Since the discovery of sophisticated fully polynomial randomized algorithms for a range of #P problems (Karzanov et al., 1991; Jerrum et al., 2001; Wilson, 2004), theoretical work on approximate inference in combinatorial spaces has focused on Markov chain Monte Carlo methods. Despite their strong theoretical guarantees, the slow running time of many of these randomized algorithms and the restrictive assumptions on the potentials have hindered the applicability of these algorithms to machine learning. Because of this, in applications to combinatorial spaces simple exact models are often preferred to more complex models that require approximate inference (Siepel et al., 2004). Variational inference would appear to provide an appealing alternative, given the success of variational methods for graphical models (Wainwright et al., 2008); unfortunately, however, it is not obvious how to develop variational approximations for combinatorial objects such as matchings, partial orders, plane partitions and sequence alignments. We propose a new framework that extends variational inference to a wide range of combinatorial spaces. Our method is based on a simple assumption: the existence of a tractable measure factorization, which we show holds in many examples. Simulations on a range of matching models show that the algorithm is more general and empirically faster than a popular fully polynomial randomized algorithm. We also apply the framework to the problem of multiple alignment of protein sequences, obtaining state-of-the-art results on the BAliBASE dataset (Thompson et al., 1999).

The design of low-level image features is critical for computer vision algorithms. Orientation histograms, such as those in SIFT [16] and HOG [3], are the most successful and popular features for visual object and scene recognition. We highlight thekernel view of orientation histograms, and show that they are equivalent to a certain type of match kernels over image patches. This novel view allows us to design a family of kernel descriptors which provide a unified and principled frameworkto turn pixel attributes (gradient, color, local binary pattern, etc.) into compact patch-level features. In particular, we introduce three types of match kernels to measure similarities between image patches, and construct compact low-dimensional kernel descriptors from these match kernels using kernel principal componentanalysis (KPCA) [23]. Kernel descriptors are easy to design and can turn any type of pixel attribute into patch-level features. They outperform carefully tuned and sophisticated features including SIFT and deep belief networks.

We tackle the problem of simultaneously detecting occlusions and estimating optical flow. We show that, under standard assumptions of Lambertian reflection and static illumination, the task can be posed as a convex minimization problem. Therefore, the solution, computed using efficient algorithms, is guaranteed to be globally optimal, for any number of independently moving objects, and any number of occlusion layers. We test the proposed algorithm on benchmark datasets, expanded to enable evaluation of occlusion detection performance.

How much information does a neural population convey about a stimulus? Answers to this question are known to strongly depend on the correlation of response variability in neural populations. These noise correlations, however, are essentially immeasurable as the number of parameters in a noise correlation matrix grows quadratically with population size. Here, we suggest to bypass this problem by imposing a parametric model on a noise correlation matrix. Our basic assumption is that noise correlations arise due to common inputs between neurons. On average, noise correlations will therefore reflect signal correlations, which can be measured in neural populations. We suggest an explicit parametric dependency between signal and noise correlations. We show how this dependency can be used to fill the gaps" in noise correlations matrices using an iterative application of the Wishart distribution over positive definitive matrices. We apply our method to data from the primary somatosensory cortex of monkeys performing a two-alternative-forced choice task. We compare the discrimination thresholds read out from the population of recorded neurons with the discrimination threshold of the monkey and show that our method predicts different results than simpler, average schemes of noise correlations."

Our objective is to train $p$-norm Multiple Kernel Learning (MKL) and, more generally, linear MKL regularised by the Bregman divergence, using the Sequential Minimal Optimization (SMO) algorithm. The SMO algorithm is simple, easy to implement and adapt, and efficiently scales to large problems. As a result, it has gained widespread acceptance and SVMs are routinely trained using SMO in diverse real world applications. Training using SMO has been a long standing goal in MKL for the very same reasons. Unfortunately, the standard MKL dual is not differentiable, and therefore can not be optimised using SMO style co-ordinate ascent. In this paper, we demonstrate that linear MKL regularised with the $p$-norm squared, or with certain Bregman divergences, can indeed be trained using SMO. The resulting algorithm retains both simplicity and efficiency and is significantly faster than the state-of-the-art specialised $p$-norm MKL solvers. We show that we can train on a hundred thousand kernels in approximately seven minutes and on fifty thousand points in less than half an hour on a single core.

We present policy gradient results within the framework of linearly-solvable MDPs. For the first time, compatible function approximators and natural policy gradients are obtained by estimating the cost-to-go function, rather than the (much larger) state-action advantage function as is necessary in traditional MDPs. We also develop the first compatible function approximators and natural policy gradients for continuous-time stochastic systems.

Remarkably easy implementation and guaranteed convergence has made the EM algorithm one of the most used algorithms for mixture modeling. On the downside, the E-step is linear in both the sample size and the number of mixture components, making it impractical for large-scale data. Based on the variational EM framework, we propose a fast alternative that uses component-specific data partitions to obtain a sub-linear E-step in sample size, while the algorithm still maintains provable convergence. Our approach builds on previous work, but is significantly faster and scales much better in the number of mixture components. We demonstrate this speedup by experiments on large-scale synthetic and real data.

We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

This paper is concerned with rank aggregation, which aims to combine multiple input rankings to get a better ranking. A popular approach to rank aggregation is based on probabilistic models on permutations, e.g., the Luce model and the Mallows model. However, these models have their limitations in either poor expressiveness or high computational complexity. To avoid these limitations, in this paper, we propose a new model, which is defined with a coset-permutation distance, and models the generation of a permutation as a stagewise process. We refer to the new model as coset-permutation distance based stagewise (CPS) model. The CPS model has rich expressiveness and can therefore be used in versatile applications, because many different permutation distances can be used to induce the coset-permutation distance. The complexity of the CPS model is low because of the stagewise decomposition of the permutation probability and the efficient computation of most coset-permutation distances. We apply the CPS model to supervised rank aggregation, derive the learning and inference algorithms, and empirically study their effectiveness and efficiency. Experiments on public datasets show that the derived algorithms based on the CPS model can achieve state-of-the-art ranking accuracy, and are much more efficient than previous algorithms.

When working with network datasets, the theoretical framework of detection theory for Euclidean vector spaces no longer applies. Nevertheless, it is desirable to determine the detectability of small, anomalous graphs embedded into background networks with known statistical properties. Casting the problem of subgraph detection in a signal processing context, this article provides a framework and empirical results that elucidate a detection theory" for graph-valued data. Its focus is the detection of anomalies in unweighted, undirected graphs through L1 properties of the eigenvectors of the graph’s so-called modularity matrix. This metric is observed to have relatively low variance for certain categories of randomly-generated graphs, and to reveal the presence of an anomalous subgraph with reasonable reliability when the anomaly is not well-correlated with stronger portions of the background graph. An analysis of subgraphs in real network datasets confirms the efficacy of this approach."