https://texonom.com/factorial-5b4059c4407b4c2f9c3be0f8357ae7ae)\| \|[Real Number](https://texonom.com/real-number-2c5c6fff21ab429da38ba685b40bacf3)\| \|[Integer](https://texonom.com/integer-e87e20fb8fb94fe98202d49d95aefbdc)\| ### Number Theory Example \|Title\| \|:-:\| \|[Analytic number theory](https://texonom.com/analytic-number-theory-2ca0555c60b344aba8890dc7741bf191)\| \|[램지이론](https://texonom.com/742ac0cefcaa43018afea17a47f3ef34)\| \|[Collatz conjecture](https://texonom.com/collatz-conjecture-d6e27f23c9d34778a8f072bcf28edc81)\| \|[BCD](https://texonom.com/bcd-1d73c802caab457486434bb9e661aa95)\|	0bf9f82f550d43d382ba1c67ebb7dae2

Bayes Theorem

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## Bayes's rule **사후확률을 사전확률과 likelihood를 이용하여 계산하는 방법** 확률적 사고방식을 표현하는 공식일 뿐 [Conditional probability](https://texonom.com/conditional-probability-89f109f0347b4a68b7f31e27dcd0794d), [Joint Probability](https://texonom.com/joint-probability-ddefdc8d4f8d4b3eb3d8dafb5706b8e5), [Marginalization](https://texonom.com/marginalization-de8a54419bb842ba8bbb0ecb951caae7) 정의로 유도되는 한 형태 관측되기 전과 후에 모델의 파라미터에 대한 확률 분포가 어떻게 변하는지에 따라 차이 그래서 자동차 열기 예시가 베이즈 확률을 잘 설명해주는 사례 prior probability과 새로운 증거evidence에 따른 업데이트된 믿음의 정도를 계산하는 공식 사후확률을 계산하기 위해 조건부확률을 사용 likelihood is probability that fits evidence among target prior $$posterior = \frac{prior * marginal \; likelihood}{data \; prior}$$ $$P(A|B) := \frac{P(B|A)P(A)}{P(B)} = P(B|A)P(A) (if B \ne P(A))$$ ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F61a64894-440b-46b9-8a3f-b0b5776bb8e2%2FUntitled.png?table=block&id=2fae2c26-69f7-4006-938d-f5dbc13ac16a&cache=v2) We can chain $\alpha, \beta$ is [Hyperparameter](https://texonom.com/hyperparameter-ef7e34566add4e98b673d4cef59fca90) used to determine prior and $P(D|\theta )$ not $P(D|\theta, \alpha, \beta)$ is the reason that 하이퍼파라미터 알파와 베타가 사전확률 분포를 결정하는 데 사용되지만, 데이터 D와 모델 파라미터 theta 간의 관계에는 영향을 미치지 않는다 $$P(\theta|D, \alpha, \beta) = \frac{P(\theta|\alpha, \beta)P(D|\theta)}{P(D|\alpha, \beta)}$$ ### Bayes Theorem Notion |Title| |:-:| |[Posterior](https://texonom.com/posterior-87e0f5df288140c7ba475b0629bdda05)| |[Prior Probability](https://texonom.com/prior-probability-34585174a5cd42bbae9094138713932b)| |[Odds](https://texonom.com/odds-fc52380a1eb842c8b76a1089ae85311c)| |[Bayes Factor](https://texonom.com/bayes-factor-d73be6d93c004384b454957f98e13aad)| |[Likelihood](https://texonom.com/likelihood-7a4315f7502440cfbb93b4a469cfe55b)| |[Evidence](https://texonom.com/evidence-80ff49d6ff4f44d8a0a212a75012908f)| ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F05ba0e17-74d6-44c3-94aa-e5cf0c9544bf%2FScreenshot_20191226-002240_YouTube.jpg?table=block&id=dd6553b3-8d59-4ac7-a73b-8caf44072aea&cache=v2) ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F2933798d-3a5d-47d8-8801-5320e1fa3a03%2FScreenshot_20191226-002138_YouTube.jpg?table=block&id=46afb5bb-de49-4736-a73b-64b05d94c285&cache=v2) > [Bayes theorem, the geometry of changing beliefs](https://www.youtube.com/watch?v=HZGCoVF3YvM)

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**Markov Chain**

Bayesian Statistics Notion

Apr 3, 2022

Alan Jo

Sep 10, 2023

[Gradient Descent](https://texonom.com/gradient-descent-c1342b13182f4fb6959023a75b5e2ff8)

### 여러 State를 갖는 Chain 형태의 구조 **특정 시점의 상태 확률은 단지 그 이전 상태에만 의존한다는 것이 핵심** **Markov assumption 을 따르는 이산 시간 확률 과정** 마코프 가정은 러시아 수학자 마코프가 1913년경에 러시아어 문헌에 나오는 글자들의 순서에 관한 모델을 구축하기 위해 제안된 개념 [Stationary distribution](https://texonom.com/stationary-distribution-33dad1d30cb44491be6156020969c62c) > [[Machine learning] Markov Chain, Gibbs Sampling, 마르코프 체인, 깁스 샘플링 (day2 / 201010)](https://huidea.tistory.com/128) > [Markov Chain Monte Carlo Without all the Bullshit](https://jeremykun.com/2015/04/06/markov-chain-monte-carlo-without-all-the-bullshit/) > [Markov Chain & Stationary Distribution](https://kim-hjun.medium.com/markov-chain-stationary-distribution-5198941234f6)

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Metropolis Algorithm

Bayesian Statistics Notion

Apr 3, 2022

Alan Jo

Jun 2, 2022

### **Metropolis–Hastings algorithm** > [Metropolis-Hastings algorithm - Wikipedia](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm)

5af42c3e93a64159a2016705eb71ef4c

Continuous Joint Probability Distribution

Bayesian Statistics Usages

Feb 3, 2020

Alan Jo

Apr 3, 2022

> [베이지언 러닝 5 - 연속형 결합확률분포(Continuous Joint Probability Distribution)](https://www.youtube.com/watch?v=yPU93luXiLw)

82734d0b70f04ebabef90d2e1395c980

**MCMC**

Bayesian Statistics Usages

Apr 3, 2022

Alan Jo

Apr 3, 2022

[Markov Chain](https://texonom.com/markovchain-497b662ec8cd4bba84c4d947067d717f) [Monte Carlo Method](https://texonom.com/monte-carlo-method-9e3e9708b973488eb0f6f3e5c66c852e) [Metropolis Algorithm](https://texonom.com/metropolis-algorithm-5af42c3e93a64159a2016705eb71ef4c)

