The downhill package provides algorithms for minimizing scalar loss
functions that are defined using Theano.
Several optimization algorithms are included:
- ADADELTA
- ADAGRAD
- Adam
- Equilibrated SGD
- Nesterov's Accelerated Gradient
- RMSProp
- Resilient Backpropagation
- Stochastic Gradient Descent
All algorithms permit the use of regular or Nesterov-style momentum as well.
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: you can use a matrix multiplication as the data model, a squared-error term for optimization, and a sparse regularizer to encourage small coefficient values.
Once you have constructed an expression for the loss, you can optimize it with a
single call to downhill.minimize:
import downhill
import numpy as np
import theano
import theano.tensor as TT
FLOAT = 'df'[theano.config.floatX == 'float32']
def rand(a, b):
return np.random.randn(a, b).astype(FLOAT)
A, B, K = 20, 5, 3
# Set up a matrix factorization problem to optimize.
u = theano.shared(rand(A, K), name='u')
v = theano.shared(rand(K, B), name='v')
z = TT.matrix()
err = TT.sqr(z - TT.dot(u, v))
loss = err.mean() + abs(u).mean() + (v * v).mean()
# Minimize the regularized loss with respect to a data matrix.
y = np.dot(rand(A, K), rand(K, B)) + rand(A, B)
# Monitor during optimization.
monitors = (('err', err.mean()),
('|u|<0.1', (abs(u) < 0.1).mean()),
('|v|<0.1', (abs(v) < 0.1).mean()))
downhill.minimize(
loss=loss,
train=[y],
patience=0,
batch_size=A, # Process y as a single batch.
max_gradient_norm=1, # Prevent gradient explosion!
learning_rate=0.1,
monitors=monitors,
monitor_gradients=True)
# Print out the optimized coefficients u and basis v.
print('u =', u.get_value())
print('v =', v.get_value())If you prefer to maintain more control over your model during optimization, downhill provides an iterative optimization interface:
opt = downhill.build(algo='rmsprop',
loss=loss,
monitors=monitors,
monitor_gradients=True)
for metrics, _ in opt.iterate(train=[[y]],
patience=0,
batch_size=A,
max_gradient_norm=1,
learning_rate=0.1):
print(metrics)If that's still not enough, you can just plain ask downhill for the updates to your model variables and do everything else yourself:
updates = downhill.build('rmsprop', loss).get_updates(
batch_size=A, max_gradient_norm=1, learning_rate=0.1)
func = theano.function([z], loss, updates=list(updates))
for _ in range(100):
print(func(y)) # Evaluate func and apply variable updates.Source: https://github.com/lmjohns3/downhill
Documentation: https://downhill.readthedocs.org
Mailing list: https://groups.google.com/forum/#!forum/downhill-users