Using Flux.jl, is there a way I can avoid overfitting by implementing some sort of early stopping functionality?
Flux.jl provides a built in Flux.early_stopping function which can be used as follows:
julia> loss = let l = 0
() -> l += 1
end; # pseudo loss function that returns increasing values
julia> es = Flux.early_stopping(loss, 3);
julia> Flux.#epochs 30 begin
es() && break
end
[ Info: Epoch 1
you can read more about this here: https://fluxml.ai/Flux.jl/stable/utilities/#Flux.early_stopping for further details on how to implement early stopping in Flux.
Related
I'd like to run heavy computations in Julia for a fixed duration, for example 10 seconds. I tried this:
timer = Timer(10.0)
while isopen(timer)
computation()
end
But this does not work, since the computations never let Julia's task scheduler take control. So I added yield() in the loop:
timer = Timer(10.0)
while isopen(timer)
yield()
computation()
end
But now there is significant overhead from calling yield(), especially when one call to computation() is short. I guess I could call yield() and isopen() only every 1000 iterations or so, but I would prefer a solution where I would not have to tweak the number of iterations every time I change the computations. Any ideas?
This pattern below uses threads and on my laptop has a latency of around 35ms for each 1,000,000 calls which is more than acceptable for any job.
Tested on Julia 1.5 release candidate:
function should_stop(timeout=10)
handle = Threads.Atomic{Bool}(false)
mytask = Threads.#spawn begin
sleep(timeout)
Threads.atomic_or!(handle, true)
end
handle
end
function do_some_job_with_timeout()
handle = should_stop(5)
res = BigInt() # save results to some object
mytask = Threads.#spawn begin
for i in 1:10_000_000
#TODO some complex computations here
res += 1 # mutate the result object
handle.value && break
end
end
wait(mytask) # wait for the job to complete
res
end
You can also used Distributed instead. The code below seems to have a much better latency - only about 1ms for each 1,000,000 timeout checks.
using Distributed
using SharedArrays
addprocs(1)
function get_termination_handle(timeout=5,workerid::Int=workers()[end])::SharedArray{Bool}
handle = SharedArray{Bool}([false])
proc = #spawnat workerid begin
sleep(timeout)
handle[1]=true
end
handle
end
function fun_within_timeout()
res = 0
h = get_termination_handle(0.1)
for i = 1:100_000_000
res += i % 2 == 0 ? 1 : 0
h[1] && break
end
res
end
I'm using NLopt for a constrained maximization problem. Regardless of the algorithm or start values, the optimization program is force stopped even before the first iteration (or so I assume because it gives me the initial value). I've attached my code here. I'm trying to find probabilities attached to a grid such that a function is maximized under some constraints. Any help is appreciated.
uk = x -> x^0.5
function objective(u,p,grd)
-p'*u.(grd)
end
function c3(grd,p)
c =[]
d =[]
for i=1:length(grd)
push!(c,quadgk(x -> (i-x)*(x <= i ? 1 : 0),0,1)[1])
push!(d,sum(p[1:i]'*(grd[1:i] .- grd[i])))
end
return append!(d-c,-p)
end
function c4(grd,p)
return (grd .* p)-quadgk(x,0,1)
end
grd = n -> collect(0:1/n:1)
opt = Opt(:LD_SLSQP,11)
inequality_constraint!(opt, p -> c3(grd(10),p))
inequality_constraint!(opt, p -> -p)
equality_constraint!(opt, p -> sum(p)-1)
equality_constraint!(opt, p -> c4(grd(10),p))
opt.min_objective = p -> objective(-uk, p, grd(10))
k = push!(ones(11)*(1/11))
(minf,minx,ret) = optimize(opt, k)
I'm not a julia developer, but I only know this, if you need exit before complete the loop for is not your best choice, you need do a while with a sentinel variable.
here you have an article that explain you how while with sentinels works
and here you have a julia example changing your for to a while with a sentinel that exit after the third loop
i = 1
third = 0
while i < length(grd) && third != 1
# of course you need change this, it is only an example that will exit in the 3 loop
if i == 3
third = 1
end
push!(c,quadgk(x -> (i-x)*(x <= i ? 1 : 0),0,1)[1])
push!(d,sum(p[1:i]'*(grd[1:i] .- grd[i])))
i += 1
end
Like in R:
a <- 2
or even better
a ← 2
which should translate to
a = 2
and if possible respect method overloading.
