1,867 research outputs found
Learning in Markov Random Fields with Contrastive Free Energies
Learning Markov random field (MRF) models is notoriously hard due to the presence of a global normalization factor. In this paper we present a new framework for learning MRF models based on the contrastive free energy (CF) objective function. In this scheme the parameters are updated in an attempt to match the average statistics of the data distribution and a distribution which is (partially or approximately) "relaxed" to the equilibrium distribution. We show that maximum likelihood, mean field, contrastive divergence and pseudo-likelihood objectives can be understood in this paradigm. Moreover, we propose and study a new learning algorithm: the "kstep Kikuchi/Bethe approximation". This algorithm is then tested on a conditional random field model with "skip-chain" edges to model long range interactions in text data. It is demonstrated that with no loss in accuracy, the training time is brought down on average from 19 hours (BP based learning) to 83 minutes, an order of magnitude improvement
Conditional Restricted Boltzmann Machines for Structured Output Prediction
Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic
models that have recently been applied to a wide range of problems, including
collaborative filtering, classification, and modeling motion capture data.
While much progress has been made in training non-conditional RBMs, these
algorithms are not applicable to conditional models and there has been almost
no work on training and generating predictions from conditional RBMs for
structured output problems. We first argue that standard Contrastive
Divergence-based learning may not be suitable for training CRBMs. We then
identify two distinct types of structured output prediction problems and
propose an improved learning algorithm for each. The first problem type is one
where the output space has arbitrary structure but the set of likely output
configurations is relatively small, such as in multi-label classification. The
second problem is one where the output space is arbitrarily structured but
where the output space variability is much greater, such as in image denoising
or pixel labeling. We show that the new learning algorithms can work much
better than Contrastive Divergence on both types of problems
Efficient Learning for Undirected Topic Models
Replicated Softmax model, a well-known undirected topic model, is powerful in
extracting semantic representations of documents. Traditional learning
strategies such as Contrastive Divergence are very inefficient. This paper
provides a novel estimator to speed up the learning based on Noise Contrastive
Estimate, extended for documents of variant lengths and weighted inputs.
Experiments on two benchmarks show that the new estimator achieves great
learning efficiency and high accuracy on document retrieval and classification.Comment: Accepted by ACL-IJCNLP 2015 short paper. 6 page
A note on the evaluation of generative models
Probabilistic generative models can be used for compression, denoising,
inpainting, texture synthesis, semi-supervised learning, unsupervised feature
learning, and other tasks. Given this wide range of applications, it is not
surprising that a lot of heterogeneity exists in the way these models are
formulated, trained, and evaluated. As a consequence, direct comparison between
models is often difficult. This article reviews mostly known but often
underappreciated properties relating to the evaluation and interpretation of
generative models with a focus on image models. In particular, we show that
three of the currently most commonly used criteria---average log-likelihood,
Parzen window estimates, and visual fidelity of samples---are largely
independent of each other when the data is high-dimensional. Good performance
with respect to one criterion therefore need not imply good performance with
respect to the other criteria. Our results show that extrapolation from one
criterion to another is not warranted and generative models need to be
evaluated directly with respect to the application(s) they were intended for.
In addition, we provide examples demonstrating that Parzen window estimates
should generally be avoided
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