A Distributed Feature Selection Algorithm Based on Distance Correlation with an Application to Microarrays.

DNA microarray datasets are characterized by a large number of features with very few samples, which is a typical cause of overfitting and poor generalization in the classification task. Here, we introduce a novel feature selection (FS) approach which employs the distance correlation (dCor) as a criterion for evaluating the dependence of the class on a given feature subset. The dCor index provides a reliable dependence measure among random vectors of arbitrary dimension, without any assumption on their distribution. Moreover, it is sensitive to the presence of redundant terms. The proposed FS method is based on a probabilistic representation of the feature subset model, which is progressively refined by a repeated process of model extraction and evaluation. A key element of the approach is a distributed optimization scheme based on a vertical partitioning of the dataset, which alleviates the negative effects of its unbalanced dimensions. The proposed method has been tested on several microarray datasets, resulting in quite compact and accurate models obtained at a reasonable computational cost.

A Feature Selection and Classification Algorithm Based on Randomized Extraction of Model Populations.

We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection (FS) and classifier design tasks. The classifier is constructed as a polynomial expansion of the original features and a selection process is applied to find the relevant model terms. The selection method progressively refines a probability distribution defined on the model structure space, by extracting sample models from the current distribution and using the aggregate information obtained from the evaluation of the population of models to reinforce the probability of extracting the most important terms. To reduce the initial search space, distance correlation filtering is optionally applied as a preprocessing technique. The proposed method is compared to other well-known FS and classification methods on standard benchmark problems. Besides the favorable properties of the method regarding classification accuracy, the obtained models have a simple structure, easily amenable to interpretation and analysis.

Policy Search for the Optimal Control of Markov Decision Processes: A Novel Particle-Based Iterative Scheme.

Classical approximate dynamic programming techniques based on state-space gridding become computationally impracticable for high-dimensional problems. Policy search techniques cope with this curse of dimensionality issue by searching for the optimal control policy in a restricted parameterized policy space. We here focus on the case of discrete action space and introduce a novel policy parametrization that adopts particles to describe the map from the state space to the action space, each particle representing a region of the state space that is mapped into a certain action. The locations and actions associated with the particles describing a policy can be tuned by means of a recently introduced policy gradient method with parameter-based exploration. The task of selecting an appropriately sized set of particles is here solved through an iterative policy building scheme that adds new particles to improve the policy performance and is also capable of removing redundant particles. Experiments demonstrate the scalability of the proposed approach as the dimensionality of the state-space grows.