= is overloaded (not in the multiple dispatch sense) a lot in Julia.
It binds a new variable. As in a = 3. You won't be able to use ← instead of = in this context, because you can't overload binding in Julia.
It gets lowered to setindex!. As in, a[i] = b gets lowered to setindex!(a, b, i). Unfortunately, setindex! takes 3 variables while ← can only take 2 variables. So you can't overload = with 3 variables.
But, you can use only 2 variables and overload a[:] = b, for example. So, you can define ←(a,b) = (a[:] = b) or ←(a,b) = setindex!(a,b,:).
a .= b gets lowered to (Base.broadcast!)(Base.identity, a, b). You can overload this by defining ←(a,b) = (a .= b) or ←(a,b) = (Base.broadcast!)(Base.identity, a, b).
So, there are two potentially nice ways of using ←. Good luck ;)
Btw, if you really want to use ← to do binding (like in 1.), the only way to do it is using macros. But then, you will have to write a macro in front of every single assignment, which doesn't look very good.
Also, if you want to explore how operators get lowered in Julia, do f(a,b) = (a .= b), for example, and then #code_lowered f(x,y).
No. = is not an operator in Julia, and cannot be assigned to another symbol.
Disclaimer: You are fully responsible if you will try my (still beginner's) experiments bellow! :P
MacroHelper is module ( big thanks to #Alexander_Morley and #DanGetz for help ) I plan to play with in future and we could probably try it here :
julia> module MacroHelper
# modified from the julia source ./test/parse.jl
function parseall(str)
pos = start(str)
exs = []
while !done(str, pos)
ex, pos = parse(str, pos) # returns next starting point as well as expr
ex.head == :toplevel ? append!(exs, ex.args) : push!(exs, ex)
end
if length(exs) == 0
throw(ParseError("end of input"))
elseif length(exs) == 1
return exs[1]
else
return Expr(:block, exs...) # convert the array of expressions
# back to a single expression
end
end
end;
With module above you could define simple test "language":
julia> module TstLang
export #tst_cmd
import MacroHelper
macro tst_cmd(a)
b = replace("$a", "←", "=") # just simply replacing ←
# in real life you would probably like
# to escape comments, strings etc
return MacroHelper.parseall(b)
end
end;
And by using it you could probably get what you want:
julia> using TstLang
julia> tst```
a ← 3
println(a)
a +← a + 3 # maybe not wanted? :P
```
3
9
What about performance?
julia> function test1()
a = 3
a += a + 3
end;
julia> function test2()
tst```
a ← 3
a +← a + 3
```
end;
julia> test1(); #time test1();
0.000002 seconds (4 allocations: 160 bytes)
julia> test2(); #time test2();
0.000002 seconds (4 allocations: 160 bytes)
If you like to see syntax highlight (for example in atom editor) then you need to use it differently:
function test3()
#tst_cmd begin
a ← 3
a ← a + a + 3 # parser don't allow you to use "+←" here!
end
end;
We could hope that future Julia IDEs could syntax highlight cmd macros too. :)
What could be problem with "solution" above? I am not so experienced julian so many things. :P (in this moment something about "macro hygiene" and "global scope" comes to mind...)
But what you want is IMHO good for some domain specific languages and not to redefine basic of language! It is because readability very counts and if everybody will redefine everything then it will end in Tower of Babel...
What happens for a global variable when running in the parallel mode?
I have a global variable, "to_be_optimized_parameterIndexSet", which is a vector of indexes that should be optimized using gamultiobj and I have set its value only in the main script(nowhere else).
