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MilesCranmer
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Parent(s):
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Browse files
eureqa.jl
ADDED
@@ -0,0 +1,440 @@
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1 |
+
using ProgressBars
|
2 |
+
|
3 |
+
# Define allowed operators
|
4 |
+
plus(x::Float64, y::Float64) = x+y
|
5 |
+
mult(x::Float64, y::Float64) = x*y;
|
6 |
+
|
7 |
+
# (Apparently using const for globals helps speed)
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8 |
+
const binops = [plus, mult]
|
9 |
+
const unaops = [sin, cos, exp];
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10 |
+
|
11 |
+
const nvar = 5;
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12 |
+
const X = rand(100, nvar);
|
13 |
+
|
14 |
+
# Here is the function we want to learn (x2^2 + cos(x3) + 5)
|
15 |
+
const y = ((cx,)->cx^2).(X[:, 2]) + cos.(X[:, 3]) .+ 5.0;
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16 |
+
|
17 |
+
# How much to punish complexity
|
18 |
+
const parsimony = 0.01
|
19 |
+
# How much to scale temperature by (T between 0 and 1)
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20 |
+
const alpha = 10.0
|
21 |
+
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22 |
+
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23 |
+
|
24 |
+
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25 |
+
id = (x,) -> x
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26 |
+
const nuna = size(unaops)[1]
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27 |
+
const nbin = size(binops)[1]
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28 |
+
const nops = nuna + nbin
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29 |
+
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30 |
+
# Define a serialization format for the symbolic equations:
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31 |
+
mutable struct Node
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32 |
+
#Holds operators, variables, constants in a tree
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33 |
+
degree::Int #0 for constant/variable, 1 for cos/sin, 2 for +/* etc.
|
34 |
+
val::Union{Float64, Int} #Either const value, or enumerates variable
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35 |
+
constant::Bool #false if variable
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36 |
+
op::Function #enumerates operator (for degree=1,2)
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37 |
+
l::Union{Node, Nothing}
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38 |
+
r::Union{Node, Nothing}
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39 |
+
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40 |
+
Node(val::Float64) = new(0, val, true, id, nothing, nothing)
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41 |
+
Node(val::Int) = new(0, val, false, id, nothing, nothing)
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42 |
+
Node(op, l::Node) = new(1, 0.0, false, op, l, nothing)
|
43 |
+
Node(op, l::Union{Float64, Int}) = new(1, 0.0, false, op, Node(l), nothing)
|
44 |
+
Node(op, l::Node, r::Node) = new(2, 0.0, false, op, l, r)
|
45 |
+
|
46 |
+
#Allow to pass the leaf value without additional node call:
|
47 |
+
Node(op, l::Union{Float64, Int}, r::Node) = new(2, 0.0, false, op, Node(l), r)
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48 |
+
Node(op, l::Node, r::Union{Float64, Int}) = new(2, 0.0, false, op, l, Node(r))
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49 |
+
Node(op, l::Union{Float64, Int}, r::Union{Float64, Int}) = new(2, 0.0, false, op, Node(l), Node(r))
|
50 |
+
end
|
51 |
+
|
52 |
+
# Evaluate a symbolic equation:
|
53 |
+
