SPRINGLab/asr-task-data · Datasets at Hugging Face

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	number which is a categorical variable which you get down so from a simple neuron we will
	parameters connected to one parameter and it can even go down by a successive stages
	of parametric connections which goes down and finally is what enters into what we call
	and what this does is that we define something as a neural network and then say that this
	neural network is able to classify images and as we go down over there now one important
	fact which you will have to take care over here is that as we are learning over here
	then that would mean that somehow with experience going by that definition somehow with experience
	which we are gaining we will be able to do that task much better
	so that means necessarily that as we show it more number of samples of features and
	which are associated number of categorical variables over there then this whole network
	over here which i call as a neural network would be able to really associate any unknown
	this learning you will have to go down through the way of gradient checking and optimizations
	this so we have the mathematical equation but lets lets get down into what it looks
	like so say i have three different variables x one x two and x three and these can be three
	the image and say over here is the average entropy of the image ok so we can have three
	different features over there for one single image given down now once we have these three
	of the image x three is also scalar and now together what we can do is we can associate
	with certain vector and then we can sort of sum them up ok so x one will be multiplied
	by a weight w one x two will be multiplied by a weight w two x three will be multiplied
	then my output over here so the form of y is something which is written down as w naught
	will be a n plus one term summation which comes down over here now from there as we
	sort of a matrix representation is what is given down over here ok so what w is basically
	and that is equal to w naught itself and x is another vector of all the ah scalars which
	are arranged in terms of a matrix over there so this is a matrix form of representation
	now once i have that one what i can do is i can relate this y to my predicted class
	this f n l can have two different forms some common forms are something like this the first
	my x s over here i dont have any sort of a control over my x so these can be anything
	from minus infinity to plus infinity for the purpose of simplicity we keep down the fact
	that let these be real valued numbers and not complex valued numbers that that does
	to plus infinity now that i have these also open ranged then what i get down from this
	to me that can be anything from minus infinity to plus infinity which would typically make
	just put a threshold over there say that if the value is greater than zero make it one
	of functions say a sigmoid non linearity so what it would do is that as my y becomes tending
	now in the same way as i go with my second non linearity which is called as a tan hyperbolic
	so you can put down your values of y is varying from minus infinity to plus infinity and you
	can very intuitively see that as the value of y goes down to minus infinity this value
	tends to minus one as the value goes to plus infinity this value tends to plus one and
	say just give down the argument that if it is greater than zero make it one less than
	i have three scalar values over here so what i can do is i can associate it to some different
	number of patterns which i want to different number of predictors which i want to do so
	being the contrast and x three being the average entropy on the image i want to classify whether
	that is a ball in the image yes or no and whether the image is a photograph or image
	down subscripted dually now with it with this dual weight subscription what happens technically
	which i want to classify and the first subscript is the one which connects down which feature
	is being connected to which target neuron over here ok
	done for y one and p one in terms of an equation now if i get down another parameter p two
	and thats what i was saying that do you have another different thing to predict and that
	may be that whether its a natural image or this was a sketched image now for that you
	will have a similar set of equation which you get down over here now you can clearly
	outputs can be designed over here
	now similarly i can extend it to some n number of some some k number of neurons over here
	now once you stand on all the row vectors you get down a rectangular matrix over there
	equation and then accordingly your predicted neurons will also be stacked into one single
	was applied on a scalar and thats why this can be extended on to a matrix valued form
	function and that will give you the same sort of a vector output which comes down over here
	now essentially what this helps you is that you can relate down some j number of input
	neurons to some k number of output neurons in in straight simple terms now from there
	once you are able to relate it down next what comes down is that i will have certain sort
	of error when i am able to relate it down it means that so using these three features
	and some combination of weights which are present over here i will be able to predict
	and there is a value which is coming down from this neuron itself ok now the difference
	between the true value say in the first case there was a ball but it predicted there wasnt
	a ball so there is its an error its a clear case of an error so but here what i would
	get done is that the error value is one ok in the other way round where say there wasnt
	the ground truth also says that there isnt a ball it means that it is ah its its a correct
	case so similarly we will have it for the second predictor as well now if you see all
	of these predictors are independent of each other so it means that the errors are also
	distance between the predicted vector over here this p that becomes a matrix
	now and the actual ground truth which is so between your p hat and your p so this will
	learning over here is in a sense that i should be somehow able to get down a network such
	essentially happens in that case is we use a method called as error back propagation
	so what it would do is say i have a set of observations x one ok so this one over here
	is no more related to one particular feature but that one which we are putting down over
	here in this relationship is actually which is related down to
	truth and i have my predicted value similarly i keep on doing such that i have n number
	of images in something which is called as a training set so what happens in a training
	set in this kind of a problem which is a supervised learning problem is that you have a set of
	images some n number of images and for each image you also know what is the class label
	given to it so here we were asking down two questions whether this there is a ball in
	image kind of thing
	so there are two vectors over here which i there is a two dimensional vector or two parameters
	which i want to predict down to class levels so that should also be known to me so there
	training set ok now on the other side i am going to predict out all of this with a certain
	given form of my weights over there now initially what i would do is i would start with a neural
	difference is coming down for each so i get the euclidean distance for each sample so
	for x one x two x three similarly it up to x n i get down this difference coming down
	you look carefully into this one
	so my p hats are what are dependent on all my excess over here ok but these x values
	they dont change in the whole data set right the only thing which changes within the network
	the whole objective is that i want to get down a particular value of w which is the
	only thing variable and adjustable within my neural network such that my cost function
	over here is minimum and this has to be minimum when you need to have done the minimum error
	over there as you get down your minimum error in this case this has to be zero so your jw
	start with a random guess of w within a k th iteration so my k at the start of it will
	be k equal to zero ok so at k equal to zero i start with some w over here now with that
	w i will be able to get down my these predictions over here p one to p n hat from there i would
	is a partial derivative of the cost function with respect to my weight at that particular
	of these predictions from there i would get down get down as the j w for w k plus one
	and then i would iterate it over such that at some point of time i would reach down this
	minimum value of w and then just stop over here ok