## **Markov chain Monte Carlo** 통계적인 특성을 이용해 무수히 뭔가를 많이 시도해본다는 의미로 Monte Carlo라는 이름 통계학의 특성 상 무한히 많은 [Simulation](https://texonom.com/simulation-e039940aa59f4efc8f6b4cefbe1d2673)을 거쳐야만 진짜 정답이 뭔지 알 수 있지만, 그렇게 하기가 현실적으로 어렵기 때문에 Finite 시도만으로 정답을 추정하자 첫 샘플을 랜덤하게 선정한 뒤, 첫 샘플에 의해 그 다음번 샘플이 추천되는 방식의 시도 반복 여기서 추천되는 방식이 각자 다르고 Markov chain에서 Monte Carlo는 Metropolis Algorithm 이용 ### **MCMC Notion** |Title| |:-:| > [Markov Chain Monte Carlo](https://angeloyeo.github.io/2020/09/17/MCMC.html) > [Untitled](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo)

80063d374ddd4a3381edc04748063826

Bias

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### Can be come from intrinsic not due to the lack of data rather caused by that the **family of models** fundamentally cannot approximate the ground truth not data

ba063cd622a54deb8a677e8fb87dfdc8

Bias-Variance Trade-off

Probability theory Notion

May 9, 2023

Alan Jo

May 11, 2023

[Bias](https://texonom.com/bias-ba063cd622a54deb8a677e8fb87dfdc8) [Variance](https://texonom.com/variance-08c1eccc7dc84957afbb815ad6b41280)

### Determine model complexity because this is perspective of model If a model is too simple and has very few parameters, then it may have large bias and small variance > It may typically suffer from underfitting If a model is too complex and has very many parameters, then it may suffer from largevariance but small bias and thus overfitting ### Theoretical background mean squared error or risk = bias^2 + variance ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F5d0f7ab4-d570-46ed-ab0b-eb1cf7ed8f1a%2FUntitled.png?table=block&id=29775cf4-8846-485a-b15d-974242966e62&cache=v2)

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Correlation

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$$-1 \leq corr(X, Y) = \frac{cov(X, Y)}{\sigma_X\sigma_Y} \leq 1$$ ### Difference with [Convolution](https://texonom.com/convolution-54def9d34de64e199ea46393675af2ce) is flip $$(f \ast g) (x, y) = \int f(i,j) I(x+i, y+j)$$ ### Correlations |Title| |:-:| |[Pearson correlation coefficient](https://texonom.com/pearson-correlation-coefficient-7a5a92a34f8944efb0d2c28dce89f913)| > [Correlation](https://en.wikipedia.org/wiki/Correlation)

d75ea902ec294bf19e1180b6bfd22137

Covariance

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### a measure of correlation $$cov(X, Y) = E[(x - E[X])(Y - E[Y])] \newline = E[XY] - E[X]E[Y]$$ - positively correlated - uncorrelated - negatively correlated

f3b864d48bf14625a4415c8f0500e688

Deviation

Probability theory Notion

Mar 16, 2023

Alan Jo

Jun 6, 2023

6637194ca1b046ac9b681c550e6b853b

Expectation value

Probability theory Notion

Mar 9, 2023

Alan Jo

Jun 5, 2023

[Expectation](https://texonom.com/expectation-e1e2f11d2f864805a5cb8a673bbfb774)

$$E[X] = \Sigma_x{xP(X= x)} = \int{xf(x)dx}$$ ### k-th moment of X defined as the expected value of x raised to the power of k $$E[X^k] =\Sigma_xx^kP(X = x)$$ ### If only X, Y is independence, $E[XY] = E[X]E[Y]$ $E[X]=0$ does not means $E[X^2] = 0$

3e14abcd31734ddea3fa0d1c92e3d63f

Mean

Probability theory Notion

Mar 7, 2023

Alan Jo

Mar 7, 2023

1ea2a9d53da24baab2bc057d4d781e41

Probability

Probability theory Notion

Apr 1, 2021

Alan Jo

Mar 7, 2023

### Probability Notion |Title| |:-:| |[Probability Space](https://texonom.com/probability-space-3fd335842e494992b50cc2c3a2b38c8b)| |[Continuous Probability](https://texonom.com/continuous-probability-858f49fcb68f43eaa7d2be67e6abca45)| |[Joint Distribution](https://texonom.com/joint-distribution-939ae5cbac404e9eb369afb843f9ba75)| ### Probability Properties |Title| |:-:| |[Conditional probability](https://texonom.com/conditional-probability-89f109f0347b4a68b7f31e27dcd0794d)| |[Marginalization](https://texonom.com/marginalization-de8a54419bb842ba8bbb0ecb951caae7)| |[Joint Probability](https://texonom.com/joint-probability-ddefdc8d4f8d4b3eb3d8dafb5706b8e5)| |[Marginal Probability](https://texonom.com/marginal-probability-ee22b391f7f44fab8b821400cf67e63d)| |[Probability Independence](https://texonom.com/probability-independence-0be53b596155414ab2819b0cd525d50d)|

6b1e766c2c6442c7a599b558453300e4

**Probability distribution**

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> [Probability distribution - Wikipedia](https://en.wikipedia.org/wiki/Probability_distribution)

2d33768bdc43438794829b004dd37804

Random Variable

Probability theory Notion

Mar 7, 2023

Alan Jo

Jun 11, 2023

### Random Variable Notion |Title| |:-:| |[Random Vector](https://texonom.com/random-vector-7e1c3cbc223d4f939e5dd65bb0da384f)| |[Indicator random variable](https://texonom.com/indicator-random-variable-cac27017b7ba4e0db0242d305884e37d)| |[Random number](https://texonom.com/random-number-23cec3dc46b74275a70c50875d9708cc)|

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Variance

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### spurious Pattern Comes from randomness of dataset Variance captures how the **random nature of the finite dataset** not family of model i.e. the sensitivity of the model to the randomness in the dataset $$Var(X) = E[(X - E[X])^2] \newline= E[X^2] - 2E[X]E[X] + E[X]^2 \newline = E[X^2] - E[X]^2$$ $$Var(X) = Cov(X, X)$$ ### Variance Usages |Title| |:-:| |[ANOVA](https://texonom.com/anova-aad04dffd648401c8c44525003c6f083)| |[law of total variance](https://texonom.com/law-of-total-variance-481cd44bdfde4e069f7f5f6913e17eb8)|

