M. H. Rohban | Searcharxiv

arXiv2016

A Bayesian Approach to the Data Description Problem

In this paper, we address the problem of data description using a Bayesian framework. The goal of data description is to draw a boundary around objects of a certain class of interest to discriminate that class from the rest of the feature space. Data description is also known as one-class learning and has a wide range of applications. The proposed approach uses a Bayesian framework to precisely compute the class boundary and therefore can utilize domain information in form of prior knowledge in the framework. It can also operate in the kernel space and therefore recognize arbitrary boundary shapes. Moreover, the proposed method can utilize unlabeled data in order to improve accuracy of discrimination. We evaluate our method using various real-world datasets and compare it with other state of the art approaches of data description. Experiments show promising results and improved performance over other data description and one-class learning algorithms.

cs.LG↗

arXiv2014

Sparse Signal Recovery under Poisson Statistics

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many conventional problems observations here are not identically distributed since they are associated with different sensing modalities. We analyze the performance of a Maximum Likelihood (ML) decoder, which for our Poisson setting involves a non-linear optimization but yet is computationally tractable. We derive fundamental sample complexity bounds for sparse recovery when the measurements are contaminated with Poisson noise. In contrast to the least-squares linear regression setting with Gaussian noise, we observe that in addition to sparsity, the scale of the parameters also fundamentally impacts sample complexity. We introduce a novel notion of Restricted Likelihood Perturbation (RLP), to jointly account for scale and sparsity. We derive sample complexity bounds for $\ell_1$ regularized ML estimators in terms of RLP and further specialize these results for deterministic and random sensing matrix designs.

math.ST↗