We uncover relations between robust MDPs and risk-sensitive MDPs. The objective of a robust MDP is to minimize a function, such as the expectation of cumulative cost, for the worst case when the parameters have uncertainties. The objective of a risk-sensitive MDP is to minimize a risk measure of the cumulative cost when the parameters are known. We show that a risk-sensitive MDP of minimizing the expected exponential utility is equivalent to a robust MDP of minimizing the worst-case expectation with a penalty for the deviation of the uncertain parameters from their nominal values, which is measured with the Kullback-Leibler divergence. We also show that a risk-sensitive MDP of minimizing an iterated risk measure that is composed of certain coherent risk measures is equivalent to a robust MDP of minimizing the worst-case expectation when the possible deviations of uncertain parameters from their nominal values are characterized with a concave function.

The representer theorem is a property that lies at the foundation of regularization theory and kernel methods. A class of regularization functionals is said to admit a linear representer theorem if every member of the class admits minimizers that lie in the finite dimensional subspace spanned by the representers of the data. A recent characterization states that certain classes of regularization functionals with differentiable regularization term admit a linear representer theorem for any choice of the data if and only if the regularization term is a radial nondecreasing function. In this paper, we extend such result by weakening the assumptions on the regularization term. In particular, the main result of this paper implies that, for a sufficiently large family of regularization functionals, radial nondecreasing functions are the only lower semicontinuous regularization terms that guarantee existence of a representer theorem for any choice of the data.

This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that have been constructed to meaningfully represent training data. By representing these probability distributions as mean embeddings in the reproducing kernel Hilbert space (RKHS), we are able to apply many standard kernel-based learning techniques in straightforward fashion. To accomplish this, we construct a generalization of the support vector machine (SVM) called a support measure machine (SMM). Our analyses of SMMs provides several insights into their relationship to traditional SVMs. Based on such insights, we propose a flexible SVM (Flex-SVM) that places different kernel functions on each training example. Experimental results on both synthetic and real-world data demonstrate the effectiveness of our proposed framework.

This technical note considers the problems of blind sparse learning and inference of electrogram (EGM) signals under atrial fibrillation (AF) conditions. First of all we introduce a mathematical model for the observed signals that takes into account the multiple foci typically appearing inside the heart during AF. Then we propose a reconstruction model based on a fixed dictionary and discuss several alternatives for choosing the dictionary. In order to obtain a sparse solution that takes into account the biological restrictions of the problem, a first alternative is using LASSO regularization followed by a post-processing stage that removes low amplitude coefficients violating the refractory period characteristic of cardiac cells. As an alternative we propose a novel regularization term, called cross products LASSO (CP-LASSO), that is able to incorporate the biological constraints directly into the optimization problem. Unfortunately, the resulting problem is non-convex, but we show how it can be solved efficiently in an approximated way making use of successive convex approximations (SCA). Finally, spectral analysis is performed on the clean activation sequence obtained from the sparse learning stage in order to estimate the number of latent foci and their frequencies. Simulations on synthetic and real data are provided to validate the proposed approach.

We study the behavior of the A* search algorithm when coupled with a heuristic h satisfying (1-epsilon1)h* <= h <=(1+epsilon2)h*, where 0 <= epsilon1, epsilon2 < 1 are small constants and h* denotes the optimal cost to a solution. We prove a rigorous, general upper bound on the time complexity of A* search on trees that depends on both the accuracy of the heuristic and the distribution of solutions. Our upper bound is essentially tight in the worst case; in fact, we show nearly matching lower bounds that are attained even by non-adversarially chosen solution sets induced by a simple stochastic model. A consequence of our rigorous results is that the effective branching factor of the search will be reduced as long as epsilon1+epsilon2 < 1 and the number of near-optimal solutions in the search tree is not too large. We go on to provide an upper bound for A* search on graphs and in this context establish a bound on running time determined by the spectrum of the graph. We then experimentally explore to what extent our rigorous upper bounds predict the behavior of A* in some natural, combinatorially-rich search spaces. We begin by applying A* to solve the knapsack problem with near-accurate admissible heuristics constructed from an efficient approximation algorithm for this problem. We additionally apply our analysis of A* search for the partial Latin square problem, where we can provide quite exact analytic bounds on the number of near-optimal solutions. These results demonstrate a dramatic reduction in effective branching factor of A* when coupled with near-accurate heuristics in search spaces with suitably sparse solution sets.