My code works properly in serial mode but when I switch to parallel mode (using "matlabpool open" and setting proper values for 'gaoptimset' ) the mentioned global variable becomes empty (=[]) in the fitness function and causes this error:
??? Error using ==> parallel_function at 598
Error in ==> PF_gaMultiFitness at 15 [THIS LINE: constants(to_be_optimized_parameterIndexSet) = individual;]
In an assignment A(I) = B, the number of elements in B and
I must be the same.
Error in ==> fcnvectorizer at 17
parfor (i = 1:popSize)
Error in ==> gamultiobjMakeState at 52
Score =
fcnvectorizer(state.Population(initScoreProvided+1:end,:),FitnessFcn,numObj,options.SerialUserFcn);
Error in ==> gamultiobjsolve at 11
state = gamultiobjMakeState(GenomeLength,FitnessFcn,output.problemtype,options);
E rror in ==> gamultiobj at 238
[x,fval,exitFlag,output,population,scores] = gamultiobjsolve(FitnessFcn,nvars, ...
Error in ==> PF_GA_mainScript at 136
[x, fval, exitflag, output] = gamultiobj(#(individual)PF_gaMultiFitness(individual, initialConstants), ...
Caused by:
Failure in user-supplied fitness function evaluation. GA cannot continue.
I have checked all the code to make sure I've not changed this global variable everywhere else.
I have a quad-core processor.
Where is the bug? any suggestion?
EDIT 1: The MATLAB code in the main script:
clc
clear
close all
format short g
global simulation_duration % PF_gaMultiFitness will use this variable
global to_be_optimized_parameterIndexSet % PF_gaMultiFitness will use this variable
global IC stimulusMoment % PF_gaMultiFitness will use these variables
[initialConstants IC] = oldCICR_Constants; %initialize state
to_be_optimized_parameterIndexSet = [21 22 23 24 25 26 27 28 17 20];
LB = [ 0.97667 0.38185 0.63529 0.046564 0.23207 0.87484 0.46014 0.0030636 0.46494 0.82407 ];
UB = [1.8486 0.68292 0.87129 0.87814 0.66982 1.3819 0.64562 0.15456 1.3717 1.8168];
PopulationSize = input('Population size? ') ;
GaTimeLimit = input('GA time limit? (second) ');
matlabpool open
nGenerations = inf;
options = gaoptimset('PopulationSize', PopulationSize, 'TimeLimit',GaTimeLimit, 'Generations', nGenerations, ...
'Vectorized','off', 'UseParallel','always');
[x, fval, exitflag, output] = gamultiobj(#(individual)PF_gaMultiFitness(individual, initialConstants), ...
length(to_be_optimized_parameterIndexSet),[],[],[],[],LB,UB,options);
matlabpool close
some other piece of code to show the results...
The MATLAB code of the fitness function, "PF_gaMultiFitness":
function objectives =PF_gaMultiFitness(individual, constants)
global simulation_duration IC stimulusMoment to_be_optimized_parameterIndexSet
%THIS FUNCTION RETURNS MULTI OBJECTIVES AND PUTS EACH OBJECTIVE IN A COLUMN
constants(to_be_optimized_parameterIndexSet) = individual;
[smcState , ~, Time]= oldCICR_CompCore(constants, IC, simulation_duration,2);
targetValue = 1; % [uM]desired [Ca]i peak concentration
afterStimulus = smcState(Time>stimulusMoment,14); % values of [Ca]i after stimulus
peak_Ca_value = max(afterStimulus); % smcState(:,14) is [Ca]i
if peak_Ca_value < 0.8 * targetValue
objectives(1,1) = inf;
else
objectives(1, 1) = abs(peak_Ca_value - targetValue);
end
pkIDX = peakFinder(afterStimulus);
nPeaks = sum(pkIDX);
if nPeaks > 1
peakIndexes = find(pkIDX);
period = Time(peakIndexes(2)) - Time(peakIndexes(1));
objectives(1,2) = 1e5* 1/period;
elseif nPeaks == 1 && peak_Ca_value > 0.8 * targetValue
objectives(1,2) = 0;
else
objectives(1,2) = inf;
end
end
Global variables do not get passed from the MATLAB client to the workers executing the body of the PARFOR loop. The only data that does get sent into the loop body are variables that occur in the text of the program. This blog entry might help.