function evalTree(tree::Node, x::Array{Float64, 1}=Float64[])::Float64
|
54 |
+
if tree.degree == 0
|
55 |
+
if tree.constant
|
56 |
+
return tree.val
|
57 |
+
else
|
58 |
+
return x[tree.val]
|
59 |
+
end
|
60 |
+
elseif tree.degree == 1
|
61 |
+
return tree.op(evalTree(tree.l, x))
|
62 |
+
else
|
63 |
+
return tree.op(evalTree(tree.l, x), evalTree(tree.r, x))
|
64 |
+
end
|
65 |
+
end
|
66 |
+
|
67 |
+
# Count the operators, constants, variables in an equation
|
68 |
+
function countNodes(tree::Node)::Int
|
69 |
+
if tree.degree == 0
|
70 |
+
return 1
|
71 |
+
elseif tree.degree == 1
|
72 |
+
return 1 + countNodes(tree.l)
|
73 |
+
else
|
74 |
+
return 1 + countNodes(tree.l) + countNodes(tree.r)
|
75 |
+
end
|
76 |
+
end
|
77 |
+
|
78 |
+
# Convert an equation to a string
|
79 |
+
function stringTree(tree::Node)::String
|
80 |
+
if tree.degree == 0
|
81 |
+
if tree.constant
|
82 |
+
return string(tree.val)
|
83 |
+
else
|
84 |
+
return "x$(tree.val)"
|
85 |
+
end
|
86 |
+
elseif tree.degree == 1
|
87 |
+
return "$(tree.op)($(stringTree(tree.l)))"
|
88 |
+
else
|
89 |
+
return "$(tree.op)($(stringTree(tree.l)), $(stringTree(tree.r)))"
|
90 |
+
end
|
91 |
+
end
|
92 |
+
|
93 |
+
# Print an equation
|
94 |
+
function printTree(tree::Node)
|
95 |
+
println(stringTree(tree))
|
96 |
+
end
|
97 |
+
|
98 |
+
# Return a random node from the tree
|
99 |
+
function randomNode(tree::Node)::Node
|
100 |
+
if tree.degree == 0
|
101 |
+
return tree
|
102 |
+
end
|
103 |
+
a = countNodes(tree)
|
104 |
+
b = 0
|
105 |
+
c = 0
|
106 |
+
if tree.degree >= 1
|
107 |
+
b = countNodes(tree.l)
|
108 |
+
end
|
109 |
+
if tree.degree == 2
|
110 |
+
c = countNodes(tree.r)
|
111 |
+
end
|
112 |
+
|
113 |
+
i = rand(1:1+b+c)
|
114 |
+
if i <= b
|
115 |
+
return randomNode(tree.l)
|
116 |
+
elseif i == b + 1
|
117 |
+
return tree
|
118 |
+
end
|
119 |
+
|
120 |
+
return randomNode(tree.r)
|
121 |
+
end
|
122 |
+
|
123 |
+
# Count the number of unary operators in the equation
|
124 |
+
function countUnaryOperators(tree::Node)::Int
|
125 |
+
if tree.degree == 0
|
126 |
+
return 0
|
127 |
+
elseif tree.degree == 1
|
128 |
+
return 1 + countUnaryOperators(tree.l)
|
129 |
+
else
|
130 |
+
return 0 + countUnaryOperators(tree.l) + countUnaryOperators(tree.r)
|
131 |
+
end
|
132 |
+
end
|
133 |
+
|
134 |
+
# Count the number of binary operators in the equation
|
135 |
+
function countBinaryOperators(tree::Node)::Int
|
136 |
+
if tree.degree == 0
|
137 |
+
return 0
|
138 |
+
elseif tree.degree == 1
|
139 |
+
return 0 + countBinaryOperators(tree.l)
|
140 |
+
else
|
141 |
+
return 1 + countBinaryOperators(tree.l) + countBinaryOperators(tree.r)
|
142 |
+
end
|
143 |
+
end
|
144 |
+
|
145 |
+
# Count the number of operators in the equation
|
146 |
+
function countOperators(tree::Node)::Int
|
147 |
+
return countUnaryOperators(tree) + countBinaryOperators(tree)
|
148 |
+
end
|
149 |
+
|
150 |
+
# Randomly convert an operator into another one (binary->binary;
|
151 |
+
# unary->unary)
|
152 |
+
function mutateOperator(tree::Node)::Node
|
153 |
+
if countOperators(tree) == 0
|
154 |
+
return tree
|
155 |
+
end
|
156 |
+
node = randomNode(tree)
|
157 |
+
while node.degree == 0
|
158 |
+
node = randomNode(tree)
|
159 |
+
end
|
160 |
+
if node.degree == 1
|
161 |
+
node.op = unaops[rand(1:length(unaops))]
|
162 |
+
else
|
163 |
+
node.op = binops[rand(1:length(binops))]
|
164 |
+
end
|
165 |
+
return tree
|
166 |
+
end
|
167 |
+
|
168 |
+
# Count the number of constants in an equation
|
169 |
+
function countConstants(tree::Node)::Int
|
170 |
+
if tree.degree == 0
|
171 |
+
return convert(Int, tree.constant)
|
172 |
+
elseif tree.degree == 1
|
173 |
+
return 0 + countConstants(tree.l)
|
174 |
+
else
|
175 |
+
return 0 + countConstants(tree.l) + countConstants(tree.r)
