fminunc alternate in numpy
Question:
Is there an alternative to the fminunc function (from octave/matlab) in python? I have a cost function for a binary classifier. Now I want to run gradient descent to get minimum value of theta. The octave/matlab implementation will look like this.
% Set options for fminunc
options = optimset('GradObj', 'on', 'MaxIter', 400);
% Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
I have converted my costFunction in python using numpy library, and looking for the fminunc or any other gradient descent algorithm implementation in numpy.
Answers:
Looks like you have to change to scipy.
There you find all basic optimization algorithms readily implemented.
There is more information about the functions of interest here: http://docs.scipy.org/doc/scipy-0.10.0/reference/tutorial/optimize.html
Also, it looks like you are doing the Coursera Machine Learning course, but in Python. You might check out http://aimotion.blogspot.com/2011/11/machine-learning-with-python-logistic.html; this guy’s doing the same thing.
I was also trying to implement logistic regression as discussed in Coursera ML course, but in python. I found scipy helpful. After trying different algorithm implementations in minimize function, I found Newton Conjugate Gradient as most helpful. Also After examining its returned value, it seems that it is equivalent to that of fminunc in Octave. I have included my implementation in python below find to optimal theta.
import numpy as np
import scipy.optimize as op
def Sigmoid(z):
return 1/(1 + np.exp(-z));
def Gradient(theta,x,y):
m , n = x.shape
theta = theta.reshape((n,1));
y = y.reshape((m,1))
sigmoid_x_theta = Sigmoid(x.dot(theta));
grad = ((x.T).dot(sigmoid_x_theta-y))/m;
return grad.flatten();
def CostFunc(theta,x,y):
m,n = x.shape;
theta = theta.reshape((n,1));
y = y.reshape((m,1));
term1 = np.log(Sigmoid(x.dot(theta)));
term2 = np.log(1-Sigmoid(x.dot(theta)));
term1 = term1.reshape((m,1))
term2 = term2.reshape((m,1))
term = y * term1 + (1 - y) * term2;
J = -((np.sum(term))/m);
return J;
# intialize X and y
X = np.array([[1,2,3],[1,3,4]]);
y = np.array([[1],[0]]);
m , n = X.shape;
initial_theta = np.zeros(n);
Result = op.minimize(fun = CostFunc,
x0 = initial_theta,
args = (X, y),
method = 'TNC',
jac = Gradient);
optimal_theta = Result.x;
Implemented as below and getting similar result of octiva:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
filepath =('C:/Pythontry/MachineLearning/dataset/couresra/ex2data1.txt')
data =pd.read_csv(filepath,sep=',',header=None)
#print(data)
X = data.values[:,:2] #(100,2)
y = data.values[:,2:3] #(100,1)
#print(np.shape(y))
#In 2
#%% ==================== Part 1: Plotting ====================
postive_value = data.loc[data[2] == 1]
#print(postive_value.values[:,2:3])
negative_value = data.loc[data[2] == 0]
#print(len(postive_value))
#print(len(negative_value))
ax1 = postive_value.plot(kind='scatter',x=0,y=1,s=50,color='b',marker="+",label="Admitted") # S is line width #https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.scatter.html#matplotlib.axes.Axes.scatter
ax2 = negative_value.plot(kind='scatter',x=0,y=1,s=50,color='y',ax=ax1,label="Not Admitted")
ax1.set_xlabel("Exam 1 score")
ax2.set_ylabel("Exam 2 score")
plt.show()
#print(ax1 == ax2)
#print(np.shape(X))
# In 3
#============ Part 2: Compute Cost and Gradient ===========
[m,n] = np.shape(X) #(100,2)
print(m,n)
additional_coulmn = np.ones((m,1))
X = np.append(additional_coulmn,X,axis=1)
initial_theta = np.zeros((n+1), dtype=int)
print(initial_theta)
# In4
#Sigmoid and cost function
def sigmoid(z):
g = np.zeros(np.shape(z));
g = 1/(1+np.exp(-z));
return g
def costFunction(theta, X, y):
J = 0;
#print(theta)
receive_theta = np.array(theta)[np.newaxis] ##This command is used to create the 1D array
#print(receive_theta)
theta = np.transpose(receive_theta)
#print(np.shape(theta))
#grad = np.zeros(np.shape(theta))
z = np.dot(X,theta) # where z = theta*X
#print(z)
h = sigmoid(z) #formula h(x) = g(z) whether g = 1/1+e(-z) #(100,1)
