Machine Learning

A Unifying Post-Processing Framework for Multi-Objective Learn-to-Defer Problems

This paper introduces a unifying framework for constrained optimization problems, mainly for classification and learn-to-defer tasks. This is a generalization of Neyman-Pearson lemma and counters the regularization paradigm.

Sample Efficient Learning of Predictors that Complement Humans

In here, we provide the first theoretical results on the joint learning of classifier and rejector, and design an active learning algorithm to achieve this. We further introduce a set of surrogate losses to enable learn-to-defer training for neural networks.

Hermite Polynomial Features for Private Data Generation

In this paper, we designed an alternative to random features to generate more efficient representations of a dataset that are privacy-preserving, while maintain the quality of the instances.

Information Theory

ARMA Processes with Discrete-Continuous Excitation: Compressibility Beyond Sparsity

In this paper, I generalize the connection between information dimension and compressibility of stochastic processes to the case of ARMA processes. I show that although ARMA processes are not sparse, they can have singular structures that lead to their compression via compressed sensing methods.

Compressibility Measures for Affinely Singular Random Vectors

In this paper, we define a set of singular distributions that naturally arise in autoregressive processes. Then, we obtain R'enyi information dimension for processes with such probability distributions. We further, find an extension to differential entropy for such class of probability measures. Then, we find information-theoretic and compressed sensing reconstruction errors for compression of samples of such processes.

On the Compressibility of Affinely Singular Random Vectors

In this paper, I find a probabilistic extension to sparsity that can lead to similar guarantees in reconstruction error in compressed sensing problems. This is done by finding R'enyi Information Dimension for probability measures with singularity.