|
176 |
+
end
|
177 |
+
end
|
178 |
+
|
179 |
+
# Randomly perturb a constant
|
180 |
+
function mutateConstant(
|
181 |
+
tree::Node, T::Float64,
|
182 |
+
probNegate::Float64=0.01)::Node
|
183 |
+
# T is between 0 and 1.
|
184 |
+
|
185 |
+
if countConstants(tree) == 0
|
186 |
+
return tree
|
187 |
+
end
|
188 |
+
node = randomNode(tree)
|
189 |
+
while node.degree != 0 || node.constant == false
|
190 |
+
node = randomNode(tree)
|
191 |
+
end
|
192 |
+
|
193 |
+
maxChange = T + 1.0
|
194 |
+
factor = maxChange^rand()
|
195 |
+
makeConstBigger = rand() > 0.5
|
196 |
+
|
197 |
+
if makeConstBigger
|
198 |
+
node.val *= factor
|
199 |
+
else
|
200 |
+
node.val /= factor
|
201 |
+
end
|
202 |
+
|
203 |
+
if rand() > probNegate
|
204 |
+
node.val *= -1
|
205 |
+
end
|
206 |
+
|
207 |
+
return tree
|
208 |
+
end
|
209 |
+
|
210 |
+
# Evaluate an equation over an array of datapoints
|
211 |
+
function evalTreeArray(
|
212 |
+
tree::Node,
|
213 |
+
x::Array{Float64, 2})::Array{Float64, 1}
|
214 |
+
return mapslices(
|
215 |
+
(cx,) -> evalTree(tree, cx),
|
216 |
+
x,
|
217 |
+
dims=[2]
|
218 |
+
)[:, 1]
|
219 |
+
end
|
220 |
+
|
221 |
+
# Sum of square error between two arrays
|
222 |
+
function SSE(x::Array{Float64}, y::Array{Float64})::Float64
|
223 |
+
return sum(((cx,)->cx^2).(x - y))
|
224 |
+
end
|
225 |
+
|
226 |
+
# Mean of square error between two arrays
|
227 |
+
function MSE(x::Array{Float64}, y::Array{Float64})::Float64
|
228 |
+
return SSE(x, y)/size(x)[1]
|
229 |
+
end
|
230 |
+
|
231 |
+
# Score an equation
|
232 |
+
function scoreFunc(
|
233 |
+
tree::Node,
|
234 |
+
X::Array{Float64, 2},
|
235 |
+
y::Array{Float64, 1},
|
236 |
+
parsimony::Float64=0.1)::Float64
|
237 |
+
return MSE(evalTreeArray(tree, X), y) + countNodes(tree)*parsimony
|
238 |
+
end
|
239 |
+
|
240 |
+
# Add a random unary/binary operation to the end of a tree
|
241 |
+
function appendRandomOp(tree::Node)::Node
|
242 |
+
node = randomNode(tree)
|
243 |
+
while node.degree != 0
|
244 |
+
node = randomNode(tree)
|
245 |
+
end
|
246 |
+
|
247 |
+
choice = rand()
|
248 |
+
makeNewBinOp = choice < nbin/nops
|
249 |
+
if rand() > 0.5
|
250 |
+
left = randn()
|
251 |
+
else
|
252 |
+
left = rand(1:nvar)
|
253 |
+
end
|
254 |
+
if rand() > 0.5
|
255 |
+
right = randn()
|
256 |
+
else
|
257 |
+
right = rand(1:nvar)
|
258 |
+
end
|
259 |
+
|
260 |
+
if makeNewBinOp
|
261 |
+
newnode = Node(
|
262 |
+
binops[rand(1:length(binops))],
|
263 |
+
left,
|
264 |
+
right
|
265 |
+
)
|
266 |
+
else
|
267 |
+
newnode = Node(
|
268 |
+
unaops[rand(1:length(unaops))],
|
269 |
+
left
|
270 |
+
)
|
271 |
+
end
|
272 |
+
node.l = newnode.l
|
273 |
+
node.r = newnode.r
|
274 |
+
node.op = newnode.op
|
275 |
+
node.degree = newnode.degree
|
276 |
+
node.val = newnode.val
|
277 |
+
node.constant = newnode.constant
|
278 |
+
return tree
|
279 |