08c1eccc7dc84957afbb815ad6b41280

**Pearson correlation coefficient**

Correlations

May 2, 2023

Alan Jo

May 2, 2023

## **PCC** - **the correlation coefficient** - **Pearson product-moment correlation coefficient** - **PPMCC** - **bivariate correlation** - **Pearson's r** ### Property - ranges from −1 to 1 ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2Fa7d2bc58-3aff-44a8-ae44-317b75bb027d%2FUntitled.png?table=block&id=e9168a5e-cb8a-4836-b5e2-391646d396b2&cache=v2) > [Pearson correlation coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient)

7a5a92a34f8944efb0d2c28dce89f913

Standard Deviation

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### SD

792bf99f68174ae38bb95a0721831fe8

Sample Mean

Mean Usages

Mar 7, 2023

Alan Jo

Mar 7, 2023

3e3c5fd01f72460aacfd4c11c94e781b

The law of Large number

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## Laplace Theorem 모집단에서 무작위로 뽑은 표본의 평균이 큰수로 갈수록 전체 모집단의 평균으로 근사한다 [de Moivre - Laplace Theorem](https://texonom.com/de-moivre--laplace-theorem-67212a2c48ee4220ad4bd709ea2982dd)

a2eeb851d5e242bea80d7a122e4f8e78

Continuous Probability

Probability Notion

Mar 7, 2023

Alan Jo

Mar 7, 2023

single point is always zero need integral ### Continuous Probability Notion |Title| |:-:| |[Probability Density Function](https://texonom.com/probability-density-function-8c4790cbb52e485586d767f4f499da49)| |[Cumulative Distribution Function](https://texonom.com/cumulative-distribution-function-379072b12ae0492abdb3178913c1a5a9)|

858f49fcb68f43eaa7d2be67e6abca45

Joint Distribution

Probability Notion

Mar 15, 2023

Alan Jo

Mar 15, 2023

It describes the likelihood of occurrence of two or more random variables

939ae5cbac404e9eb369afb843f9ba75

Probability Space

Probability Notion

Mar 7, 2023

Alan Jo

Mar 27, 2023

### defined by triplet - sample space $\Omega$ set of all possible outcomes - $\sigma$- Field F (set of subset with sample space for the probability case) $F \subset 2^{\Omega}$ - Probability P : F → [0, 1] ### event E is subset of Omega > [Probability spaces and random variables](https://www.youtube.com/watch?v=DqGUwoz4d4M)

3fd335842e494992b50cc2c3a2b38c8b

Cumulative Distribution Function

Continuous Probability Notion

Mar 7, 2023

Alan Jo

Mar 7, 2023

### CDF

379072b12ae0492abdb3178913c1a5a9

Probability Density Function

Continuous Probability Notion

Mar 7, 2023

Alan Jo

Mar 7, 2023

### PDF can be greater than 1 at a particular point

8c4790cbb52e485586d767f4f499da49

Conditional probability

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### Pipe | is typically read as ‘given that’ however can also indicate Conditional Probability $$P(A|B) = P(A, B) / P(B)$$ 최적값을 구하려고 하는 게 항상 조건에 간다 ### Semicolon ; is grand kind of comma > [What does a semicolon denote in the context of probability and statistics?](https://math.stackexchange.com/questions/2559085/what-does-a-semicolon-denote-in-the-context-of-probability-and-statistics) > [What do vertical bars mean in statistical distributions?](https://stats.stackexchange.com/questions/110194/what-do-vertical-bars-mean-in-statistical-distributions)

89f109f0347b4a68b7f31e27dcd0794d

Joint Probability

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ddefdc8d4f8d4b3eb3d8dafb5706b8e5

Marginal Probability

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### 다른 확률 변수의 값을 무시한 부분 집합 속의 확률 변수의 분포 calculated by summing or integrating the joint probability distribution function over all possible values of the variables probability distribution of a single variable without taking into account the values of other variables 그 부분 집합에 속한 확률 변수들의 확률분포 위의 부분 집합에 속한 확률 변수들을 Marginal Variable

ee22b391f7f44fab8b821400cf67e63d

Marginalization

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## Law of total Probability 조건부 확률로부터 조건이 붙지 않은 확률을 계산할 때 $P(A) = \Sigma{P(A, B_i)} = \Sigma{P(A|B_i)}P(B_i)$ After that we can decide independence

de8a54419bb842ba8bbb0ecb951caae7

Probability Independence

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### Difference Between mutual independent and pairwise independent 서로서로 동시에 영향 안준다고 합쳐졌을 때 영향 없는 것은 아님 $P(A, B) = P(A)P(B)$ [Conditionally Independent](https://texonom.com/conditionally-independent-8fe069550d0b4a28b031eed8293a7392)

0be53b596155414ab2819b0cd525d50d

Conditionally Independent

Probability Independence

null

8fe069550d0b4a28b031eed8293a7392

Random Vector

Random Variable Notion

Mar 9, 2023

Alan Jo

Mar 9, 2023

7e1c3cbc223d4f939e5dd65bb0da384f

chi Square

Probability theory Usages

Jan 23, 2022

Alan Jo

Apr 3, 2022

### 합을 이용해서 오차 또는 편차를 정의 자유도는 몇개의 표준정규분포 변수를 더한건가 1. 각 표준정규분포 샘플 하나 추출 2. 제곱합한 값의 위치 분포 우리가 얻은 데이터들은 모델의 출력값을 중심으로 하는 정규분포에서 랜덤하게 샘플링되어 얻은 값이라고 보고 error를 정규분포로 설계한다는 점 ### chi Square Notion |Title| |:-:| |[chi Square Distribution](https://texonom.com/chi-square-distribution-014792b9b4f849f38edcbe52e9d8deb1)| |[chi Square Test](https://texonom.com/chi-square-test-a34793e6d05e432f968f1249c09b505b)| |[Pearson's chi-squared statistics](https://texonom.com/pearsons-chi-squared-statistics-954324a08d9e4a8494a62493a56ea3e7)| > [카이제곱 분포와 검정](https://www.youtube.com/watch?v=_GrdeYtYLO4) > [카이제곱 분포와 검정](https://angeloyeo.github.io/2021/12/13/chi_square.html)