We propose AD3, a new algorithm for approximate maximum a posteriori (MAP) inference on factor graphs based on the alternating directions method of multipliers. Like dual decomposition algorithms, AD3 uses worker nodes to iteratively solve local subproblems and a controller node to combine these local solutions into a global update. The key characteristic of AD3 is that each local subproblem has a quadratic regularizer, leading to a faster consensus than subgradient-based dual decomposition, both theoretically and in practice. We provide closed-form solutions for these AD3 subproblems for binary pairwise factors and factors imposing first-order logic constraints. For arbitrary factors (large or combinatorial), we introduce an active set method which requires only an oracle for computing a local MAP configuration, making AD3 applicable to a wide range of problems. Experiments on synthetic and realworld problems show that AD3 compares favorably with the state-of-the-art.

A plethora of words are used to describe the spectrum of human emotions, but how many emotions are there really, and how do they interact? Over the past few decades, several theories of emotion have been proposed, each based around the existence of a set of 'basic emotions', and each supported by an extensive variety of research including studies in facial expression, ethology, neurology and physiology. Here we present research based on a theory that people transmit their understanding of emotions through the language they use surrounding emotion keywords. Using a labelled corpus of over 21,000 tweets, six of the basic emotion sets proposed in existing literature were analysed using Latent Semantic Clustering (LSC), evaluating the distinctiveness of the semantic meaning attached to the emotional label. We hypothesise that the more distinct the language is used to express a certain emotion, then the more distinct the perception (including proprioception) of that emotion is, and thus more 'basic'. This allows us to select the dimensions best representing the entire spectrum of emotion. We find that Ekman's set, arguably the most frequently used for classifying emotions, is in fact the most semantically distinct overall. Next, taking all analysed (that is, previously proposed) emotion terms into account, we determine the optimal semantically irreducible basic emotion set using an iterative LSC algorithm. Our newly-derived set (Accepting, Ashamed, Contempt, Interested, Joyful, Pleased, Sleepy, Stressed) generates a 6.1% increase in distinctiveness over Ekman's set (Angry, Disgusted, Joyful, Sad, Scared). We also demonstrate how using LSC data can help visualise emotions. We introduce the concept of an Emotion Profile and briefly analyse compound emotions both visually and mathematically.

In some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this framework. Whereas median SOM is based on a rough representation of the prototypes, relational SOM allows representing these prototypes by a virtual combination of all elements in the data set. However, this latter approach suffers from two main drawbacks. First, its complexity can be large. Second, only a batch version of this algorithm has been studied so far and it often provides results having a bad topographic organization. In this article, an on-line version of relational SOM is described and justified. The algorithm is tested on several datasets, including categorical data and graphs, and compared with the batch version and with other SOM algorithms for non vector data.

Accumulation of standardized data collections is opening up novel opportunities for holistic characterization of genome function. The limited scalability of current preprocessing techniques has, however, formed a bottleneck for full utilization of contemporary microarray collections. While short oligonucleotide arrays constitute a major source of genome-wide profiling data, scalable probe-level preprocessing algorithms have been available only for few measurement platforms based on pre-calculated model parameters from restricted reference training sets. To overcome these key limitations, we introduce a fully scalable online-learning algorithm that provides tools to process large microarray atlases including tens of thousands of arrays. Unlike the alternatives, the proposed algorithm scales up in linear time with respect to sample size and is readily applicable to all short oligonucleotide platforms. This is the only available preprocessing algorithm that can learn probe-level parameters based on sequential hyperparameter updates at small, consecutive batches of data, thus circumventing the extensive memory requirements of the standard approaches and opening up novel opportunities to take full advantage of contemporary microarray data collections. Moreover, using the most comprehensive data collections to estimate probe-level effects can assist in pinpointing individual probes affected by various biases and provide new tools to guide array design and quality control. The implementation is freely available in R/Bioconductor at http://www.bioconductor.org/packages/devel/bioc/html/RPA.html

In the last decade, a new computational paradigm was introduced in the field of Machine Learning, under the name of Reservoir Computing (RC). RC models are neural networks which a recurrent part (the reservoir) that does not participate in the learning process, and the rest of the system where no recurrence (no neural circuit) occurs. This approach has grown rapidly due to its success in solving learning tasks and other computational applications. Some success was also observed with another recently proposed neural network designed using Queueing Theory, the Random Neural Network (RandNN). Both approaches have good properties and identified drawbacks. In this paper, we propose a new RC model called Echo State Queueing Network (ESQN), where we use ideas coming from RandNNs for the design of the reservoir. ESQNs consist in ESNs where the reservoir has a new dynamics inspired by recurrent RandNNs. The paper positions ESQNs in the global Machine Learning area, and provides examples of their use and performances. We show on largely used benchmarks that ESQNs are very accurate tools, and we illustrate how they compare with standard ESNs.