Stopping Criteria in Contrastive Divergence: Alternatives to the Reconstruction Error
Authors: David Buchaca, Enrique Romero, Ferran Mazzanti, Jordi Delgado
ICLR 2014

Abstract: Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used to decide whether the approximation provided by the CD algorithm is good enough, though several authors (Schulz et al., 2010; Fischer & Igel, 2010) have raised doubts concerning the feasibility of this procedure. However, not many alternatives to the reconstruction error have been used in the literature. In this manuscript we investigate simple alternatives to the reconstruction error in order to detect as soon as possible the decrease in the log-likelihood during learning.


Peer review:
[Review]:
Dear authors,

Let me reveal my identity before I continue. I'm Kyunghyun Cho who wrote the earlier review (by an unexpected coincidence). The previous comments reflect what I wanted/want to say as an official reviewer, and I will not write another separate review. 

Instead, let me answer briefly to the response to my review from the authors:

(Authors) 'If you change the value of the hidden units in any way, this delicate equilibrium is broken and you expect to get much lower probabilities for the visible variables.' 

=> I cannot agree with this. Intuitively, if we believe that training makes latent variables learn potentially lower-dimensional manifold on which training samples lie, any small (or even large) change in the latent representation shouldn't correspond to a change in the input space that moves the point away from the manifold. I'd agree with your argument much more, if you were flipping all the bits of the input variable.

(Authors) 'CD_1 as it is the cheapest way we know'

=> Computationally, I don't see why CD-1 should be cheaper than PCD. Memory-wise, if you follow the usual practice of maintaining only a few persistent samples, it shouldn't matter too much as well. Though, I agree that it's easier to train an RBM with CD-1 using a much higher learning rate, which may make learning progress faster.

- Cho