697c74917a0b4a9c83b1856d89bde6af

The Goodhart's Law

Probability theory Usages

May 31, 2021

Alan Jo

May 2, 2023

[Gamification](https://texonom.com/gamification-ffc99e95fb57466fbcf5e13ee4ebbed6) [Overfitting](https://texonom.com/overfitting-24c3b183372845e8999ad7f7a0ba5035)

### 측정값이 목표가 되면 더 이상 좋은 측정값이 아니다 관측된 통계적 규칙성은 그것을 조종할 목적으로 개입할 경우 사라져버리는 경향 특정 수치를 만족시키기 위해 시스템을 "게임화"함으로써 국소적으로만 최적화하는 경향 영국의 경제학자 Charles Goodhart의 이름을 따서 명명

ccece645e5e3484381fe0721d6ba2cd8

chi Square Distribution

chi Square Notion

Jan 23, 2022

Alan Jo

Jan 23, 2022

014792b9b4f849f38edcbe52e9d8deb1

chi Square Test

chi Square Notion

Jan 23, 2022

Alan Jo

Jan 23, 2022

오차를 검증하려는 것에서 우연히 발생한 것인지 숨겨진 의미가 있는지 판별가능 [Goodness of fit Test](https://texonom.com/goodness-of-fit-test-6c9fc48cd54c47d0accec760b8e1beb3) [Cross Tabulation Analysis](https://texonom.com/cross-tabulation-analysis-379ac6e0176146ecbfcc09fb487696ab)

a34793e6d05e432f968f1249c09b505b

Pearson's chi-squared statistics

chi Square Notion

Jan 23, 2022

Alan Jo

Jan 23, 2022

세트 간 관측 된 차이가 우연히 발생했을 가능성을 평가 카이 제곱 분포를 참조하여 결과를 평가하는 통계 절차 인 여러 카이 제곱 검정 중 가장 널리 사용 편차의 제곱을 기댓값으로 나눠 정규화 표준편차로 나누지 못하는 이유는 통계량 증명 과정에서 있다 > [카이제곱 분포와 검정](https://www.youtube.com/watch?v=_GrdeYtYLO4)

954324a08d9e4a8494a62493a56ea3e7

Cross Tabulation Analysis

chi Square Test

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교차분석 범주형 변수가 여러 개인 경우 적용 여러 번주형 변수의 범주간 차이가 기댓값에서 유의미하게 벗어나는지

379ac6e0176146ecbfcc09fb487696ab

Goodness of fit Test

chi Square Test

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적합도 검정 범주형 변수(독립)가 하나이고 이론적으로 기대되는 빈도의 분포(frequency distribution)와 관찰한 빈도의 분포를 비교하기 위해

6c9fc48cd54c47d0accec760b8e1beb3

**Autoregressive**

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시간에 따라 변하는 특정 프로세스를 설명 출력 변수가 자신의 이전 값과 확률적 항에 선형적으로 의존함을 의미

93cf5710b4b54730a7e7efcc6e0fc642

Bayesian

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## Subjectivism, epistemic, logical probability Bayesian school 확률의 신뢰도로 해석하고 그에 기반한다 발생 가능성에 대해 알고 있을때, 이를 직접적으로 이용하여 계산 ## Relative probability

abfa2017bb054f3a9dfcbc9a6c1042f6

BP

Statistics Terms

Mar 27, 2022

Alan Jo

Jun 6, 2023

### BPS ### Basic Point 0.01%

512f1e376cbc4448adec9a1f5acb66a6

Degrees of Freedom

Statistics Terms

Jan 22, 2022

Alan Jo

Jun 6, 2023

### 자유도 독립적으로 달라질 수있는 시스템의 매개 변수의 수 평면의 한 점은 변환에 대해 두 개의 자유도를 갖는다 number of values in the final calculation of a [statistic](https://en.wikipedia.org/wiki/Statistic) that are free to vary 통계적 제한을 받지 않고 자유롭게 변화를 줄수 있는 독립 원소의 수 > [Degrees of freedom (statistics) - Wikipedia](https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)) > [통계의 자유도(degree of freedom : df)](https://wiserloner.tistory.com/1013)

35beaefd93fd46d58172097155eedab9

Frequentist

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### Frequentism, Classical Probability, Frequentist school no [Posterior](https://texonom.com/posterior-87e0f5df288140c7ba475b0629bdda05) [Prior Probability](https://texonom.com/prior-probability-34585174a5cd42bbae9094138713932b) 확률의 빈도로 해석 관찰된 데이터와 관찰되지 않은 데이터들에 의한 우도에 의존 계산량이 적다

c7636520ad8d4ae3ba69b8c24f516ab1

Mean

Statistics Terms

May 2, 2023

Alan Jo

Jun 6, 2023

## Average ### Averages |Title| |:-:| |[Arithmetic Average](https://texonom.com/arithmetic-average-86fa34b8da344ec38c89ceff73b67a60)| |[Geometric Average](https://texonom.com/geometric-average-8dcca049c6a94778815ec6b114d89125)|

e903056370974e0082893cb8ea8952dd

**p-value**

Statistics Terms

Jun 6, 2023

Alan Jo

Jun 6, 2023

[t-value](https://texonom.com/t-value-4f1e6fb2b0034235910718dd48de8096)

### **우리가 얻은 검정 통계량보다 크거나 같은 값을 얻을 수 있을 확률** 계산하는 검정 통계량들은 거의 대부분이 [Null Hypothesis](https://texonom.com/null-hypothesis-ce9a2477f77f48b09553e7a0c47da050) **을 가정**하고 얻게되는 값 다시 말해 두 표본 평균의 차이를 검증한다고 할 때, 두 표본 집단의 모집단은 같다는 가정을 전제 두 표본 집단의 특징값의 평균이 통계적으로 유의한 차이가 있는지 검증 p-value는 이 [t-value](https://texonom.com/t-value-4f1e6fb2b0034235910718dd48de8096) 에 관한 확률 보통은 5% 기준을 많이 사용한다. 그래서 p-value가 5%보다 작으면 유의한 차이가 있다고 얘기 효과의 크기(effect size)와 표본의 크기(n 수)의 정보를 한꺼번에 담고있다 즉 실제로 한 모집단에서 두 표본 집단이 나왔음에도 n의 차이로 p-value는 0.05보다 낮을 수 있다 그러므로 p-value를 맹신하지 말아야 한다 > [p-value의 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/03/29/p_value.html)

