Optim using gradient Error: "no match method"
I'm trying to optimize a function using one of the algorithms that require a gradient. Basically I'm trying to learn how to optimize a function with a gradient in Julia. I'm pretty sure my gradient is correct. I know this because a similarly defined Matlab function for gradient gives me the same values as Julia for some test argument values. Also, the Matlab version using fminunc with a gradient seems to optimize the penalty function.
However, when I run the Julia script, I seem to get the following error:
julia> include("ex2b.jl")
ERROR: `g!` has no method matching g!(::Array{Float64,1}, ::Array{Float64,1})
while loading ...\ex2b.jl, in ex
pression starting on line 64
I am running Julia 0.3.2 on Windows 7 32bit machine. Here is the code (mostly translating some Matlabs to Julia):
using Optim
function mapFeature(X1, X2)
degrees = 5
out = ones(size(X1)[1])
for i in range(1, degrees+1)
for j in range(0, i+1)
term = reshape( (X1.^(i-j) .* X2.^(j)), size(X1.^(i-j))[1], 1)
out = hcat(out, term)
end
end
return out
end
function sigmoid(z)
return 1 ./ (1 + exp(-z))
end
function costFunc_logistic(theta, X, y, lam)
m = length(y)
regularization = sum(theta[2:end].^2) * lam / (2 * m)
return sum( (-y .* log(sigmoid(X * theta)) - (1 - y) .* log(1 - sigmoid(X * theta))) ) ./ m + regularization
end
function costFunc_logistic_gradient!(theta, X, y, lam, m)
grad= X' * ( sigmoid(X * theta) .- y ) ./ m
grad[2:end] = grad[2:end] + theta[2:end] .* lam / m
return grad
end
data = readcsv("ex2data2.txt")
X = mapFeature(data[:,1], data[:,2])
m, n = size(data)
y = data[:, end]
theta = zeros(size(X)[2])
lam = 1.0
f(theta::Array) = costFunc_logistic(theta, X, y, lam)
g!(theta::Array) = costFunc_logistic_gradient!(theta, X, y, lam, m)
optimize(f, g!, theta, method = :l_bfgs)
And here are some of the data:
0.051267,0.69956,1
-0.092742,0.68494,1
-0.21371,0.69225,1
-0.375,0.50219,1
-0.51325,0.46564,1
-0.52477,0.2098,1
-0.39804,0.034357,1
-0.30588,-0.19225,1
0.016705,-0.40424,1
0.13191,-0.51389,1
0.38537,-0.56506,1
0.52938,-0.5212,1
0.63882,-0.24342,1
0.73675,-0.18494,1
0.54666,0.48757,1
0.322,0.5826,1
0.16647,0.53874,1
-0.046659,0.81652,1
-0.17339,0.69956,1
-0.47869,0.63377,1
-0.60541,0.59722,1
-0.62846,0.33406,1
-0.59389,0.005117,1
-0.42108,-0.27266,1
-0.11578,-0.39693,1
0.20104,-0.60161,1
0.46601,-0.53582,1
0.67339,-0.53582,1
-0.13882,0.54605,1
-0.29435,0.77997,1
-0.26555,0.96272,1
-0.16187,0.8019,1
-0.17339,0.64839,1
-0.28283,0.47295,1
-0.36348,0.31213,1
-0.30012,0.027047,1
-0.23675,-0.21418,1
-0.06394,-0.18494,1
0.062788,-0.16301,1
0.22984,-0.41155,1
0.2932,-0.2288,1
0.48329,-0.18494,1
0.64459,-0.14108,1
0.46025,0.012427,1
0.6273,0.15863,1
0.57546,0.26827,1
0.72523,0.44371,1
0.22408,0.52412,1
0.44297,0.67032,1
0.322,0.69225,1
0.13767,0.57529,1
-0.0063364,0.39985,1
-0.092742,0.55336,1
-0.20795,0.35599,1
-0.20795,0.17325,1
-0.43836,0.21711,1
-0.21947,-0.016813,1
-0.13882,-0.27266,1
0.18376,0.93348,0
0.22408,0.77997,0
Let me know if you need more details. By the way, this is related to the courier training course, if you're interested.
source to share
The gradient should not be a function to calculate the gradient, but a function to store it (hence the exclamation mark in the function name and the second argument in the error message).
The following seems to work.
function g!(theta::Array, storage::Array)
storage[:] = costFunc_logistic_gradient!(theta, X, y, lam, m)
end
optimize(f, g!, theta, method = :l_bfgs)
source to share
It's the same using closures and currying (version for those who are used to a function that returns cost and gradient):
function cost_gradient(θ, X, y, λ)
m = length(y);
return (θ::Array) -> begin
h = sigmoid(X * θ); #(m,n+1)*(n+1,1) -> (m,1)
J = (1 / m) * sum(-y .* log(h) .- (1 - y) .* log(1 - h)) + λ / (2 * m) * sum(θ[2:end] .^ 2);
end, (θ::Array, storage::Array) -> begin
h = sigmoid(X * θ); #(m,n+1)*(n+1,1) -> (m,1)
storage[:] = (1 / m) * (X' * (h .- y)) + (λ / m) * [0; θ[2:end]];
end
end
Then, somewhere in the code:
initialθ = zeros(n,1);
f, g! = cost_gradient(initialθ, X, y, λ);
res = optimize(f, g!, initialθ, method = :cg, iterations = your_iterations);
θ = res.minimum;
source to share