Shaan ul Haque | Searcharxiv

arXiv2025

Learning to Speak on Behalf of a Group: Medium Access Control for Sending a Shared Message

The rapid development of Internet of Things (IoT) technologies has not only enabled new applications, but also presented new challenges for reliable communication with limited resources. In this work, we define a novel problem that can arise in these scenarios, in which a set of sensors need to communicate a joint observation. This observation is shared by a random subset of the nodes, which need to propagate it to the rest of the network, but coordination is complex: as signaling constraints require the use of random access schemes over shared channels, sensors need to implicitly coordinate, so that at least one transmission gets through without collisions. Unlike the majority of existing medium access schemes, the goal is to make sure that the shared message gets through, regardless of the sender. We analyze this coordination problem theoretically and provide low-complexity solutions. While a clustering-based approach is near-optimal if the sensors have prior knowledge, we provide a distributed multi-armed bandit (MAB) solution for the more general case and validate it by simulation.

cs.NI↗

arXiv2022

Joint Probability Estimation Using Tensor Decomposition and Dictionaries

In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be decomposed and approximated by a mixture of product densities/mass functions. The problem of estimating the joint probability density function (PDF) using semi-parametric techniques such as Gaussian Mixture Models (GMMs) is widely studied. However such techniques yield poor results when the underlying densities are mixtures of various other families of distributions such as Laplacian or generalized Gaussian, uniform, Cauchy, etc. Further, GMMs are not the best choice to estimate joint distributions which are hybrid in nature, i.e., some random variables are discrete while others are continuous. We present a novel approach for estimating the PDF using ideas from dictionary representations in signal processing coupled with low rank tensor decompositions. To the best our knowledge, this is the first work on estimating joint PDFs employing dictionaries alongside tensor decompositions. We create a dictionary of various families of distributions by inspecting the data, and use it to approximate each decomposed factor of the product in the mixture. Our approach can naturally handle hybrid $N$-dimensional distributions. We test our approach on a variety of synthetic and real datasets to demonstrate its effectiveness in terms of better classification rates and lower error rates, when compared to state of the art estimators.

cs.LG↗