73c98ef557494f86a7ae0c1dba8f81df

Percent

Statistics Terms

Mar 27, 2022

Alan Jo

Jun 6, 2023

> [당신이 미처 몰랐던 확률 개념](https://youtube.com/watch?v=Exjc8D8drP0&feature=shares)

f4c541ab49fe4ffb92ec673995898108

Robust

Statistics Terms

Jun 28, 2021

Alan Jo

Jun 6, 2023

이상값에 영향을 적게 받는 통계량을 로버스트한 통계량 > [로버스트(robust) 하다?](https://m.blog.naver.com/vnf3751/220827101273)

062dfadfcdd64fff9b828cca5442a684

**Statistical parameter**

Statistics Terms

Jun 6, 2023

Alan Jo

Jun 25, 2023

### Parameter 전체 집단의 모든 데이터를 알지 못하더라도 수학적으로 그 분포를 기술할 수 있는 특성값들을 알 수만 있다면 그걸 모수라고 함 - [Expectation value](https://texonom.com/expectation-value-3e14abcd31734ddea3fa0d1c92e3d63f) - [Variance](https://texonom.com/variance-08c1eccc7dc84957afbb815ad6b41280) - [Standard Deviation](https://texonom.com/standard-deviation-792bf99f68174ae38bb95a0721831fe8) ### **Statistical parameter Notion** |Title| |:-:| |[Confidence interval](https://texonom.com/confidence-interval-68004b3ce6204c808b5994a38464c4a2)| |[Confidence Level](https://texonom.com/confidence-level-046400554651433cac5f5dec69f542f0)| |[Effect Size](https://texonom.com/effect-size-14b3f7443cfb49fd94ccb2604bc16434)| > [표본과 표준 오차의 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/02/12/standard_error.html)

0e888c61f6cd48b7a2df1217087f07d1

**Statistical **Population

Statistics Terms

Jun 6, 2023

Alan Jo

Jun 25, 2023

### ****모집단**** 관심 대상의 전체 집합 [Statistical parameter](https://texonom.com/statistical-parameter-0e888c61f6cd48b7a2df1217087f07d1) > [표본과 표준 오차의 의미 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/02/12/standard_error.html)

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**Test statistic**

Statistics Terms

Jun 6, 2023

Alan Jo

Jun 6, 2023

## 검정 통계량 **통계적 가설의 진위 여부를 검정하기 위해** 표본으로 부터 계산하는 통계량 즉 **표본 통계량을 2차 가공한 것** ### **Test statistics** |Title| |:-:| |[t-value](https://texonom.com/t-value-4f1e6fb2b0034235910718dd48de8096)| |[f test](https://texonom.com/f-test-60ca3e84894c4929b6b1dbecb61f3385)| > [Test statistic](https://en.wikipedia.org/wiki/Test_statistic)

11746f80eefb4309b516bc06160718d6

Arithmetic Average

Averages

May 2, 2023

Alan Jo

May 2, 2023

null

86fa34b8da344ec38c89ceff73b67a60

Geometric Average

Averages

May 2, 2023

Alan Jo

May 2, 2023

null

$$(\Pi a_i)^{1/n}$$ [compounding effect](https://texonom.com/compounding-effect-4c3ebe3d22a0458b8518c5a87bc1130d) compounding effect 반영가

8dcca049c6a94778815ec6b114d89125

compounding effect

Geometric Average

null

4c3ebe3d22a0458b8518c5a87bc1130d

**Confidence interval**

Statistical parameter Notion

Jun 6, 2023

Alan Jo

Jun 6, 2023

> [Confidence interval](https://en.wikipedia.org/wiki/Confidence_interval)

68004b3ce6204c808b5994a38464c4a2

**Confidence Level**

Statistical parameter Notion

Jun 6, 2023

Alan Jo

Jun 6, 2023

046400554651433cac5f5dec69f542f0

Effect Size

Statistical parameter Notion

Jun 6, 2023

Alan Jo

Jun 6, 2023

14b3f7443cfb49fd94ccb2604bc16434

Cohen's D

Effect Size Types

Jun 6, 2023

Alan Jo

Jun 6, 2023

null

e406e8e0848d457188a631df615b8755

f test

Test statistics

Jul 13, 2023

Alan Jo

Jul 13, 2023

[F Distribution](https://texonom.com/f-distribution-491a1836300446499b51b79e388b9e80)

60ca3e84894c4929b6b1dbecb61f3385

t-value

Test statistics

Jun 6, 2023

Alan Jo

Jun 6, 2023

### Paired *t*-test ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F1160b548-031e-4a43-95a2-da68ce36e9f2%2FUntitled.png?table=block&id=7844eb5b-76de-4561-8d12-53cfa355abea&cache=v2) > [t-value의 의미와 스튜던트의 T 테스트 - 공돌이의 수학정리노트 (Angelo's Math Notes)](https://angeloyeo.github.io/2020/02/13/Students_t_test.html)

4f1e6fb2b0034235910718dd48de8096

Statistical Inference

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![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F3a8a3f1e-02ef-49ad-b017-39b7a61e6fe2%2FUntitled.png?table=block&id=9209f048-47cd-486c-b54b-8cc2cf432859&cache=v2) > [Statistical inference - Wikipedia](https://en.wikipedia.org/wiki/Statistical_inference) > [통계적 추론 - Big Picture](https://angeloyeo.github.io/2020/02/11/big_picture_stats_infer.html)

