In categorical data there is often structure in the number of variables that take on each label. For example, the total number of objects in an image and the number of highly relevant documents per query in web search both tend to follow a structured distribution. In this paper, we study a probabilistic model that explicitly includes a prior distribution over such counts, along with a count-conditional likelihood that defines probabilities over all subsets of a given size. When labels are binary and the prior over counts is a Poisson-Binomial distribution, a standard logistic regression model is recovered, but for other count distributions, such priors induce global dependencies and combinatorics that appear to complicate learning and inference. However, we demonstrate that simple, efficient learning procedures can be derived for more general forms of this model. We illustrate the utility of the formulation by exploring applications to multi-object classification, learning to rank, and top-K classification.

The human mind has a remarkable ability to store a vast amount of information in memory, and an even more remarkable ability to retrieve these experiences when needed. Understanding the representations and algorithms that underlie human memory search could potentially be useful in other information retrieval settings, including internet search. Psychological studies have revealed clear regularities in how people search their memory, with clusters of semantically related items tending to be retrieved together. These findings have recently been taken as evidence that human memory search is similar to animals foraging for food in patchy environments, with people making a rational decision to switch away from a cluster of related information as it becomes depleted. We demonstrate that the results that were taken as evidence for this account also emerge from a random walk on a semantic network, much like the random web surfer model used in internet search engines. This offers a simpler and more unified account of how people search their memory, postulating a single process rather than one process for exploring a cluster and one process for switching between clusters.

Finding maximum aposteriori (MAP) assignments in graphical models is an important task in many applications. Since the problem is generally hard, linear programming (LP) relaxations are often used. Solving these relaxations efficiently is thus an important practical problem. In recent years, several authors have proposed message passing updates corresponding to coordinate descent in the dual LP. However,these are generally not guaranteed to converge to a global optimum. One approach to remedy this is to smooth the LP, and perform coordinate descent on the smoothed dual. However, little is known about the convergence rate of this procedure. Here we perform a thorough rate analysis of such schemes and derive primal and dual convergence rates. We also provide a simple dual to primal mapping that yields feasible primal solutions with a guaranteed rate of convergence. Empirical evaluation supports our theoretical claims and shows that the method is highly competitive with state of the art approaches that yield global optima.

A weighted graph is used as an underlying structure of many algorithms like semi-supervised learning and spectral clustering. The edge weights are usually deter-mined by a single similarity measure, but it often hard if not impossible to capture all relevant aspects of similarity when using a single similarity measure. In par-ticular, in the case of visual object matching it is beneficial to integrate different similarity measures that focus on different visual representations. In this paper, a novel approach to integrate multiple similarity measures is pro-posed. First pairs of similarity measures are combined with a diffusion process on their tensor product graph (TPG). Hence the diffused similarity of each pair of ob-jects becomes a function of joint diffusion of the two original similarities, which in turn depends on the neighborhood structure of the TPG. We call this process Fusion with Diffusion (FD). However, a higher order graph like the TPG usually means significant increase in time complexity. This is not the case in the proposed approach. A key feature of our approach is that the time complexity of the dif-fusion on the TPG is the same as the diffusion process on each of the original graphs, Moreover, it is not necessary to explicitly construct the TPG in our frame-work. Finally all diffused pairs of similarity measures are combined as a weighted sum. We demonstrate the advantages of the proposed approach on the task of visual tracking, where different aspects of the appearance similarity between the target object in frame t and target object candidates in frame t+1 are integrated. The obtained method is tested on several challenge video sequences and the experimental results show that it outperforms state-of-the-art tracking methods.

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.

Linear Support Vector Machines (SVMs) have become very popular in vision as part of state-of-the-art object recognition and other classification tasks but require high dimensional feature spaces for good performance. Deep learning methods can find more compact representations but current methods employ multilayer perceptrons that require solving a difficult, non-convex optimization problem. We propose a deep non-linear classifier whose layers are SVMs and which incorporates random projection as its core stacking element. Our method learns layers of linear SVMs recursively transforming the original data manifold through a random projection of the weak prediction computed from each layer. Our method scales as linear SVMs, does not rely on any kernel computations or nonconvex optimization, and exhibits better generalization ability than kernel-based SVMs. This is especially true when the number of training samples is smaller than the dimensionality of data, a common scenario in many real-world applications. The use of random projections is key to our method, as we show in the experiments section, in which we observe a consistent improvement over previous --often more complicated-- methods on several vision and speech benchmarks.

In this paper, we consider the problem of clustering data points into lowdimensional subspacesin the presence of outliers. We pose the problem using a density estimation formulation with an associated generative model. Based on this probability model, we first develop an iterative expectation-maximization (EM) algorithm andthen derive its global solution. In addition, we develop two Bayesian methods based on variational Bayesian (VB) approximation, which are capable of automatic dimensionality selection. While the first method is based on an alternating optimizationscheme for all unknowns, the second method makes use of recent results in VB matrix factorization leading to fast and effective estimation. Both methods are extended to handle sparse outliers for robustness and can handle missingvalues. Experimental results suggest that proposed methods are very effective in subspace clustering and identifying outliers.

We propose a novel method for scalable parallelization of SMC algorithms, Entangled Monte Carlo simulation (EMC). EMC avoids the transmission of particles between nodes, and instead reconstructs them from the particle genealogy. In particular, we show that we can reduce the communication to the particle weights for each machine while efficiently maintaining implicit global coherence of the parallel simulation. We explain methods to efficiently maintain a genealogy of particles from which any particle can be reconstructed. We demonstrate using examples from Bayesian phylogenetic that the computational gain from parallelization using EMC significantly outweighs the cost of particle reconstruction. The timing experiments show that reconstruction of particles is indeed much more efficient as compared to transmission of particles.

Parametric policy search algorithms are one of the methods of choice for the optimisation of Markov Decision Processes, with Expectation Maximisation and natural gradient ascent being considered the current state of the art in the field. In this article we provide a unifying perspective of these two algorithms by showing that their step-directions in the parameter space are closely related to the search direction of an approximate Newton method. This analysis leads naturally to the consideration of this approximate Newton method as an alternative gradient-based method for Markov Decision Processes. We are able show that the algorithm has numerous desirable properties, absent in the naive application of Newton's method, that make it a viable alternative to either Expectation Maximisation or natural gradient ascent. Empirical results suggest that the algorithm has excellent convergence and robustness properties, performing strongly in comparison to both Expectation Maximisation and natural gradient ascent.

We describe a new model for learning meaningful representations of text documents from an unlabeled collection of documents. This model is inspired by the recently proposed Replicated Softmax, an undirected graphical model of word counts that was shown to learn a better generative model and more meaningful document representations. Specifically, we take inspiration from the conditional mean-field recursive equations of the Replicated Softmax in order to define a neural network architecture that estimates the probability of observing a new word in a given document given the previously observed words. This paradigm also allows us to replace the expensive softmax distribution over words with a hierarchical distribution over paths in a binary tree of words. The end result is a model whose training complexity scales logarithmically with the vocabulary size instead of linearly as in the Replicated Softmax. Our experiments show that our model is competitive both as a generative model of documents and as a document representation learning algorithm.