it really depends on the type of variable you're putting in. i need to see more of your code to point out the flaw, but in general it is good practice to avoid assuming complicated variables will be passed to each worker. In other words anything more then a primitive may need to be reinitialized inside a parallel routine or may need have specific function calls (like using feval for function handles).
My advice: RTM
Ok, first up, this is NOT for a class, test, or other student type activity.
I'm a scripter for a game, and am trying to implement the math library for all to use, and unfortunately, all I have available to me is very basic lua. The implemented version cannot be changed, and does not include any libraries. For those wondering, its for scripting in Fold.It.
Here's what I have...
math={}
math.fact = function(b) if(b==1)or(b==0) then return 1 end e=1 for c=b,1,-1 do e=e*c end return e end
math.pow = function(b,p) e=b if(p==0) then return 1 end if(p<0) then p=p*(-1) end for c=p,2,-1 do e=e*b end return e end
math.cos = function(b,p) e=0 p=p or 10 for i=1,p do e=e+(math.pow(-1,i)*math.pow(b,2*i)/math.fact(2*i)) end return e end
To clarify above, math.fact returns factorial, which is returning accurate to about 10 points of precision, and is a new function I've done to aid in cosine calculation.
The math.pow is also a new function to handle returning powers, also working as expected.
The issue is with the cosine function. Its returning unexpected values. Here's an easier to digest version (I've been writing my library stuff ultra lean)...
function math.cos(value,precision)
result=0
precision=precision or 10
for i=1,precision do
result=result+(math.pow(-1,i)*math.pow(value,2*i)/math.fact(2*i))
end
return e
end
The problem is, with those functions, for print(math.cos(90)) it returns 4.77135... when I'm expecting -0.44807... (based on calc in scientific mode, or using an online tool to cos(90)).
I'm also having issues with sin and tan, however they are similarly written to cos, which seems to have been done in many languages. If I can figure out what I'm doing wrong, I can get them all fixed.
EDIT: Corrected typo
First, your lua doesn't run. Second, you need to make your variables local. Third, cosine starts with a one.
The problem is because the Taylor series you are using only converges on the correct values of cosine close to zero. You would have to use a far more terms of the series to get it to handle 90 correctly. You can fix this for your implementation two ways:
Add a pi constant. Then use a while loop to adjust the value such that abs(value) < 2*pi:
math.pi = 3.14159265358
while value > math.pi*2 do
value = value - math.pi * 2
end
while value < -math.pi*2 do
value = value + math.pi * 2
end
Or - find or implement a version of fmod in lua.
Here is the corrected code (you can minify it):
math={}
math.fact = function(b)
if(b==1)or(b==0) then
return 1
end
local e=1
for c=b,1,-1 do
e=e*c
end
return e
end
math.pow = function(b,p)
local e=b
if(p==0) then
return 1
end
if(p<0) then
p=p*(-1)
end
for c=p,2,-1 do
e=e*b
end
return e
end
math.cos = function(b,p)
local e=1
b = math.correctRadians(b)
p=p or 10
for i=1,p do
e=e+(math.pow(-1,i)*math.pow(b,2*i)/math.fact(2*i))
end
return e
end
math.pi = 3.1415926545358
math.correctRadians = function( value )
while value > math.pi*2 do
value = value - math.pi * 2
end
while value < -math.pi*2 do
value = value + math.pi * 2
end
return value
end
interactive lua run:
imac:~ root$ lua -i temp.lua
Lua 5.1.4 Copyright (C) 1994-2008 Lua.org, PUC-Rio
> print( math.cos( 90 ) )
-0.44807359244883
>