Feature selection in reinforcement learning (RL), i.e. choosing basis functions such that useful approximations of the unkown value function can be obtained, is one of the main challenges in scaling RL to real-world applications. Here we consider the Gaussian process based framework GPTD for approximate policy evaluation, and propose feature selection through marginal likelihood optimization of the associated hyperparameters. Our approach has two appealing benefits: (1) given just sample transitions, we can solve the policy evaluation problem fully automatically (without looking at the learning task, and, in theory, independent of the dimensionality of the state space), and (2) model selection allows us to consider more sophisticated kernels, which in turn enable us to identify relevant subspaces and eliminate irrelevant state variables such that we can achieve substantial computational savings and improved prediction performance.

We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower bound shows that the popular Gaussian assumption is not robust in this regard. We also construct an upper bound for the supremum Bayes error by constraining the decision boundary to be linear.

In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this paper we show that a small proportion of atypical observations might have serious adverse effects on the solutions found by the sparse clustering algorithm of Witten and Tibshirani (2010). We propose a robustification of their sparse K-means algorithm based on the trimmed K-means algorithm of Cuesta-Albertos et al. (1997) Our proposal is also able to handle datasets with missing values. We illustrate the use of our method on microarray data for cancer patients where we are able to identify strong biological clusters with a much reduced number of genes. Our simulation studies show that, when there are outliers in the data, our robust sparse K-means algorithm performs better than other competing methods both in terms of the selection of features and also the identified clusters. This robust sparse K-means algorithm is implemented in the R package RSKC which is publicly available from the CRAN repository.

In medical risk modeling, typical data are "scarce": they have relatively small number of training instances (N), censoring, and high dimensionality (M). We show that the problem may be effectively simplified by reducing it to bipartite ranking, and introduce new bipartite ranking algorithm, Smooth Rank, for robust learning on scarce data. The algorithm is based on ensemble learning with unsupervised aggregation of predictors. The advantage of our approach is confirmed in comparison with two "gold standard" risk modeling methods on 10 real life survival analysis datasets, where the new approach has the best results on all but two datasets with the largest ratio N/M. For systematic study of the effects of data scarcity on modeling by all three methods, we conducted two types of computational experiments: on real life data with randomly drawn training sets of different sizes, and on artificial data with increasing number of features. Both experiments demonstrated that Smooth Rank has critical advantage over the popular methods on the scarce data; it does not suffer from overfitting where other methods do.

Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching schemes. In contrast, we present an approach that identifies the need to select features based on their discriminatory ability among classes. Area of overlap between inter-class and intra-class distances resulting from feature to feature comparison of an attribute is used as a measure of discriminatory ability of the feature. A set of nearest attributes in a pattern having the lowest area of overlap within a degree of tolerance defined by a selection threshold is selected to represent the best available discriminable features. State of the art recognition results are reported for pattern classification problems by using the proposed feature selection scheme with the nearest neighbour classifier. These results are reported with benchmark databases having high dimensional feature vectors in the problems involving images and micro array data.

Data collection at a massive scale is becoming ubiquitous in a wide variety of settings, from vast offline databases to streaming real-time information. Learning algorithms deployed in such contexts must rely on single-pass inference, where the data history is never revisited. In streaming contexts, learning must also be temporally adaptive to remain up-to-date against unforeseen changes in the data generating mechanism. Although rapidly growing, the online Bayesian inference literature remains challenged by massive data and transient, evolving data streams. Non-parametric modelling techniques can prove particularly ill-suited, as the complexity of the model is allowed to increase with the sample size. In this work, we take steps to overcome these challenges by porting standard streaming techniques, like data discarding and downweighting, into a fully Bayesian framework via the use of informative priors and active learning heuristics. We showcase our methods by augmenting a modern non-parametric modelling framework, dynamic trees, and illustrate its performance on a number of practical examples. The end product is a powerful streaming regression and classification tool, whose performance compares favourably to the state-of-the-art.

We consider the problem of online linear regression on individual sequences. The goal in this paper is for the forecaster to output sequential predictions which are, after T time rounds, almost as good as the ones output by the best linear predictor in a given L1-ball in R^d. We consider both the cases where the dimension d is small and large relative to the time horizon T. We first present regret bounds with optimal dependencies on the sizes U, X and Y of the L1-ball, the input data and the observations. The minimax regret is shown to exhibit a regime transition around the point d = sqrt(T) U X / (2 Y). Furthermore, we present efficient algorithms that are adaptive, i.e., they do not require the knowledge of U, X, and Y, but still achieve nearly optimal regret bounds.

Support Vector Machines, SVMs, and the Large Margin Nearest Neighbor algorithm, LMNN, are two very popular learning algorithms with quite different learning biases. In this paper we bring them into a unified view and show that they have a much stronger relation than what is commonly thought. We analyze SVMs from a metric learning perspective and cast them as a metric learning problem, a view which helps us uncover the relations of the two algorithms. We show that LMNN can be seen as learning a set of local SVM-like models in a quadratic space. Along the way and inspired by the metric-based interpretation of SVM s we derive a novel variant of SVMs, epsilon-SVM, to which LMNN is even more similar. We give a unified view of LMNN and the different SVM variants. Finally we provide some preliminary experiments on a number of benchmark datasets in which show that epsilon-SVM compares favorably both with respect to LMNN and SVM.

We propose the concept of Action-Related Place (ARPlace) as a powerful and flexible representation of task-related place in the context of mobile manipulation. ARPlace represents robot base locations not as a single position, but rather as a collection of positions, each with an associated probability that the manipulation action will succeed when located there. ARPlaces are generated using a predictive model that is acquired through experience-based learning, and take into account the uncertainty the robot has about its own location and the location of the object to be manipulated. When executing the task, rather than choosing one specific goal position based only on the initial knowledge about the task context, the robot instantiates an ARPlace, and bases its decisions on this ARPlace, which is updated as new information about the task becomes available. To show the advantages of this least-commitment approach, we present a transformational planner that reasons about ARPlaces in order to optimize symbolic plans. Our empirical evaluation demonstrates that using ARPlaces leads to more robust and efficient mobile manipulation in the face of state estimation uncertainty on our simulated robot.

Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinite programming which improves the method sensitivity to a broad variety of deviations from normality. We also discuss the procedures which allows to recover the structure when its effective dimension is unknown.