The downhill package provides algorithms for minimizing scalar loss functions that are defined using Theano.

Several optimization algorithms are included:

• First-order stochastic gradient descent: SGD and NAG.
• First-order stochastic techniques with adaptive learning rates: RProp, RMSProp, Equilibrated SGD, Adam, and ADADELTA.
• Wrappers for several algorithms from scipy.optimize.minimize.

Let's say you have 100 samples of 1000-dimensional data, and you want to represent your data as 100 coefficients in a 10-dimensional basis. This is pretty straightforward to model using Theano, using a matrix multiplication. Once you have constructed an expression for the loss, you can optimize it using downhill:

import climate
import downhill
import numpy as np
import theano
import theano.tensor as TT

climate.enable_default_logging()

A, B, K = 100, 1000, 10

x = TT.matrix('x')

y = np.arange(A * B).reshape((A, B)).astype('f')
u = theano.shared(np.random.randn(A, K).astype('f'), name='u')
v = theano.shared(np.random.randn(K, B).astype('f'), name='v')

err = TT.sqr(x - TT.dot(u, v))

downhill.minimize(
    loss=err.mean() + abs(u).mean() + (v * v).mean(),
    params=[u, v],
    inputs=[x],
    train=[y],
    batch_size=A,
    monitors=(
        ('u<0.1', 100 * (abs(u) < 0.1).mean()),
        ('v<0.1', 100 * (abs(v) < 0.1).mean()),
    ))

Source: http://github.com/lmjohns3/downhill

Documentation: http://downhill.readthedocs.org

Mailing list: https://groups.google.com/forum/#!forum/downhill-users