number which is a categorical variable which you get down so from a simple neuron we will

parameters connected to one parameter and it can even go down by a successive stages

of parametric connections which goes down and finally is what enters into what we call

and what this does is that we define something as a neural network and then say that this

neural network is able to classify images and as we go down over there now one important

fact which you will have to take care over here is that as we are learning over here

then that would mean that somehow with experience going by that definition somehow with experience

which we are gaining we will be able to do that task much better

so that means necessarily that as we show it more number of samples of features and

which are associated number of categorical variables over there then this whole network

over here which i call as a neural network would be able to really associate any unknown

this learning you will have to go down through the way of gradient checking and optimizations

this so we have the mathematical equation but lets lets get down into what it looks

like so say i have three different variables x one x two and x three and these can be three

the image and say over here is the average entropy of the image ok so we can have three

different features over there for one single image given down now once we have these three

of the image x three is also scalar and now together what we can do is we can associate

with certain vector and then we can sort of sum them up ok so x one will be multiplied

by a weight w one x two will be multiplied by a weight w two x three will be multiplied

then my output over here so the form of y is something which is written down as w naught

will be a n plus one term summation which comes down over here now from there as we

sort of a matrix representation is what is given down over here ok so what w is basically

and that is equal to w naught itself and x is another vector of all the ah scalars which

are arranged in terms of a matrix over there so this is a matrix form of representation

now once i have that one what i can do is i can relate this y to my predicted class

this f n l can have two different forms some common forms are something like this the first

my x s over here i dont have any sort of a control over my x so these can be anything

from minus infinity to plus infinity for the purpose of simplicity we keep down the fact

that let these be real valued numbers and not complex valued numbers that that does

to plus infinity now that i have these also open ranged then what i get down from this

to me that can be anything from minus infinity to plus infinity which would typically make