#print(np.shape(h))
#J = np.sum(((-y)*np.log(h)-(1-y)*np.log(1-h))/m);
J = np.sum(np.dot((-y.T),np.log(h))-np.dot((1-y).T,np.log(1-h)))/m
#J = (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()
#error = h-y
#print(np.shape(error))
#print(np.shape(X))
grad =np.dot(X.T,(h-y))/m
#print(grad)
return J,grad
#In5
[cost, grad] = costFunction(initial_theta, X, y)
print('Cost at initial theta (zeros):', cost)
print('Expected cost (approx): 0.693n')
print('Gradient at initial theta (zeros): n',grad)
print('Expected gradients (approx):n -0.1000n -12.0092n -11.2628n')
In6 # Compute and display cost and gradient with non-zero theta
test_theta = [-24, 0.2, 0.2]
#test_theta_value = np.array([-24, 0.2, 0.2])[np.newaxis] #This command is used to create the 1D row array
#test_theta = np.transpose(test_theta_value) # Transpose
#test_theta = test_theta_value.transpose()
[cost, grad] = costFunction(test_theta, X, y)
print('nCost at test theta: n', cost)
print('Expected cost (approx): 0.218n')
print('Gradient at test theta: n',grad);
print('Expected gradients (approx):n 0.043n 2.566n 2.647n')
#IN6
# ============= Part 3: Optimizing using range =============
import scipy.optimize as opt
#initial_theta_initialize = np.array([0, 0, 0])[np.newaxis]
#initial_theta = np.transpose(initial_theta_initialize)
print ('Executing minimize function...n')
# Working models
#result = opt.minimize(costFunction,initial_theta,args=(X,y),method='TNC',jac=True,options={'maxiter':400})
result = opt.fmin_tnc(func=costFunction, x0=initial_theta, args=(X, y))
# Not working model
#costFunction(initial_theta,X,y)
#model = opt.minimize(fun = costFunction, x0 = initial_theta, args = (X, y), method = 'TNC',jac = costFunction)
print('Thetas found by fmin_tnc function: ', result);
print('Cost at theta found : n', cost);
print('Expected cost (approx): 0.203n');
print('theta: n',result[0]);
print('Expected theta (approx):n');
print(' -25.161n 0.206n 0.201n');
output:
Executing minimize function…
Thetas found by fmin_tnc function: (array([-25.16131854, 0.20623159, 0.20147149]), 36, 0)
Cost at theta found :
0.218330193827
Expected cost (approx): 0.203
theta:
[-25.16131854 0.20623159 0.20147149]
Expected theta (approx):
-25.161
0.206
0.201
Thanks! This code helped me to understand how scipy optimize works. I believe that in the "Not Working Model" you should separate Cost and Gradiate Functions as in
the example SciPy minimize with gradient
and in accordance with the jac field description in the documentation https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize
Is there an alternative to the fminunc function (from octave/matlab) in python? I have a cost function for a binary classifier. Now I want to run gradient descent to get minimum value of theta. The octave/matlab implementation will look like this.
% Set options for fminunc
options = optimset('GradObj', 'on', 'MaxIter', 400);
% Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
I have converted my costFunction in python using numpy library, and looking for the fminunc or any other gradient descent algorithm implementation in numpy.
Looks like you have to change to scipy.
There you find all basic optimization algorithms readily implemented.
There is more information about the functions of interest here: http://docs.scipy.org/doc/scipy-0.10.0/reference/tutorial/optimize.html
Also, it looks like you are doing the Coursera Machine Learning course, but in Python. You might check out http://aimotion.blogspot.com/2011/11/machine-learning-with-python-logistic.html; this guy’s doing the same thing.
I was also trying to implement logistic regression as discussed in Coursera ML course, but in python. I found scipy helpful. After trying different algorithm implementations in minimize function, I found Newton Conjugate Gradient as most helpful. Also After examining its returned value, it seems that it is equivalent to that of fminunc in Octave. I have included my implementation in python below find to optimal theta.
