Markov random fields (MRFs), or undirected graphical models, provide a powerful framework for modeling complex dependencies among random variables. Maximum likelihood learning in MRFs is hard due to the presence of the global normalizing constant. In this paper we consider a class of stochastic approximation algorithms of Robbins-Monro type that uses Markov chain Monte Carlo to do approximate maximum likelihood learning. We show that using MCMC operators based on tempered transitions enables the stochastic approximation algorithm to better explore highly multimodal distributions, which considerably improves parameter estimates in large densely-connected MRFs. Our results on MNIST and NORB datasets demonstrate that we can successfully learn good generative models of high-dimensional, richly structured data and perform well on digit and object recognition tasks.

Canonical Correlation Analysis (CCA) is a useful technique for modeling dependencies between two (or more) sets of variables. Building upon the recently suggested probabilistic interpretation of CCA, we propose a nonparametric, fully Bayesian framework that can automatically select the number of correlation components, and effectively capture the sparsity underlying the projections. In addition, given (partially) labeled data, our algorithm can also be used as a (semi)supervised dimensionality reduction technique, and can be applied to learn useful predictive features in the context of learning a set of related tasks. Experimental results demonstrate the efficacy of the proposed approach for both CCA as a stand-alone problem, and when applied to multi-label prediction.

A score function induced by a generative model of the data can provide a feature vectorof a fixed dimension for each data sample. Data samples themselves may be of differing lengths (e.g., speech segments, or other sequence data), but as a score function is based on the properties of the data generation process, it produces a fixed-length vector in a highly informative space, typically referred to as a "score space". Discriminative classifiers have been shown to achieve higher performance in appropriately chosen score spaces than is achievable by either the corresponding generative likelihood-based classifiers, or the discriminative classifiers usingstandard feature extractors. In this paper, we present a novel score space that exploits the free energy associated with a generative model. The resulting freeenergy score space (FESS) takes into account latent structure of the data at various levels, and can be trivially shown to lead to classification performance that at least matches the performance of the free energy classifier based on the same generative model, and the same factorization of the posterior. We also show that in several typical vision and computational biology applications the classifiers optimized in FESS outperform the corresponding pure generative approaches, as well as a number of previous approaches to combining discriminating and generative models.

This paper studies the forward greedy strategy in sparse nonparametric regression. Foradditive models, we propose an algorithm called additive forward regression; forgeneral multivariate models, we propose an algorithm called generalized forward regression. Both algorithms simultaneously conduct estimation and variable selection in nonparametric settings for the high dimensional sparse learning problem. Our main emphasis is empirical: on both simulated and real data, these two simple greedy methods can clearly outperform several state-ofthe-art competitors,including LASSO, a nonparametric version of LASSO called the sparse additive model (SpAM) and a recently proposed adaptive parametric forward-backward algorithm called Foba. We also provide some theoretical justifications ofspecific versions of the additive forward regression.

Fast retrieval methods are increasingly critical for many large-scale analysis tasks, and there have been several recent methods that attempt to learn hash functions for fast and accurate nearest neighbor searches. In this paper, we develop an algorithm for learning hash functions based on explicitly minimizing the reconstruction error between the original distances and the Hamming distances of the corresponding binary embeddings. We develop a scalable coordinate-descent algorithm for our proposed hashing objective that is able to efficiently learn hash functions in a variety of settings. Unlike existing methods such as semantic hashing and spectral hashing, our method is easily kernelized and does not require restrictive assumptions about the underlying distribution of the data. We present results over several domains to demonstrate that our method outperforms existing state-of-the-art techniques.

Humans are typically able to infer how many objects their environment contains and to recognize when the same object is encountered twice. We present a simple statisticalmodel that helps to explain these abilities and evaluate it in three behavioral experiments. Our first experiment suggests that humans rely on prior knowledge when deciding whether an object token has been previously encountered. Oursecond and third experiments suggest that humans can infer how many objects they have seen and can learn about categories and their properties even when they are uncertain about which tokens are instances of the same object. From an early age, humans and other animals [1] appear to organize the flux of experience into a series of encounters with discrete and persisting objects.

We present a novel and highly effective approach for multi-body motion segmentation. Drawing inspiration from robust statistical model fitting, we estimate putative subspace hypotheses from the data. However, instead of ranking them we encapsulate the hypotheses in a novel Mercer kernel which elicits the potential of two point trajectories to have emerged from the same subspace. The kernel permits the application of well-established statistical learning methods for effective outlier rejection, automatic recovery of the number of motions and accurate segmentation of the point trajectories. The method operates well under severe outliers arising from spurious trajectories or mistracks. Detailed experiments on a recent benchmark dataset (Hopkins 155) show that our method is superior to other state-of-the-art approaches in terms of recovering the number of motions, segmentation accuracy, robustness against gross outliers and computational efficiency.

We study an encoding/decoding mechanism accounting for the relative spike timing of the signals propagating from peripheral nerve fibers to second-order somatosensory neurons in the cuneate nucleus (CN). The CN is modeled as a population of spiking neurons receiving as inputs the spatiotemporal responses of real mechanoreceptors obtained via microneurography recordings in humans. The efficiency of the haptic discrimination process is quantified by a novel definition of entropy that takes into full account the metrical properties of the spike train space. This measure proves to be a suitable decoding scheme for generalizing the classical Shannon entropy to spike-based neural codes. It permits an assessment of neurotransmission in the presence of a large output space (i.e. hundreds of spike trains) with 1 ms temporal precision. It is shown that the CN population code performs a complete discrimination of 81 distinct stimuli already within 35 ms of the first afferent spike, whereas a partial discrimination (80% of the maximum information transmission) is possible as rapidly as 15 ms. This study suggests that the CN may not constitute a mere synaptic relay along the somatosensory pathway but, rather, it may convey optimal contextual accounts (in terms of fast and reliable information transfer) of peripheral tactile inputs to downstream structures of the central nervous system.

Pruning can massively accelerate the computation of feature expectations in large models. However, any single pruning mask will introduce bias. We present a novel approach which employs a randomized sequence of pruning masks. Formally, we apply auxiliary variable MCMC sampling to generate this sequence of masks, thereby gaining theoretical guarantees about convergence. Because each mask is generally able to skip large portions of an underlying dynamic program, our approach is particularly compelling for high-degree algorithms. Empirically, we demonstrate our method on bilingual parsing, showing decreasing bias as more masks are incorporated, and outperforming fixed tic-tac-toe pruning.

We address the problem of learning classifiers when observations have multiple views, some of which may not be observed for all examples. We assume the existence of view generating functions which may complete the missing views in an approximate way. This situation corresponds for example to learning text classifiers from multilingual collections where documents are not available in all languages. In that case, Machine Translation (MT) systems may be used to translate each document in the missing languages. We derive a generalization error bound for classifiers learned on examples with multiple artificially created views. Our result uncovers a trade-off between the size of the training set, the number of views, and the quality of the view generating functions. As a consequence, we identify situations where it is more interesting to use multiple views for learning instead of classical single view learning. An extension of this framework is a natural way to leverage unlabeled multi-view data in semi-supervised learning. Experimental results on a subset of the Reuters RCV1/RCV2 collections support our findings by showing that additional views obtained from MT may significantly improve the classification performance in the cases identified by our trade-off.