just put a threshold over there say that if the value is greater than zero make it one

of functions say a sigmoid non linearity so what it would do is that as my y becomes tending

now in the same way as i go with my second non linearity which is called as a tan hyperbolic

so you can put down your values of y is varying from minus infinity to plus infinity and you

can very intuitively see that as the value of y goes down to minus infinity this value

tends to minus one as the value goes to plus infinity this value tends to plus one and

say just give down the argument that if it is greater than zero make it one less than

i have three scalar values over here so what i can do is i can associate it to some different

number of patterns which i want to different number of predictors which i want to do so

being the contrast and x three being the average entropy on the image i want to classify whether

that is a ball in the image yes or no and whether the image is a photograph or image

down subscripted dually now with it with this dual weight subscription what happens technically

which i want to classify and the first subscript is the one which connects down which feature

is being connected to which target neuron over here ok

done for y one and p one in terms of an equation now if i get down another parameter p two

and thats what i was saying that do you have another different thing to predict and that

may be that whether its a natural image or this was a sketched image now for that you

will have a similar set of equation which you get down over here now you can clearly

outputs can be designed over here

now similarly i can extend it to some n number of some some k number of neurons over here

now once you stand on all the row vectors you get down a rectangular matrix over there

equation and then accordingly your predicted neurons will also be stacked into one single

was applied on a scalar and thats why this can be extended on to a matrix valued form

function and that will give you the same sort of a vector output which comes down over here

now essentially what this helps you is that you can relate down some j number of input

neurons to some k number of output neurons in in straight simple terms now from there

once you are able to relate it down next what comes down is that i will have certain sort

of error when i am able to relate it down it means that so using these three features

and some combination of weights which are present over here i will be able to predict

and there is a value which is coming down from this neuron itself ok now the difference

between the true value say in the first case there was a ball but it predicted there wasnt

a ball so there is its an error its a clear case of an error so but here what i would

get done is that the error value is one ok in the other way round where say there wasnt

the ground truth also says that there isnt a ball it means that it is ah its its a correct

case so similarly we will have it for the second predictor as well now if you see all

of these predictors are independent of each other so it means that the errors are also

distance between the predicted vector over here this p that becomes a matrix

now and the actual ground truth which is so between your p hat and your p so this will

learning over here is in a sense that i should be somehow able to get down a network such

essentially happens in that case is we use a method called as error back propagation

so what it would do is say i have a set of observations x one ok so this one over here

is no more related to one particular feature but that one which we are putting down over

here in this relationship is actually which is related down to

truth and i have my predicted value similarly i keep on doing such that i have n number

of images in something which is called as a training set so what happens in a training

set in this kind of a problem which is a supervised learning problem is that you have a set of

images some n number of images and for each image you also know what is the class label

given to it so here we were asking down two questions whether this there is a ball in

image kind of thing

so there are two vectors over here which i there is a two dimensional vector or two parameters

which i want to predict down to class levels so that should also be known to me so there

training set ok now on the other side i am going to predict out all of this with a certain

given form of my weights over there now initially what i would do is i would start with a neural

difference is coming down for each so i get the euclidean distance for each sample so

for x one x two x three similarly it up to x n i get down this difference coming down

you look carefully into this one

so my p hats are what are dependent on all my excess over here ok but these x values

they dont change in the whole data set right the only thing which changes within the network

the whole objective is that i want to get down a particular value of w which is the

only thing variable and adjustable within my neural network such that my cost function

over here is minimum and this has to be minimum when you need to have done the minimum error

over there as you get down your minimum error in this case this has to be zero so your jw

start with a random guess of w within a k th iteration so my k at the start of it will

be k equal to zero ok so at k equal to zero i start with some w over here now with that

w i will be able to get down my these predictions over here p one to p n hat from there i would

is a partial derivative of the cost function with respect to my weight at that particular

of these predictions from there i would get down get down as the j w for w k plus one

and then i would iterate it over such that at some point of time i would reach down this

minimum value of w and then just stop over here ok