+
end
|
280 |
+
|
281 |
+
# Select a random node, and replace it an the subtree
|
282 |
+
# with a variable or constant
|
283 |
+
function deleteRandomOp(tree::Node)::Node
|
284 |
+
node = randomNode(tree)
|
285 |
+
# Can "delete" variable or constant too
|
286 |
+
if rand() > 0.5
|
287 |
+
val = randn()
|
288 |
+
else
|
289 |
+
val = rand(1:nvar)
|
290 |
+
end
|
291 |
+
newnode = Node(val)
|
292 |
+
node.l = newnode.l
|
293 |
+
node.r = newnode.r
|
294 |
+
node.op = newnode.op
|
295 |
+
node.degree = newnode.degree
|
296 |
+
node.val = newnode.val
|
297 |
+
node.constant = newnode.constant
|
298 |
+
return tree
|
299 |
+
end
|
300 |
+
|
301 |
+
# Go through one simulated annealing mutation cycle
|
302 |
+
# exp(-delta/T) defines probability of accepting a change
|
303 |
+
function iterate(
|
304 |
+
tree::Node, T::Float64,
|
305 |
+
X::Array{Float64, 2}, y::Array{Float64, 1},
|
306 |
+
alpha::Float64=1.0,
|
307 |
+
mult::Float64=0.1
|
308 |
+
)::Node
|
309 |
+
prev = deepcopy(tree)
|
310 |
+
|
311 |
+
mutationChoice = rand()
|
312 |
+
weights = [8, 1, 1, 1]
|
313 |
+
weights /= sum(weights)
|
314 |
+
cweights = cumsum(weights)
|
315 |
+
|
316 |
+
if mutationChoice < cweights[1]
|
317 |
+
tree = mutateConstant(tree, T)
|
318 |
+
elseif mutationChoice < cweights[2]
|
319 |
+
tree = mutateOperator(tree)
|
320 |
+
elseif mutationChoice < cweights[3]
|
321 |
+
tree = appendRandomOp(tree)
|
322 |
+
elseif mutationChoice < cweights[4]
|
323 |
+
tree = deleteRandomOp(tree)
|
324 |
+
end
|
325 |
+
|
326 |
+
try
|
327 |
+
beforeLoss = scoreFunc(prev, X, y, mult)
|
328 |
+
afterLoss = scoreFunc(tree, X, y, mult)
|
329 |
+
delta = afterLoss - beforeLoss
|
330 |
+
probChange = exp(-delta/(T*alpha))
|
331 |
+
|
332 |
+
if probChange > rand()
|
333 |
+
return tree
|
334 |
+
end
|
335 |
+
|
336 |
+
return prev
|
337 |
+
catch error
|
338 |
+
# Sometimes too many chained exp operators
|
339 |
+
if isa(error, DomainError)
|
340 |
+
return prev
|
341 |
+
else
|
342 |
+
throw(error)
|
343 |
+
end
|
344 |
+
end
|
345 |
+
end
|
346 |
+
|
347 |
+
# Create a random equation by appending random operators
|
348 |
+
function genRandomTree(length::Int)::Node
|
349 |
+
tree = Node(1.0)
|
350 |
+
for i=1:length
|
351 |
+
tree = appendRandomOp(tree)
|
352 |
+
end
|
353 |
+
return tree
|
354 |
+
end
|
355 |
+
|
356 |
+
|
357 |
+
# Define a member of population by equation, score, and age
|
358 |
+
mutable struct PopMember
|
359 |
+
tree::Node
|
360 |
+
score::Float64
|
361 |
+
birth::Float64
|
362 |
+
|
363 |
+
PopMember(t) = new(t, scoreFunc(t, X, y, parsimony), time()-1.6e9)
|
364 |
+
end
|
365 |
+
|
366 |
+
# A list of members of the population, with easy constructors,
|
367 |
+
# which allow for random generation of new populations
|
368 |
+
mutable struct Population
|
369 |
+
members::Array{PopMember, 1}
|
370 |
+
