In our work, we propose a novel formulation for supervised dimensionality reduction based on a nonlinear dependency criterion called Statistical Distance Correlation, Szekely et. al. (2007). We propose an objective which is free of distributional assumptions on regression variables and regression model assumptions. Our proposed formulation is based on learning a low-dimensional feature representation $\mathbf{z}$, which maximizes the squared sum of Distance Correlations between low dimensional features $\mathbf{z}$ and response $y$, and also between features $\mathbf{z}$ and covariates $\mathbf{x}$. We propose a novel algorithm to optimize our proposed objective using the Generalized Minimization Maximizaiton method of \Parizi et. al. (2015). We show superior empirical results on multiple datasets proving the effectiveness of our proposed approach over several relevant state-of-the-art supervised dimensionality reduction methods.

In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively based on previously drawn samples. The algorithm's efficiency is ensured by a test that controls the evolution of the set of support points. This extra stage controls the computational cost and the convergence of the proposal density to the target. Each part of the novel family of algorithms is discussed and several examples are provided. Although the novel algorithms are presented for univariate target densities, we show that they can be easily extended to the multivariate context within a Gibbs-type sampler. The ergodicity is ensured and discussed. Exhaustive numerical examples illustrate the efficiency of sticky schemes, both as a stand-alone methods to sample from complicated one-dimensional pdfs and within Gibbs in order to draw from multi-dimensional target distributions.

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.

We propose a robust portfolio optimization approach based on quantile statistics. The proposed method is robust to extreme events in asset returns, and accommodates large portfolios under limited historical data. Specifically, we show that the risk of the estimated portfolio converges to the oracle optimal risk with parametric rate under weakly dependent asset returns. The theory does not rely on higher order moment assumptions, thus allowing for heavy-tailed asset returns. Moreover, the rate of convergence quantifies that the size of the portfolio under management is allowed to scale exponentially with the sample size of the historical data. The empirical effectiveness of the proposed method is demonstrated under both synthetic and real stock data. Our work extends existing ones by achieving robustness in high dimensions, and by allowing serial dependence.

We study contextual bandits with budget and time constraints under discrete contexts, referred to as constrained contextual bandits. The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time. To gain insight, we first study unit-cost systems with known context distribution. When the expected rewards are known, we develop an approximation of the oracle, referred to Adaptive-Linear-Programming(ALP), which achieves near-optimality and only requires the ordering of expected rewards. With these highly desirable features, we then combine ALP with the upper-confidence-bound (UCB) method in the general case where the expected rewards are unknown a priori. We show that the proposed UCB-ALP algorithm achieves logarithmic regret except in certain boundary cases.Further, we design algorithms and obtain similar regret analysis results for more general systems with unknown context distribution or heterogeneous costs. To the best of our knowledge, this is the first work that shows how to achieve logarithmic regret in constrained contextual bandits. Moreover, this work also sheds light on the study of computationally efficient algorithms for general constrained contextual bandits.

Max-product Belief Propagation (BP) is a popular message-passing algorithm for computing a Maximum-A-Posteriori (MAP) assignment over a distribution represented by a Graphical Model (GM). It has been shown that BP can solve a number of combinatorial optimization problems including minimum weight matching, shortest path, network flow and vertex cover under the following common assumption: the respective Linear Programming (LP) relaxation is tight, i.e., no integrality gap is present. However, when LP shows an integrality gap, no model has been known which can be solved systematically via sequential applications of BP. In this paper, we develop the first such algorithm, coined Blossom-BP, for solving the minimum weight matching problem over arbitrary graphs. Each step of the sequential algorithm requires applying BP over a modified graph constructed by contractions and expansions of blossoms, i.e., odd sets of vertices. Our scheme guarantees termination in O(n^2) of BP runs, where n is the number of vertices in the original graph. In essence, the Blossom-BP offers a distributed version of the celebrated Edmonds' Blossom algorithm by jumping at once over many sub-steps with a single BP. Moreover, our result provides an interpretation of the Edmonds' algorithm as a sequence of LPs.

We investigate two novel mixed robust/average-case submodular data partitioning problems that we collectively call Submodular Partitioning. These problems generalize purelyrobust instances of the problem, namely max-min submodular fair allocation (SFA) [12] and min-max submodular load balancing (SLB) [25], and also average-case instances, that is the submodular welfare problem (SWP) [26] and submodular multiway partition (SMP) [5]. While the robust versions have been studied in the theory community [11, 12, 16, 25, 26], existing work has focused on tight approximation guarantees, and the resultant algorithms are not generally scalable to large real-world applications. This is in contrast to the average case, where most of the algorithms are scalable. In the present paper, we bridge this gap, by proposing several new algorithms (including greedy, majorization-minimization, minorization-maximization, and relaxation algorithms) that not only scale to large datasets but that also achieve theoretical approximation guarantees comparable to the state-of-the-art. We moreover provide new scalable algorithms that apply to additive combinations of the robust and average-case objectives. We show that these problems have many applications in machine learning (ML), including data partitioning and load balancing for distributed ML, data clustering, and image segmentation. Weempirically demonstrate the efficacy of our algorithms on real-world problems involving data partitioning for distributed optimization (of convex and deep neural network objectives), and also purely unsupervised image segmentation.

We study the restless bandit problem where arms are associated with stationary $\varphi$-mixing processes and where rewards are therefore dependent: the question that arises from this setting is that of carefully recovering some independence by `ignoring' the values of some rewards. As we shall see, the bandit problem we tackle requires us to address the exploration/exploitation/independence trade-off, which we do by considering the idea of a {\em waiting arm} in the new Remix-UCB algorithm, a generalization of Improved-UCB for the problem at hand, that we introduce. We provide a regret analysis for this bandit strategy; two noticeable features of Remix-UCB are that i) it reduces to the regular Improved-UCB when the $\varphi$-mixing coefficients are all $0$, i.e. when the i.i.d scenario is recovered, and ii) when $\varphi(n)=O(n^{-\alpha})$, it is able to ensure a controlled regret of order $\Ot\left( \Delta_*^{(\alpha- 2)/\alpha} \log^{1/\alpha} T\right),$ where $\Delta_*$ encodes the distance between the best arm and the best suboptimal arm, even in the case when $\alpha<1$, i.e. the case when the $\varphi$-mixing coefficients {\em are not} summable.

This page includes forthcoming AAAI sponsored conferences, conferences presented by AAAI Affiliates, and conferences held in cooperation with AAAI. AI Magazine also maintains a calendar listing that includes nonaffiliated conferences at www.aaai.org/Magazine/calendar.php. AAAI-16 will be held Principles of Knowledge Representation on Semantic Computing. ICSC will February 12-17, 2016 in Phoenix, Arizona and Reasoning (KR 2016) be held February 3-5, 2016, in Laguna USA. Twenty-Ninth International Florida on Biomedical Engineering Systems IAAI-16 will be held will be AI Research Society Conference. and Technologies.

This issue of AI Magazine includes six articles on cognitive orthoses, which we broadly conceive as technological approaches that amplify or enhance individual or team cognition across a wide range of goals and activities. The articles are grouped by how they relate to orthoses enhanced socio-technical team intelligence at three different cognitive levels—sensorimotor physical, professional learning, and networked knowledge.