The Restricted Boltzmann Machine (RBM) is a popular density model that is also good for extracting features. A main source of tractability in RBM models is the model's assumption that given an input, hidden units activate independently from one another. Sparsity and competition in the hidden representation is believed to be beneficial, and while an RBM with competition among its hidden units would acquire some of the attractive properties of sparse coding, such constraints are not added due to the widespread belief that the resulting model would become intractable. In this work, we show how a dynamic programming algorithm developed in 1981 can be used to implement exact sparsity in the RBM's hidden units. We then expand on this and show how to pass derivatives through a layer of exact sparsity, which makes it possible to fine-tune a deep belief network (DBN) consisting of RBMs with sparse hidden layers. We show that sparsity in the RBM's hidden layer improves the performance of both the pre-trained representations and of the fine-tuned model.

Multiple-output regression models require estimating multiple functions, one for each output. To improve parameter estimation in such models, methods based on structural regularization of the model parameters are usually needed. In this paper, we present a multiple-output regression model that leverages the covariance structure of the functions (i.e., how the multiple functions are related with each other) as well as the conditional covariance structure of the outputs. This is in contrast with existing methods that usually take into account only one of these structures. More importantly, unlike most of the other existing methods, none of these structures need be known a priori in our model, and are learned from the data. Several previously proposed structural regularization based multiple-output regression models turn out to be special cases of our model. Moreover, in addition to being a rich model for multiple-output regression, our model can also be used in estimating the graphical model structure of a set of variables (multivariate outputs) conditioned on another set of variables (inputs). Experimental results on both synthetic and real datasets demonstrate the effectiveness of our method.

Given a probabilistic graphical model, its density of states is a distribution that, for any likelihood value, gives the number of configurations with that probability. Weintroduce a novel message-passing algorithm called Density Propagation (DP) for estimating this distribution. We show that DP is exact for tree-structured graphical models and is, in general, a strict generalization of both sum-product and max-product algorithms. Further, we use density of states and tree decomposition to introduce a new family of upper and lower bounds on the partition function. For any tree decomposition, the new upper bound based on finer-grained density of state information is provably at least as tight as previously known bounds based on convexity of the log-partition function, and strictly stronger if a general condition holds.We conclude with empirical evidence of improvement over convex relaxations and mean-field based bounds.

A challenging problem in hierarchical classification is to leverage the hierarchical relations among classes for improving classification performance. An even greater challenge is to do so in a manner that is computationally feasible for the large scale problems usually encountered in practice. This paper proposes a set of Bayesian methods to model hierarchical dependencies among class labels using multivari- ate logistic regression. Specifically, the parent-child relationships are modeled by placing a hierarchical prior over the children nodes centered around the parame- ters of their parents; thereby encouraging classes nearby in the hierarchy to share similar model parameters. We present new, efficient variational algorithms for tractable posterior inference in these models, and provide a parallel implementa- tion that can comfortably handle large-scale problems with hundreds of thousands of dimensions and tens of thousands of classes. We run a comparative evaluation on multiple large-scale benchmark datasets that highlights the scalability of our approach, and shows a significant performance advantage over the other state-of- the-art hierarchical methods.

We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes.On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster,we used non-saturating neurons and a very efficient GPU implementation ofthe convolution operation. To reduce overfitting in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.

Accurate and detailed models of the progression of neurodegenerative diseases such as Alzheimer's (AD) are crucially important for reliable early diagnosis and the determination and deployment of effective treatments. In this paper, we introduce the ALPACA (Alzheimer's disease Probabilistic Cascades) model, a generative model linking latent Alzheimer's progression dynamics to observable biomarker data. In contrast with previous works which model disease progression as a fixed ordering of events, we explicitly model the variability over such orderings among patients which is more realistic, particularly for highly detailed disease progression models. We describe efficient learning algorithms for ALPACA and discuss promising experimental results on a real cohort of Alzheimer's patients from the Alzheimer's Disease Neuroimaging Initiative.

In many large economic markets, goods are sold through sequential auctions. Such domains include eBay, online ad auctions, wireless spectrum auctions, and the Dutch flower auctions. Bidders in these domains face highly complex decision-making problems, as their preferences for outcomes in one auction often depend on the outcomes of other auctions, and bidders have limited information about factors that drive outcomes, such as other bidders' preferences and past actions. In this work, we formulate the bidder's problem as one of price prediction (i.e., learning) and optimization. We define the concept of stable price predictions and show that (approximate) equilibrium in sequential auctions can be characterized as a profile of strategies that (approximately) optimize with respect to such (approximately) stable price predictions. We show how equilibria found with our formulation compare to known theoretical equilibria for simpler auction domains, and we find new approximate equilibria for a more complex auction domain where analytical solutions were heretofore unknown.

In many applications, one has information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks nearby that pre-specified target region. Locally-biased problems of this sort are particularly challenging for popular eigenvector-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities. In this paper, we address this issue by providing a methodology to construct semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these locally-biased eigenvectors can be used to perform locally-biased machine learning. These semi-supervised eigenvectors capture successively-orthogonalized directions of maximum variance, conditioned on being well-correlated with an input seed set of nodes that is assumed to be provided in a semi-supervised manner. We also provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning.

The question of aggregating pairwise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR’s TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining ranking, finding ‘scores’ for each object (e.g. player’s rating) is of interest to understanding the intensity of the preferences. In this paper, we propose a novel iterative rank aggregation algorithm for discovering scores for objects from pairwise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with edges present between two objects if they are compared; the scores turn out to be the stationary probability of this random walk. The algorithm is model independent. To establish the efficacy of our method, however, we consider the popular Bradley-Terry-Luce (BTL) model in which each object has an associated score which determines the probabilistic outcomes of pairwise comparisons between objects. We bound the finite sample error rates between the scores assumed by the BTL model and those estimated by our algorithm. This, in essence, leads to order-optimal dependence on the number of samples required to learn the scores well by our algorithm. Indeed, the experimental evaluation shows that our (model independent) algorithm performs as well as the Maximum Likelihood Estimator of the BTL model and outperforms a recently proposed algorithm by Ammar and Shah [1].

Sparse learning models typically combine a smooth loss with a nonsmooth penalty, such as trace norm. Although recent developments in sparse approximation have offered promising solution methods, current approaches either apply only to matrix-norm constrained problems or provide suboptimal convergence rates. In this paper, we propose a boosting method for regularized learning that guarantees $\epsilon$ accuracy within $O(1/\epsilon)$ iterations. Performance is further accelerated by interlacing boosting with fixed-rank local optimization---exploiting a simpler local objective than previous work. The proposed method yields state-of-the-art performance on large-scale problems. We also demonstrate an application to latent multiview learning for which we provide the first efficient weak-oracle.