168ef97c06d24b44bb49653d70516e73

Statistics Tool

Statistics Usages

Oct 6, 2021

Alan Jo

Apr 3, 2022

### Statistics Tools |Title| |:-:| |[statsmodels](https://texonom.com/statsmodels-96fb7be66a01419cbd417f6342f384d6)| |[numpy](https://texonom.com/numpy-8a514dfb88ef49c19959f85d43b2fafc)| |[Pandas](https://texonom.com/pandas-c7aa68bdc16545418519cf18e791c346)| |[scikit-learn](https://texonom.com/scikit-learn-e37a30b2d2ac4edea30825c8be0c7ddf)| |[StatsForecast](https://texonom.com/statsforecast-17a112dd5c554673be0b654758ba92fb)|

cd8ad9a0f6be46b4979d8e302c6dbd52

numpy

Statistics Tools

Sep 24, 2020

Alan Jo

Aug 19, 2023

### numpy Usages |Title| |:-:| |[numpy subsampling](https://texonom.com/numpy-subsampling-567f9cfa79d5415ea17b357c71d59ebc)| |[numpy.sqrt](https://texonom.com/numpysqrt-9a01904b3df24cce877c513b3a133f1d)| |[numpy.pad](https://texonom.com/numpypad-3ec51ac35c954b6294a5b37099655261)| |[numpy.ones](https://texonom.com/numpyones-121a1bfaa2274e06b0b2d521057af876)| |[numpy.zeros_like](https://texonom.com/numpyzeroslike-caa460eb53c44c84821e77344ee7d29b)| |[numpy.sum](https://texonom.com/numpysum-63171863a2064059825bd42833f31aad)| |[numpy.dstack](https://texonom.com/numpydstack-261094d453194bb6aff5526b4bb11c5a)| |[np.conj](https://texonom.com/npconj-b8fa8274980447deb35dc20ff7a2c2fe)| |[numpy.arrange](https://texonom.com/numpyarrange-5abc5c6dd50b4af5be9c5d9e86557037)| |[numpy.reshape](https://texonom.com/numpyreshape-d9797e899197489981b55c67849e710f)| |[numpy.full()](https://texonom.com/numpyfull-8e57ff0d90854ab6a7747ca384e4a6fa)| |[numpy.empty()](https://texonom.com/numpyempty-3a55645bdeee4266920c3e415d9525fc)| |[numpy.memmap](https://texonom.com/numpymemmap-a26cd2ad2e4f49338d8d5d1d5cdd1d31)| ### numpy Notion |Title| |:-:| |[numpy Boolean Indexing](https://texonom.com/numpy-boolean-indexing-55e814616d504e4cb921d506f8110713)| |[numpy broadcasting semantic](https://texonom.com/numpy-broadcasting-semantic-9ac806088cbe4a869f6e5676f4e91b2d)| > [NumPy documentation — NumPy v1.24 Manual](https://numpy.org/doc/stable/index.html)

8a514dfb88ef49c19959f85d43b2fafc

Pandas

Statistics Tools

Nov 5, 2019

Alan Jo

Seong-lae Cho

May 1, 2023

append 도 그냥 return 만 하고 자동 업데이트 안해서 좀 뻘짓했다.. pandas 자체 성격이 그런듯 ### Pandas Notion |Title| |:-:| |[Pandas Class](https://texonom.com/pandas-class-54f6fe2fea2b4faf82041da11e8d33dc)| ### pandas Usages |Title| |:-:| |[polars](https://texonom.com/polars-2df74bdc72e44bbfa0b2e0e816f8651e)| |[](https://texonom.com/95f186e7c7174acba2d8b0e1c3729e6c)| |[pandas AI](https://texonom.com/pandas-ai-46da363d6b444fe7955bab2f60085f2c)| > [Python| Pandas dataframe.append() - GeeksforGeeks](https://www.geeksforgeeks.org/python-pandas-dataframe-append/)

c7aa68bdc16545418519cf18e791c346

scikit-learn

Statistics Tools

Oct 16, 2021

Alan Jo

May 24, 2023

e37a30b2d2ac4edea30825c8be0c7ddf

StatsForecast

Statistics Tools

Aug 21, 2022

Alan Jo

Aug 21, 2022

[Numba](https://texonom.com/numba-92b190dc95ab40308495541afc11a0d1)

[statsforecast](https://github.com/Nixtla/statsforecast)

17a112dd5c554673be0b654758ba92fb

statsmodels

Statistics Tools

Oct 6, 2021

Alan Jo

Oct 6, 2021

### statsmodels Usage |Title| |:-:| > [Introduction - statsmodels](https://www.statsmodels.org/stable/index.html) > [Untitled](https://notebook.community/zzsza/Datascience_School/13.%20Scikit-Learn%2C%20Statsmodel/05.%20statsmodels%20%ED%8C%A8%ED%82%A4%EC%A7%80%20%EC%86%8C%EA%B0%9C)

96fb7be66a01419cbd417f6342f384d6

numpy Boolean Indexing

numpy Notion

Sep 24, 2020

Alan Jo

Aug 19, 2023

```typea[b > 0] = b[b > 0]```

55e814616d504e4cb921d506f8110713

numpy broadcasting semantic

numpy Notion

May 25, 2023

Alan Jo

Aug 19, 2023

data copy 없이 ### **In-place semantics** broadcasting에 따라 in-place tensor의 모양이 변경되지 않는다 ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F72309b61-e4f1-4d08-8fc0-3f50b44b0042%2FUntitled.png?table=block&id=e43379de-3b70-4a33-a85b-aa58e7de5036&cache=v2) 1차원은 broadcasting되는데 2차원부터 안되니까 1차원만 되는 이유 차원 없다면 뒤부터 둔다 ![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F8a1d486d-e229-46ad-981d-c4c094f05088%2FUntitled.png?table=block&id=47c2b71b-8bc5-4684-9744-0e24448f0750&cache=v2) 즉 위 첫 케이스에서 3을 중간에 둘 수 없다 ### **Backwards compatibility** > [How does pytorch broadcasting work?](https://stackoverflow.com/questions/51371070/how-does-pytorch-broadcasting-work) > [pytorch broadcasting](https://velog.io/@optjyy/pytorch-broad-casting)

9ac806088cbe4a869f6e5676f4e91b2d

np.conj

numpy Usages

Apr 14, 2023

Alan Jo

Apr 26, 2023

### np.conjugate Return the complex conjugate

b8fa8274980447deb35dc20ff7a2c2fe

numpy subsampling

numpy Usages

Oct 20, 2020

Alan Jo

Apr 13, 2023

```type[start::jump]``` or random > [subsampling every nth entry in a numpy array](https://stackoverflow.com/questions/25876640/subsampling-every-nth-entry-in-a-numpy-array)

567f9cfa79d5415ea17b357c71d59ebc

numpy.arrange

numpy Usages

Apr 19, 2023

Alan Jo

Apr 19, 2023

like range function > [(파이썬) numpy.arange](https://codepractice.tistory.com/88)

