Maximum a posteriori (MAP) inference over discrete Markov random fields is a fundamental task spanning a wide spectrum of real-world applications, which is known to be NP-hard for general graphs. In this paper, we propose a novel semidefinite relaxation formulation (referred to as SDR) to estimate the MAP assignment. Algorithmically, we develop an accelerated variant of the alternating direction method of multipliers (referred to as SDPAD-LR) that can effectively exploit the special structure of the new relaxation. Encouragingly, the proposed procedure allows solving SDR for large-scale problems, e.g., problems on a grid graph comprising hundreds of thousands of variables with multiple states per node. Compared with prior SDP solvers, SDPAD-LR is capable of attaining comparable accuracy while exhibiting remarkably improved scalability, in contrast to the commonly held belief that semidefinite relaxation can only been applied on small-scale MRF problems. We have evaluated the performance of SDR on various benchmark datasets including OPENGM2 and PIC in terms of both the quality of the solutions and computation time. Experimental results demonstrate that for a broad class of problems, SDPAD-LR outperforms state-of-the-art algorithms in producing better MAP assignment in an efficient manner.

The trimming scheme with a prefixed cutoff portion is known as a method of improving the robustness of statistical models such as multivariate Gaussian mixture models (MG- MMs) in small scale tests by alleviating the impacts of outliers. However, when this method is applied to real- world data, such as noisy speech processing, it is hard to know the optimal cut-off portion to remove the outliers and sometimes removes useful data samples as well. In this paper, we propose a new method based on measuring the dispersion degree (DD) of the training data to avoid this problem, so as to realise automatic robust estimation for MGMMs. The DD model is studied by using two different measures. For each one, we theoretically prove that the DD of the data samples in a context of MGMMs approximately obeys a specific (chi or chi-square) distribution. The proposed method is evaluated on a real-world application with a moderately-sized speaker recognition task. Experiments show that the proposed method can significantly improve the robustness of the conventional training method of GMMs for speaker recognition.

In this paper we consider the problem of online stochastic optimization of a locally smooth function under bandit feedback. We introduce the high-confidence tree (HCT) algorithm, a novel any-time $\mathcal{X}$-armed bandit algorithm, and derive regret bounds matching the performance of existing state-of-the-art in terms of dependency on number of steps and smoothness factor. The main advantage of HCT is that it handles the challenging case of correlated rewards, whereas existing methods require that the reward-generating process of each arm is an identically and independent distributed (iid) random process. HCT also improves on the state-of-the-art in terms of its memory requirement as well as requiring a weaker smoothness assumption on the mean-reward function in compare to the previous anytime algorithms. Finally, we discuss how HCT can be applied to the problem of policy search in reinforcement learning and we report preliminary empirical results.

In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the uncertainty in these selection procedures. In this paper, we propose a new method for inference in high dimensions using a score test based on penalized regression. In this test, we perform penalized regression of an outcome on all but a single feature, and test for correlation of the residuals with the held-out feature. This procedure is applied to each feature in turn. Interestingly, when an $\ell_1$ penalty is used, the sparsity pattern of the lasso corresponds exactly to a decision based on the proposed test. Further, when an $\ell_2$ penalty is used, the test corresponds precisely to a score test in a mixed effects model, in which the effects of all but one feature are assumed to be random. We formulate the hypothesis being tested as a compromise between the null hypotheses tested in simple linear regression on each feature and in multiple linear regression on all features, and develop reference distributions for some well-known penalties. We also examine the behavior of the test on real and simulated data.

We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of nonlinear relationship and no latent confounders. However, the estimation results could be distorted if either assumption is actually violated. In this paper, we first propose a new linear non-Gaussian acyclic structural equation model with individual-specific effects that allows latent confounders to be considered. We then propose an empirical Bayesian approach for estimating possible causal direction using the new model. We demonstrate the effectiveness of our method using artificial and real-world data.

Enzyme sequences and structures are routinely used in the biological sciences as queries to search for functionally related enzymes in online databases. To this end, one usually departs from some notion of similarity, comparing two enzymes by looking for correspondences in their sequences, structures or surfaces. For a given query, the search operation results in a ranking of the enzymes in the database, from very similar to dissimilar enzymes, while information about the biological function of annotated database enzymes is ignored. In this work we show that rankings of that kind can be substantially improved by applying kernel-based learning algorithms. This approach enables the detection of statistical dependencies between similarities of the active cleft and the biological function of annotated enzymes. This is in contrast to search-based approaches, which do not take annotated training data into account. Similarity measures based on the active cleft are known to outperform sequence-based or structure-based measures under certain conditions. We consider the Enzyme Commission (EC) classification hierarchy for obtaining annotated enzymes during the training phase. The results of a set of sizeable experiments indicate a consistent and significant improvement for a set of similarity measures that exploit information about small cavities in the surface of enzymes.

We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on sampling theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The sampling theory for graph signals aims to extend the traditional Nyquist-Shannon sampling theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.

Artificial fish swarm algorithm (AFSA) is one of the swarm intelligence optimization algorithms that works based on population and stochastic search. In order to achieve acceptable result, there are many parameters needs to be adjusted in AFSA. Among these parameters, visual and step are very significant in view of the fact that artificial fish basically move based on these parameters. In standard AFSA, these two parameters remain constant until the algorithm termination. Large values of these parameters increase the capability of algorithm in global search, while small values improve the local search ability of the algorithm. In this paper, we empirically study the performance of the AFSA and different approaches to balance between local and global exploration have been tested based on the adaptive modification of visual and step during algorithm execution. The proposed approaches have been evaluated based on the four well-known benchmark functions. Experimental results show considerable positive impact on the performance of AFSA.

This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also give conditions under which no relevant variables are excluded. Next, non-asymptotic probabilities are given for the Adaptive LASSO to select the correct sparsity pattern. We then give conditions under which the Adaptive LASSO reveals the correct sparsity pattern asymptotically. We establish that the estimates of the non-zero coefficients are asymptotically equivalent to the oracle assisted least squares estimator. This is used to show that the rate of convergence of the estimates of the non-zero coefficients is identical to the one of least squares only including the relevant covariates.

We propose a new two stage algorithm LING for large scale regression problems. LING has the same risk as the well known Ridge Regression under the fixed design setting and can be computed much faster. Our experiments have shown that LING performs well in terms of both prediction accuracy and computational efficiency compared with other large scale regression algorithms like Gradient Descent, Stochastic Gradient Descent and Principal Component Regression on both simulated and real datasets.