Rate-Distortion Classification for Self-Tuning IoT Networks

Many future wireless sensor networks and the Internet of Things are expected to follow a software defined paradigm, where protocol parameters and behaviors will be dynamically tuned as a function of the signal statistics. New protocols will be then injected as a software as certain events occur. For instance, new data compressors could be (re)programmed on-the-fly as the monitored signal type or its statistical properties change. We consider a lossy compression scenario, where the application tolerates some distortion of the gathered signal in return for improved energy efficiency. To reap the full benefits of this paradigm, we discuss an automatic sensor profiling approach where the signal class, and in particular the corresponding rate-distortion curve, is automatically assessed using machine learning tools (namely, support vector machines and neural networks). We show that this curve can be reliably estimated on-the-fly through the computation of a small number (from ten to twenty) of statistical features on time windows of a few hundreds samples

Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization

Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance. In this paper, we generalize HTP from compressive sensing to a generic problem setup of sparsity-constrained convex optimization. The proposed algorithm iterates between a standard gradient descent step and a hard thresholding step with or without debiasing. We prove that our method enjoys the strong guarantees analogous to HTP in terms of rate of convergence and parameter estimation accuracy. Numerical evidences show that our method is superior to the state-of-the-art greedy selection methods in sparse logistic regression and sparse precision matrix estimation tasks

A D.C. Programming Approach to the Sparse Generalized Eigenvalue Problem

In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), sparse canonical correlation analysis (CCA) and sparse Fisher discriminant analysis (FDA) as special cases. Unlike the $\ell_1$-norm approximation to the cardinality constraint, which previous methods have used in the context of sparse PCA, we propose a tighter approximation that is related to the negative log-likelihood of a Student's t-distribution. The problem is then framed as a d.c. (difference of convex functions) program and is solved as a sequence of convex programs by invoking the majorization-minimization method. The resulting algorithm is proved to exhibit \emph{global convergence} behavior, i.e., for any random initialization, the sequence (subsequence) of iterates generated by the algorithm converges to a stationary point of the d.c. program. The performance of the algorithm is empirically demonstrated on both sparse PCA (finding few relevant genes that explain as much variance as possible in a high-dimensional gene dataset) and sparse CCA (cross-language document retrieval and vocabulary selection for music retrieval) applications.Comment: 40 page

A time series causal model

Cause-effect relations are central in economic analysis. Uncovering empirical cause-effect relations is one of the main research activities of empirical economics. In this paper we develop a time series casual model to explore casual relations among economic time series. The time series causal model is grounded on the theory of inferred causation that is a probabilistic and graph-theoretic approach to causality featured with automated learning algorithms. Applying our model we are able to infer cause-effect relations that are implied by the observed time series data. The empirically inferred causal relations can then be used to test economic theoretical hypotheses, to provide evidence for formulation of theoretical hypotheses, and to carry out policy analysis. Time series causal models are closely related to the popular vector autoregressive (VAR) models in time series analysis. They can be viewed as restricted structural VAR models identified by the inferred causal relations.Inferred Causation, Automated Learning, VAR, Granger Causality, Wage-Price Spiral