5abc5c6dd50b4af5be9c5d9e86557037

numpy.dstack

numpy Usages

Apr 13, 2023

Alan Jo

Apr 13, 2023

261094d453194bb6aff5526b4bb11c5a

numpy.empty()

numpy Usages

May 29, 2023

Alan Jo

May 29, 2023

3a55645bdeee4266920c3e415d9525fc

numpy.full()

numpy Usages

May 29, 2023

Alan Jo

May 29, 2023

8e57ff0d90854ab6a7747ca384e4a6fa

numpy.ones

numpy Usages

Apr 13, 2023

Alan Jo

Apr 13, 2023

create array which has all components 1

121a1bfaa2274e06b0b2d521057af876

numpy.pad

numpy Usages

Oct 20, 2020

Alan Jo

Apr 13, 2023

[Matrix Padding](https://texonom.com/matrix-padding-0f44aaaee9d54bb3a6960130541ac90a)

### Padding ```typenumpy.pad```

3ec51ac35c954b6294a5b37099655261

numpy.reshape

numpy Usages

Apr 19, 2023

Alan Jo

Apr 19, 2023

d9797e899197489981b55c67849e710f

numpy.sqrt

numpy Usages

Sep 24, 2020

Alan Jo

Apr 13, 2023

> [numpy.sqrt - NumPy v1.19 Manual](https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html)

9a01904b3df24cce877c513b3a133f1d

numpy.sum

numpy Usages

Apr 13, 2023

Alan Jo

Apr 13, 2023

63171863a2064059825bd42833f31aad

numpy.zeros_like

numpy Usages

Apr 13, 2023

Alan Jo

Apr 13, 2023

caa460eb53c44c84821e77344ee7d29b

Pandas Class

Pandas Notion

Nov 5, 2019

Alan Jo

Seong-lae Cho

Jun 2, 2023

54f6fe2fea2b4faf82041da11e8d33dc

Pandas DataFrame

Pandas Classes

Nov 5, 2019

Alan Jo

Seong-lae Cho

Jun 2, 2023

```typepd.DataFrame(data)``` list of dictionary can be converted directly ### Add same value column ```typedf['Name'] = 'abc'``` ### Pandas DataFrame Usages |Title| |:-:| |[Dataframe to list of dict](https://texonom.com/dataframe-to-list-of-dict-04751c84aabb4a41a7444b0fbff4fe2d)| |[lance rs](https://texonom.com/lance-rs-d2dc40c991944ef2b1e0e35392d809cf)| |[Draft py](https://texonom.com/draft-py-077240b76a714c99b317025991bfc2f3)| > [Untitled](https://stackoverflow.com/questions/29517072/add-column-to-dataframe-with-default-value) > [Convert list of dictionaries to a pandas DataFrame](https://stackoverflow.com/questions/20638006/convert-list-of-dictionaries-to-a-pandas-dataframe)

ade738f428f542b0a5e884467b841290

Pandas Series

Pandas Classes

Nov 5, 2019

Alan Jo

Seong-lae Cho

Jun 2, 2023

1차원

6dc9909d3e98499896b66ffc41542fbb

Dataframe to list of dict

Pandas DataFrame Usages

Sep 10, 2020

Alan Jo

Jun 2, 2023

```typedf.to_dict('records'):``` > [Pandas DataFrame to List of Dictionaries](https://stackoverflow.com/questions/29815129/pandas-dataframe-to-list-of-dictionaries)

04751c84aabb4a41a7444b0fbff4fe2d

Draft py

Pandas DataFrame Usages

Jun 11, 2023

Alan Jo

Jun 11, 2023

[Daft](https://github.com/Eventual-Inc/Daft)

077240b76a714c99b317025991bfc2f3

lance rs

Pandas DataFrame Usages

Jun 2, 2023

Alan Jo

Jun 2, 2023

[lance](https://github.com/lancedb/lance)

d2dc40c991944ef2b1e0e35392d809cf

[pygwalker](https://github.com/Kanaries/pygwalker)

pandas Usages

Jul 15, 2022

Alan Jo

May 1, 2023

95f186e7c7174acba2d8b0e1c3729e6c

pandas AI

pandas Usages

May 1, 2023

Alan Jo

May 1, 2023

[pandas-ai](https://github.com/gventuri/pandas-ai)

46da363d6b444fe7955bab2f60085f2c

polars

pandas Usages

Jul 15, 2022

Alan Jo

May 1, 2023

rust. and py

2df74bdc72e44bbfa0b2e0e816f8651e

scikit-llm

scikit-learn Usages

May 24, 2023

Alan Jo

May 24, 2023

‣

5f9754697e81460eaa6aab50031f2088

Algebra

null

### Algebra Areas |Title| |:-:| |[Linear Algebra](https://texonom.com/linear-algebra-a5879da463c442d89c51891d124f97ac)| |[Lie Algebra](https://texonom.com/lie-algebra-77e6ab22461948778fff08818171cdae)| |[Universal algebra](https://texonom.com/universal-algebra-8f94ab573ea2438b84deac618daafeda)| |[Algebraic Structure](https://texonom.com/algebraic-structure-4fb610f539064ec18d3edf2b310b7759)|

e7024eed5b654acbaae54725ccc6b15f

Arithmetic

Math fields

Dec 17, 2021

Alan Jo

Jun 6, 2023

[Number Theory](https://texonom.com/number-theory-0bf9f82f550d43d382ba1c67ebb7dae2)

### 숫자가 들어가는 순간 어느정도의 이산성이 주입된다 산술은 수학의 가장 역사 깊은 분야로, 수의 개념이나 수에 대하여 간단한 계산을 하는 방법, 그 성질이나 계산의 법칙 등의 이론적인 방법을 다루는 학문 특히 정수, 유리수, 실수, 복소수를 사용하여 계산하는 방법 ### Arithmetic Notion |Title| |:-:| |[Number Theory](https://texonom.com/number-theory-0bf9f82f550d43d382ba1c67ebb7dae2)| |[Fixed-point arithmetic](https://texonom.com/fixed-point-arithmetic-c46e0722c58c4e2fbc1d2f7027bf6fbe)| |[Arithmetic Precision](https://texonom.com/arithmetic-precision-baffc5389f06430eb20806e985685c9b)| |[Elementary arithmetic](https://texonom.com/elementary-arithmetic-57a9f00b3f30433299816f32b4d49fbd)| |[Exponentiation](https://texonom.com/exponentiation-760c53a791ee4d6696e819b079afe066)|

