We consider the problem of bounding from above the log-partition function corresponding to second-order Ising models for binary distributions. We introduce a new bound, the cardinality bound, which can be computed via convex optimization. The corresponding error on the logpartition function is bounded above by twice the distance, in model parameter space, to a class of "standard" Ising models, for which variable interdependence is described via a simple mean field term. In the context of maximum-likelihood, using the new bound instead of the exact log-partition function, while constraining the distance to the class of standard Ising models, leads not only to a good approximation to the log-partition function, but also to a model that is parsimonious, and easily interpretable.

Motivated by applications like elections, webpage ranking, revenue maximization etc., we consider the question of inferring popular rankings using constrained data. More specifically, we consider the problem of inferring a probability distribution over the group of permutations using its first order marginals. We first prove that it is not possible to recover more than O(n) permutations over n elements with the given information. We then provide a simple and novel algorithm that can recover up to O(n) permutations under a natural stochastic model; in this sense, the algorithm is optimal. In certain applications, the interest is in recovering only the most popular (or mode) ranking. As a second result, we provide an algorithm based on the Fourier Transform over the symmetric group to recover the mode under a natural majority condition; the algorithm turns out to be a maximum weight matching on an appropriately defined weighted bipartite graph. The questions considered are also thematically related to Fourier Transforms over the symmetric group and the currently popular topic of compressed sensing.

The recently proposed \emph{additive noise model} has advantages over previous structure learning algorithms, when attempting to recover some true data generating mechanism, since it (i) does not assume linearity or Gaussianity and (ii) can recover a unique DAG rather than an equivalence class. However, its original extension to the multivariate case required enumerating all possible DAGs, and for some special distributions, e.g. linear Gaussian, the model is invertible and thus cannot be used for structure learning. We present a new approach which combines a PC style search using recent advances in kernel measures of conditional dependence with local searches for additive noise models in substructures of the equivalence class. This results in a more computationally efficient approach that is useful for arbitrary distributions even when additive noise models are invertible. Experiments with synthetic and real data show that this method is more accurate than previous methods when data are nonlinear and/or non-Gaussian.

The proposal that cortical activity in the visual cortex is optimized for sparse neural activity is one of the most established ideas in computational neuroscience. However, direct experimental evidence for optimal sparse coding remains inconclusive, mostly due to the lack of reference values on which to judge the measured sparseness. Here we analyze neural responses to natural movies in the primary visual cortex of ferrets at different stages of development, and of rats while awake and under different levels of anesthesia. In contrast with prediction from a sparse coding model, our data shows that population and lifetime sparseness decrease with visual experience, and increase from the awake to anesthetized state. These results suggest that the representation in the primary visual cortex is not actively optimized to maximize sparseness.

We present an approach for learning stochastic geometric models of object categories from single view images. We focus here on models expressible as a spatially contiguous assemblage of blocks. Model topologies are learned across groups of images, and one or more such topologies is linked to an object category (e.g. chairs). Fitting learned topologies to an image can be used to identify the object class, as well as detail its geometry. The latter goes beyond labeling objects, as it provides the geometric structure of particular instances. We learn the models using joint statistical inference over structure parameters, camera parameters, and instance parameters. These produce an image likelihood through a statistical imaging model. We use trans-dimensional sampling to explore topology hypotheses, and alternate between Metropolis-Hastings and stochastic dynamics to explore instance parameters. Experiments on images of furniture objects such as tables and chairs suggest that this is an effective approach for learning models that encode simple representations of category geometry and the statistics thereof, and support inferring both category and geometry on held out single view images.

The problem of ranking arises ubiquitously in almost every aspect of life, and in particular in Machine Learning/Information Retrieval. A statistical model for ranking predicts how humans rank subsets V of some universe U. In this work we define a statistical model for ranking that satisfies certain desirable properties. The model automatically gives rise to a logistic regression based approach to learning how to rank, for which the score and comparison based approaches are dual views. This offers a new generative approach to ranking which can be used for IR.

We adapt a probabilistic latent variable model, namely GaP (Gamma-Poisson) [6], to ad targeting in the contexts of sponsored search (SS) and behaviorally targeted (BT) display advertising. We also approach the important problem of ad positional biasby formulating a one-latent-dimension GaP factorization. Learning from click-through data is intrinsically large scale, even more so for ads. We scale up the algorithm to terabytes of real-world SS and BT data that contains hundreds of millions of users and hundreds of thousands of features, by leveraging the scalability characteristicsof the algorithm and the inherent structure of the problem including data sparsity and locality. Specifically, we demonstrate two somewhat orthogonal philosophies of scaling algorithms to large-scale problems, through the SS and BT implementations, respectively. Finally, we report the experimental resultsusing Yahoo's vast datasets, and show that our approach substantially outperform the state-of-the-art methods in prediction accuracy. For BT in particular, theROC area achieved by GaP is exceeding 0.95, while one prior approach using Poisson regression [11] yielded 0.83. For computational performance, we compare a single-node sparse implementation with a parallel implementation using HadoopMapReduce, the results are counterintuitive yet quite interesting. We therefore provide insights into the underlying principles of large-scale learning.

We present a nonparametric Bayesian method for texture learning and synthesis. A texture image is represented by a 2D-Hidden Markov Model (2D-HMM) where the hidden states correspond to the cluster labeling of textons and the transition matrix encodes their spatial layout (the compatibility between adjacent textons). 2D-HMM is coupled with the Hierarchical Dirichlet process (HDP) which allows the number of textons and the complexity of transition matrix grow as the input texture becomes irregular. The HDP makes use of Dirichlet process prior which favors regular textures by penalizing the model complexity. This framework (HDP-2D-HMM) learns the texton vocabulary and their spatial layout jointly and automatically. The HDP-2D-HMM results in a compact representation of textures which allows fast texture synthesis with comparable rendering quality over the state-of-the-art image-based rendering methods. We also show that HDP-2D-HMM can be applied to perform image segmentation and synthesis.

Online learning algorithms have impressive convergence properties when it comes to risk minimization and convex games on very large problems. However, they are inherently sequential in their design which prevents them from taking advantage of modern multi-core architectures. In this paper we prove that online learning with delayed updates converges well, thereby facilitating parallel online learning.

We introduce a new family of distributions, called $L_p${\em -nested symmetric distributions}, whose densities access the data exclusively through a hierarchical cascade of $L_p$-norms. This class generalizes the family of spherically and $L_p$-spherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family also includes the Independent Subspace Analysis (ISA) model, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. $L_p$-nested distributions are easy to estimate and allow us to explore the variety of models between ISA and the $L_p$-spherically symmetric models. Our main findings are that, without a preprocessing step of contrast gain control, the independent subspaces of ISA are in fact more dependent than the individual filter coefficients within a subspace and, with contrast gain control, where ISA finds more than one subspace, the filter responses were almost independent anyway.