`scipy.optimize` functions hang even with `maxiter=0` - optimization

Question

I am trying to train the MNIST data (which I downloaded from Kaggle) with simple multi-class logistic regression, but the scipy.optimize functions hang.
Here's the code:
import csv
from math import exp
from numpy import *
from scipy.optimize import fmin, fmin_cg, fmin_powell, fmin_bfgs
# Prepare the data
def getIiter(ifname):
"""
Get the iterator from a csv file with filename ifname
"""
ifile = open(ifname, 'r')
iiter = csv.reader(ifile)
iiter.__next__()
return iiter
def parseRow(s):
y = [int(x) for x in s]
lab = y[0]
z = y[1:]
return (lab, z)
def getAllRows(ifname):
iiter = getIiter(ifname)
x = []
l = []
for row in iiter:
lab, z = parseRow(row)
x.append(z)
l.append(lab)
return x, l
def cutData(x, y):
"""
70% training
30% testing
"""
m = len(x)
t = int(m * .7)
return [(x[:t], y[:t]), (x[t:], y[t:])]
def num2IndMat(l):
t = array(l)
tt = [vectorize(int)((t == i)) for i in range(10)]
return array(tt).T
def readData(ifname):
x, l = getAllRows(ifname)
t = [[1] + y for y in x]
return array(t), num2IndMat(l)
#Calculate the cost function
def sigmoid(x):
return 1 / (1 + exp(-x))
vSigmoid = vectorize(sigmoid)
vLog = vectorize(log)
def costFunction(theta, x, y):
sigxt = vSigmoid(dot(x, theta))
cm = (- y * vLog(sigxt) - (1 - y) * vLog(1 - sigxt)) / m / N
return sum(cm)
def unflatten(flatTheta):
return [flatTheta[i * N : (i + 1) * N] for i in range(n + 1)]
def costFunctionFlatTheta(flatTheta):
return costFunction(unflatten(flatTheta), trainX, trainY)
def costFunctionFlatTheta1(flatTheta):
return costFunction(flatTheta.reshape(785, 10), trainX, trainY)
x, y = readData('train.csv')
[(trainX, trainY), (testX, testY)] = cutData(x, y)
m = len(trainX)
n = len(trainX[0]) - 1
N = len(trainY[0])
initTheta = zeros(((n + 1), N))
flatInitTheta = ndarray.flatten(initTheta)
flatInitTheta1 = initTheta.reshape(1, -1)
In the last two lines we flatten initTheta because the fmin{,_cg,_bfgs,_powell} functions seem to only take vectors as the initial value argument x0. I also flatten initTheta using reshape in hope this answer can be of help.
There is no problem computing the cost function which takes up less than 2 seconds on my computer:
print(costFunctionFlatTheta(flatInitTheta), costFunctionFlatTheta1(flatInitTheta1))
# 0.69314718056 0.69314718056
But all the fmin functions hang, even if I set maxiter=0.
e.g.
newFlatTheta = fmin(costFunctionFlatTheta, flatInitTheta, maxiter=0)
or
newFlatTheta1 = fmin(costFunctionFlatTheta1, flatInitTheta1, maxiter=0)
When I interrupt the program, it seems to me it all hangs at lines in optimize.py calling the cost functions, lines like this:
return function(*(wrapper_args + args))
For example, if I use fmin_cg, this would be line 292 in optimize.py (Version 0.5).
How do I solve this problem?

Answer 1

OK I found a way to stop fmin_cg from hanging.
Basically I just need to write a function that computes the gradient of the cost function, and pass it to the fprime parameter of fmin_cg.
def gradient(theta, x, y):
return dot(x.T, vSigmoid(dot(x, theta)) - y) / m / N
def gradientFlatTheta(flatTheta):
return ndarray.flatten(gradient(flatTheta.reshape(785, 10), trainX, trainY))
Then
newFlatTheta = fmin_cg(costFunctionFlatTheta, flatInitTheta, fprime=gradientFlatTheta, maxiter=0)
terminates within seconds, and setting maxiter to a higher number (say 100) one can train the model within reasonable amount of time.
The documentation of fmin_cg says the gradient would be numerically computed if no fprime is given, which is what I suspect caused the hanging.
Thanks to this notebook by zgo2016#Kaggle which helped me find the solution.