0c758b320acb4e919df40892427248d0

Calculus

null

### 인간에게 연속적인 것을 직관적으로 이해시킨 방법론 ### Calculus Notion |Title| |:-:| |[Derivation](https://texonom.com/derivation-79d0547aee0d45ce93cdae0f26bc3ce6)| |[Integral](https://texonom.com/integral-ed91b8e9d33d49bfa6a32e93f7bfdfca)| |[Inflection point](https://texonom.com/inflection-point-6448287d912942cea85ee85a981505d6)| |[Vector Calculus](https://texonom.com/vector-calculus-77976c6127ad49c9a6611e16a40f337f)| |[Explicit Function](https://texonom.com/explicit-function-df8104e2876c42e9b112f6308718e3bc)| |[Implicit Function](https://texonom.com/implicit-function-1e383ff61a8b4831abca72e4c37649bd)| |[Local extremum point](https://texonom.com/local-extremum-point-f7a7579a29474436b2a8670a28fed921)| |[Convex Point](https://texonom.com/convex-point-160b14cc61114a8a9be9797578e11c7a)| |[Concave Point](https://texonom.com/concave-point-c3f6835eb9ef4378830d3b916da3f074)| ### Calculus Examples |Title| |:-:| |[The Tower Function](https://texonom.com/the-tower-function-7a63cab2617a402782fbf88c9055d43c)|

8e37e7dac61e435da6a6970da7296f73

Chaos Theory

null

조그만 변화로 크게 변화 ### Chaos Theory Notion |Title| |:-:| |[Lorenz Attractor](https://texonom.com/lorenz-attractor-b3249a819200420797f82e204cc9d58c)| |[Butterfly Effect](https://texonom.com/butterfly-effect-62e1b65850da4b3ab2d429292473f8a1)| |[Complex System](https://texonom.com/complex-system-b2457d8f6fcc4fe2abffd71828908a1f)|

2fbd6b2c5e474a63b6f07a90803b8f9d

Discrete Math

null

### Discrete Math Topics |Title| |:-:| |[Pigeonhole principle](https://texonom.com/pigeonhole-principle-998c7a67c04e43d28b132eaa02d5f0d8)| |[Order Theory](https://texonom.com/order-theory-8c7e8fb9638f41b19b6829d686fc6f9b)| |[Combinatorics](https://texonom.com/combinatorics-887b47c6bb1c46388a8387d89bd304cf)|

6cd7d73a0fe94fd981f0d59b2c906714

**Ergodic theory**

Math fields

Apr 3, 2022

Alan Jo

Apr 5, 2022

### **Ergodic theory Notion** |Title| |:-:| |[Poincare Recurrence Theorem](https://texonom.com/poincare-recurrence-theorem-1aca4c4a3d2446c1892de56b1071953c)| |[Dynamical System](https://texonom.com/dynamical-system-a4e33185067b49b28e8f62454028f7b1)| > [Ergodic theory - Wikipedia](https://en.wikipedia.org/wiki/Ergodic_theory)

ead101eaed774cacbd95b2497b8837c6

**Foundations of Mathematics**

Math fields

Jun 19, 2022

Alan Jo

May 13, 2023

[Mathematical Logic](https://texonom.com/mathematical-logic-dc5a5765623c4cef9f76a78cca288960) [Set Theory](https://texonom.com/set-theory-a74b3919af5e4e6e885862f6f76103f9)

### **Foundations of Mathematics Notion** |Title| |:-:| |[Gödel’s incompleteness theorem](https://texonom.com/gdels-incompleteness-theorem-820d082fd9bf424f8125dda3bf9e859b)| |[Langlands program](https://texonom.com/langlands-program-629d720ec59b4bf4a42c0b066675b220)| |[Set Theory](https://texonom.com/set-theory-a74b3919af5e4e6e885862f6f76103f9)| |[Type Theory](https://texonom.com/type-theory-a6967220456b47498b951f11598381f7)| |[Category Theory](https://texonom.com/category-theory-1b6594b7d4ce4c128ec2f9aed95d9f3c)| > [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://www.youtube.com/watch?v=oippSXvxUlw&t=590s)

62157cb1d60a461cace32359d099137f

Measure Theory

null

### Measure Theory Notion |Title| |:-:| |[Lebesgue Theorem](https://texonom.com/lebesgue-theorem-50dd4d0d814244799c6b43126d669c5d)| |[Null Set](https://texonom.com/null-set-1f83671ec46848a4b8232daad30419bd)| |[Measure Zero](https://texonom.com/measure-zero-84f55b9439c743f390eb69ddbd5f4a5b)| > [당신이 수학을 모르는 이유. (feat. 불완전성의 정리)](https://youtu.be/oippSXvxUlw) > [당신이 미처 몰랐던 확률 개념](https://youtube.com/watch?v=Exjc8D8drP0&feature=shares)

4fb6210801ea4d7abcb937cd068ba461

Number Theory

Arithmetic Notion

Nov 5, 2019

Alan Jo

Seong-lae Cho

Sep 3, 2023

[Arithmetic](https://texonom.com/arithmetic-0c758b320acb4e919df40892427248d0) [Harmonic Analysis](https://texonom.com/harmonic-analysis-e1e54ebeffd0407088bebab57acbfd53)

### Number Theory Notion |Title| |:-:| |[Infinite](https://texonom.com/infinite-f4d16a6949084f6c9c9763e78492486b)| |[Number System](https://texonom.com/number-system-4bfd6d8ac2e34aef9e0c847ccd7c1378)| |[Factorial](https://texonom.com/factorial-5b4059c4407b4c2f9c3be0f8357ae7ae)| |[Real Number](https://texonom.com/real-number-2c5c6fff21ab429da38ba685b40bacf3)| |[Integer](https://texonom.com/integer-e87e20fb8fb94fe98202d49d95aefbdc)| ### Number Theory Example |Title| |:-:| |[Analytic number theory](https://texonom.com/analytic-number-theory-2ca0555c60b344aba8890dc7741bf191)| |[램지이론](https://texonom.com/742ac0cefcaa43018afea17a47f3ef34)| |[Collatz conjecture](https://texonom.com/collatz-conjecture-d6e27f23c9d34778a8f072bcf28edc81)| |[BCD](https://texonom.com/bcd-1d73c802caab457486434bb9e661aa95)|

0bf9f82f550d43d382ba1c67ebb7dae2