n::Int
|
371 |
+
|
372 |
+
Population(pop::Array{PopMember, 1}) = new(pop, size(pop)[1])
|
373 |
+
Population(npop::Int64) = new([PopMember(genRandomTree(3)) for i=1:npop], npop)
|
374 |
+
Population(npop::Int64, nlength::Int64) = new([PopMember(genRandomTree(nlength)) for i=1:npop], npop)
|
375 |
+
|
376 |
+
end
|
377 |
+
|
378 |
+
# Sample 10 random members of the population, and make a new one
|
379 |
+
function samplePop(pop::Population)::Population
|
380 |
+
idx = rand(1:pop.n, 10)
|
381 |
+
return Population(pop.members[idx])#Population(deepcopy(pop.members[idx]))
|
382 |
+
end
|
383 |
+
|
384 |
+
# Sample the population, and get the best member from that sample
|
385 |
+
function bestOfSample(pop::Population)::PopMember
|
386 |
+
sample = samplePop(pop)
|
387 |
+
best_idx = argmin([sample.members[member].score for member=1:sample.n])
|
388 |
+
return sample.members[best_idx]
|
389 |
+
end
|
390 |
+
|
391 |
+
# Mutate the best sampled member of the population
|
392 |
+
function iterateSample(pop::Population, T::Float64)::PopMember
|
393 |
+
allstar = bestOfSample(pop)
|
394 |
+
new = iterate(allstar.tree, T, X, y, alpha, parsimony)
|
395 |
+
allstar.tree = new
|
396 |
+
allstar.score = scoreFunc(new, X, y, parsimony)
|
397 |
+
allstar.birth = time() - 1.6e9
|
398 |
+
return allstar
|
399 |
+
end
|
400 |
+
|
401 |
+
# Pass through the population several times, replacing the oldest
|
402 |
+
# with the fittest of a small subsample
|
403 |
+
function regEvolCycle(pop::Population, T::Float64)::Population
|
404 |
+
for i=1:Int(pop.n/10)
|
405 |
+
baby = iterateSample(pop, T)
|
406 |
+
oldest = argmin([pop.members[member].birth for member=1:pop.n])
|
407 |
+
pop.members[oldest] = baby
|
408 |
+
end
|
409 |
+
return pop
|
410 |
+
end
|
411 |
+
|
412 |
+
# Cycle through regularized evolution many times,
|
413 |
+
# printing the fittest equation every 10% through
|
414 |
+
function run(ncycles::Int,
|
415 |
+
npop::Int=100,
|
416 |
+
annealing::Bool=false)::Population
|
417 |
+
|
418 |
+
allT = LinRange(1.0, 0.0, ncycles)
|
419 |
+
pop = Population(npop, 3)
|
420 |
+
bestScore = Inf
|
421 |
+
for iT in tqdm(1:size(allT)[1])
|
422 |
+
if annealing
|
423 |
+
pop = regEvolCycle(pop, allT[iT])
|
424 |
+
else
|
425 |
+
pop = regEvolCycle(pop, 0.0)
|
426 |
+
end
|
427 |
+
bestCurScoreIdx = argmin([pop.members[member].score for member=1:pop.n])
|
428 |
+
bestCurScore = pop.members[bestCurScoreIdx].score
|
429 |
+
if bestCurScore < bestScore
|
430 |
+
bestScore = bestCurScore
|
431 |
+
println(bestScore, " is the score for ", stringTree(pop.members[bestCurScoreIdx].tree))
|
432 |
+
end
|
433 |
+
end
|
434 |
+
return pop
|
435 |
+
end
|
436 |
+
|
437 |
+
println("Lets try to learn (x2^2 + cos(x3) + 5) using regularized evolution from scratch")
|
438 |
+
pop = run(10000, 1000, false);
|
439 |
+
|
440 |
+
|