112 research outputs found
On the quantitative analysis of Deep Belief Networks
Deep Belief Networks (DBNâs) are generative models that contain many layers of hidden variables. Efficient greedy algorithms for learning and approximate inference have allowed these models to be applied successfully in many application domains. The main building block of a DBN is a bipartite undirected graphical model called a restricted Boltzmann machine (RBM). Due to the presence of the partition function, model selection, complexity control, and exact maximum likelihood learning in RBM's are intractable. We show that Annealed Importance Sampling (AIS) can be used to efficiently estimate the partition function of an RBM, and we present a novel AIS scheme for comparing RBM's with different architectures. We further show how an AIS estimator, along with approximate inference, can be used to estimate a lower bound on the log-probability that a DBN model with multiple hidden layers assigns to the test data. This is, to our knowledge, the first step towards obtaining quantitative results that would allow us to directly assess the performance of Deep Belief Networks as generative models of data
Relaxations for inference in restricted Boltzmann machines
We propose a relaxation-based approximate inference algorithm that samples
near-MAP configurations of a binary pairwise Markov random field. We experiment
on MAP inference tasks in several restricted Boltzmann machines. We also use
our underlying sampler to estimate the log-partition function of restricted
Boltzmann machines and compare against other sampling-based methods.Comment: ICLR 2014 workshop track submissio
Metric-Free Natural Gradient for Joint-Training of Boltzmann Machines
This paper introduces the Metric-Free Natural Gradient (MFNG) algorithm for
training Boltzmann Machines. Similar in spirit to the Hessian-Free method of
Martens [8], our algorithm belongs to the family of truncated Newton methods
and exploits an efficient matrix-vector product to avoid explicitely storing
the natural gradient metric . This metric is shown to be the expected second
derivative of the log-partition function (under the model distribution), or
equivalently, the variance of the vector of partial derivatives of the energy
function. We evaluate our method on the task of joint-training a 3-layer Deep
Boltzmann Machine and show that MFNG does indeed have faster per-epoch
convergence compared to Stochastic Maximum Likelihood with centering, though
wall-clock performance is currently not competitive
Accelerating sparse restricted Boltzmann machine training using non-Gaussianity measures
In recent years, sparse restricted Boltzmann machines have gained popularity as unsupervised feature extractors. Starting from the observation that their training process is biphasic, we investigate how it can be accelerated: by determining when it can be stopped based on the non-Gaussianity of the distribution of the model parameters, and by increasing the learning rate when the learnt filters have locked on to their preferred configurations. We evaluated our approach on the CIFAR-10, NORB and GTZAN datasets
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