import numpy as np
import scipy.optimize as op
def Sigmoid(z):
return 1/(1 + np.exp(-z));
def Gradient(theta,x,y):
m , n = x.shape
theta = theta.reshape((n,1));
y = y.reshape((m,1))
sigmoid_x_theta = Sigmoid(x.dot(theta));
grad = ((x.T).dot(sigmoid_x_theta-y))/m;
return grad.flatten();
def CostFunc(theta,x,y):
m,n = x.shape;
theta = theta.reshape((n,1));
y = y.reshape((m,1));
term1 = np.log(Sigmoid(x.dot(theta)));
term2 = np.log(1-Sigmoid(x.dot(theta)));
term1 = term1.reshape((m,1))
term2 = term2.reshape((m,1))
term = y * term1 + (1 - y) * term2;
J = -((np.sum(term))/m);
return J;
# intialize X and y
X = np.array([[1,2,3],[1,3,4]]);
y = np.array([[1],[0]]);
m , n = X.shape;
initial_theta = np.zeros(n);
Result = op.minimize(fun = CostFunc,
x0 = initial_theta,
args = (X, y),
method = 'TNC',
jac = Gradient);
optimal_theta = Result.x;
Implemented as below and getting similar result of octiva:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
filepath =('C:/Pythontry/MachineLearning/dataset/couresra/ex2data1.txt')
data =pd.read_csv(filepath,sep=',',header=None)
#print(data)
X = data.values[:,:2] #(100,2)
y = data.values[:,2:3] #(100,1)
#print(np.shape(y))
#In 2
#%% ==================== Part 1: Plotting ====================
postive_value = data.loc[data[2] == 1]
#print(postive_value.values[:,2:3])
negative_value = data.loc[data[2] == 0]
#print(len(postive_value))
#print(len(negative_value))
ax1 = postive_value.plot(kind='scatter',x=0,y=1,s=50,color='b',marker="+",label="Admitted") # S is line width #https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.scatter.html#matplotlib.axes.Axes.scatter
ax2 = negative_value.plot(kind='scatter',x=0,y=1,s=50,color='y',ax=ax1,label="Not Admitted")
ax1.set_xlabel("Exam 1 score")
ax2.set_ylabel("Exam 2 score")
plt.show()
#print(ax1 == ax2)
#print(np.shape(X))
# In 3
#============ Part 2: Compute Cost and Gradient ===========
[m,n] = np.shape(X) #(100,2)
print(m,n)
additional_coulmn = np.ones((m,1))
X = np.append(additional_coulmn,X,axis=1)
initial_theta = np.zeros((n+1), dtype=int)
print(initial_theta)
# In4
#Sigmoid and cost function
def sigmoid(z):
g = np.zeros(np.shape(z));
g = 1/(1+np.exp(-z));
return g
def costFunction(theta, X, y):
J = 0;
#print(theta)
receive_theta = np.array(theta)[np.newaxis] ##This command is used to create the 1D array
#print(receive_theta)
theta = np.transpose(receive_theta)
#print(np.shape(theta))
#grad = np.zeros(np.shape(theta))
z = np.dot(X,theta) # where z = theta*X
#print(z)
h = sigmoid(z) #formula h(x) = g(z) whether g = 1/1+e(-z) #(100,1)
#print(np.shape(h))
#J = np.sum(((-y)*np.log(h)-(1-y)*np.log(1-h))/m);
J = np.sum(np.dot((-y.T),np.log(h))-np.dot((1-y).T,np.log(1-h)))/m
#J = (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()
#error = h-y
#print(np.shape(error))
#print(np.shape(X))
grad =np.dot(X.T,(h-y))/m
#print(grad)
return J,grad
#In5
[cost, grad] = costFunction(initial_theta, X, y)
print('Cost at initial theta (zeros):', cost)
print('Expected cost (approx): 0.693n')
print('Gradient at initial theta (zeros): n',grad)
print('Expected gradients (approx):n -0.1000n -12.0092n -11.2628n')
In6 # Compute and display cost and gradient with non-zero theta
test_theta = [-24, 0.2, 0.2]
#test_theta_value = np.array([-24, 0.2, 0.2])[np.newaxis] #This command is used to create the 1D row array
#test_theta = np.transpose(test_theta_value) # Transpose
#test_theta = test_theta_value.transpose()
[cost, grad] = costFunction(test_theta, X, y)
print('nCost at test theta: n', cost)
print('Expected cost (approx): 0.218n')
print('Gradient at test theta: n',grad);
print('Expected gradients (approx):n 0.043n 2.566n 2.647n')
#IN6
# ============= Part 3: Optimizing using range =============
import scipy.optimize as opt
#initial_theta_initialize = np.array([0, 0, 0])[np.newaxis]
#initial_theta = np.transpose(initial_theta_initialize)
print ('Executing minimize function...n')
# Working models
#result = opt.minimize(costFunction,initial_theta,args=(X,y),method='TNC',jac=True,options={'maxiter':400})
result = opt.fmin_tnc(func=costFunction, x0=initial_theta, args=(X, y))
# Not working model
#costFunction(initial_theta,X,y)
#model = opt.minimize(fun = costFunction, x0 = initial_theta, args = (X, y), method = 'TNC',jac = costFunction)
print('Thetas found by fmin_tnc function: ', result);
print('Cost at theta found : n', cost);
print('Expected cost (approx): 0.203n');
print('theta: n',result[0]);
print('Expected theta (approx):n');
print(' -25.161n 0.206n 0.201n');
output:
Executing minimize function…
Thetas found by fmin_tnc function: (array([-25.16131854, 0.20623159, 0.20147149]), 36, 0)
Cost at theta found :
0.218330193827
Expected cost (approx): 0.203
theta:
[-25.16131854 0.20623159 0.20147149]
Expected theta (approx):
-25.161
0.206
0.201
Thanks! This code helped me to understand how scipy optimize works. I believe that in the "Not Working Model" you should separate Cost and Gradiate Functions as in
the example SciPy minimize with gradient
and in accordance with the jac field description in the documentation https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize