We focus on the problem of efficient learning of dependency trees. It is well-known that given the pairwise mutual information coefficients, a minimum-weight spanning tree algorithm solves this problem exactly and in polynomial time. However, for large data-sets it is the construction of the correlation matrix that dominates the running time. We have developed a new spanning-tree algorithm which is capable of exploiting partial knowledge about edge weights. The partial knowledge we maintain is a probabilistic confidence interval on the coefficients, which we derive by examining just a small sample of the data. The algorithm is able to flag the need to shrink an interval, which translates to inspection of more data for the particular attribute pair. Experimental results show running time that is near-constant in the number of records, without significant loss in accuracy of the generated trees. Interestingly, our spanning-tree algorithm is based solely on Tarjan's red-edge rule, which is generally considered a guaranteed recipe for bad performance.

In this paper, we propose a Bayesian framework, which constructs shared-state triphone HMMs based on a variational Bayesian approach, and recognizes speech based on the Bayesian prediction classification; variational Bayesian estimation and clustering for speech recognition (VBEC). An appropriate model structure with high recognition performance can be found within a VBEC framework. Unlike conventional methods, including BIC or MDL criterion based on the maximum likelihood approach, the proposed model selection is valid in principle, even when there are insufficient amounts of data, because it does not use an asymptotic assumption. In isolated word recognition experiments, we show the advantage of VBEC over conventional methods, especially when dealing with small amounts of data.

We propose a model for natural images in which the probability of an image is proportional to the product of the probabilities of some filter outputs. We encourage the system to find sparse features by using a Studentt distribution to model each filter output. If the t-distribution is used to model the combined outputs of sets of neurally adjacent filters, the system learns a topographic map in which the orientation, spatial frequency and location of the filters change smoothly across the map. Even though maximum likelihood learning is intractable in our model, the product form allows a relatively efficient learning procedure that works well even for highly overcomplete sets of filters. Once the model has been learned it can be used as a prior to derive the "iterated Wiener filter" for the purpose of denoising images.

This paper focuses on people's short-run behavior by examining dynamical versions of these three theories, and comparing their predictions to a real-world dataset.

Machine learning has reached a point where many probabilistic methods can be understood as variations, extensions and combinations of a much smaller set of abstract themes, e.g., as different instances of the EM algorithm. This enables the systematic derivation of algorithms customized for different models.

We propose a dynamic Bayesian model for motifs in biopolymer sequences which captures rich biological prior knowledge and positional dependencies in motif structure in a principled way. Our model posits that the position-specific multinomial parameters for monomer distribution are distributed as a latent Dirichlet-mixture random variable, and the position-specific Dirichlet component is determined by a hidden Markov process. Model parameters can be fit on training motifs using a variational EM algorithm within an empirical Bayesian framework. Variational inference is also used for detecting hidden motifs. Our model improves over previous models that ignore biological priors and positional dependence. It has much higher sensitivity to motifs during detection and a notable ability to distinguish genuine motifs from false recurring patterns.

Identity uncertainty is a pervasive problem in real-world data analysis. It arises whenever objects are not labeled with unique identifiers or when those identifiers may not be perceived perfectly. In such cases, two observations may or may not correspond to the same object. In this paper, we consider the problem in the context of citation matching--the problem of deciding which citations correspond to the same publication. Our approach is based on the use of a relational probability model to define a generative model for the domain, including models of author and title corruption and a probabilistic citation grammar. Identity uncertainty is handled by extending standard models to incorporate probabilities over the possible mappings between terms in the language and objects in the domain. Inference is based on Markov chain Monte Carlo, augmented with specific methods for generating efficient proposals when the domain contains many objects. Results on several citation data sets show that the method outperforms current algorithms for citation matching. The declarative, relational nature of the model also means that our algorithm can determine object characteristics such as author names by combining multiple citations of multiple papers.

We present a hierarchical Bayesian model for learning efficient codes of higher-order structure in natural images. The model, a nonlinear generalization of independent component analysis, replaces the standard assumption of independence for the joint distribution of coefficients with a distribution that is adapted to the variance structure of the coefficients of an efficient image basis. This offers a novel description of higherorder image structure and provides a way to learn coarse-coded, sparsedistributed representations of abstract image properties such as object location, scale, and texture.

We describe a method for learning sparse multiscale image representations using a sparse prior distribution over the basis function coefficients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coefficients to have exact zero values. Coefficients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Denoising using the learned image model is demonstrated for some standard test images, with results that compare favorably with other denoising methods.

Accurate representation of articulated motion is a challenging problem for machine perception. Several successful tracking algorithms have been developed that model human body as an articulated tree. We propose a learning-based method for creating such articulated models from observations of multiple rigid motions. This paper is concerned with recovering topology of the articulated model, when the rigid motion of constituent segments is known. Our approach is based on finding the Maximum Likelihood tree shaped factorization of the joint probability density function (PDF) of rigid segment motions. The topology of graphical model formed from this factorization corresponds to topology of the underlying articulated body. We demonstrate the performance of our algorithm on both synthetic and real motion capture data.