def fit(self, x, y, method='Newton-Raphson', max_iter=20):
""" Learn the parameters of the model, i.e. self.params.
Parameters
----------
x : array of shape nb_samples*nb_features
y : array of shape nb_samples*output_dim
method : string indicating the type of optimization
- 'Newton-Raphson'
nb_iter : the maximum number of iterations
Returns
-------
params : the matrix of parameters
Examples
--------
>>> from esnlm.nodes import LogisticRegression
>>> x = np.array([[1., 0.],[0., 1]]
>>> y = np.array([[0., 1.],[1., 0]]
>>> params = LogisticRegression(2,2).fit(x, y)
"""
if type(y) == type([]):
y = np.eye(self.output_dim)[y]
def _objective_function(params):
py_given_x = softmax(np.dot(x, params.reshape(self.params.shape)))
lik = np.prod(py_given_x**y, axis=1)
return np.sum(np.log(lik+1e-7))
params = np.array(self.params)
old_value = _objective_function(params)
if method == 'Newton-Raphson':
print "... Newton-Raphson:",
for i in range(max_iter):
if self.verbose == True:
print i,
post = softmax(np.dot(x, params))
grad = gradient(x, y, post, np.ones((y.shape[0], )))
hess = hessian(x, y, post, np.ones((y.shape[0], )))
params = newton_raphson(grad, hess, params, _objective_function)
new_value = _objective_function(params)
if new_value < old_value + 1:
break
old_value = new_value
self.params = params.reshape(self.params.shape)
if self.verbose == True:
print "The End."
else:
from scipy.optimize import minimize
def obj(params):
return -_objective_function(params)
def grd(params):
post = softmax(np.dot(x, params.reshape(self.params.shape)))
return -gradient(x, y, post, np.ones((y.shape[0], ))).squeeze()
def hsn(params):
post = softmax(np.dot(x, params.reshape(self.params.shape)))
return -hessian(x, y, post, np.ones((y.shape[0], )))
params = params.reshape(params.size)
res = minimize(obj, params,jac=grd, hess=hsn, method=method,
options={'maxiter':100, 'xtol': 1e-4, 'disp': True})
params = res.x
self.params = params.reshape(self.params.shape)
return params
def hsn(params):
post = softmax(np.dot(x, params.reshape(self.params.shape)))
return -hessian(x, y, post, np.ones((y.shape[0], )))