arXiv subjects

Malhar A. Managoli

Publications and source records attributed to Malhar A. Managoli.

4 recordsLinked to original sources

arXiv2026

Memory Constrained Adversarial Hypothesis Testing

We study adversarial binary hypothesis testing under memory constraints. The test is a time-invariant randomized finite state machine (FSM) with S states. Associated with each hypothesis is a set of distributions. Given the hypothesis, the distribution of each sample is chosen from the set associated with the hypothesis by an adversary who has access to past samples and the history of states of the FSM so far. We obtain upper and lower bounds on the minimax asymptotic probability of error as a function of S. The bounds have the same exponential behaviour in S and match for a class of problems.

cs.IT↗

arXiv2025

Robust Federated Personalised Mean Estimation for the Gaussian Mixture Model

Federated learning with heterogeneous data and personalization has received significant recent attention. Separately, robustness to corrupted data in the context of federated learning has also been studied. In this paper we explore combining personalization for heterogeneous data with robustness, where a constant fraction of the clients are corrupted. Motivated by this broad problem, we formulate a simple instantiation which captures some of its difficulty. We focus on the specific problem of personalized mean estimation where the data is drawn from a Gaussian mixture model. We give an algorithm whose error depends almost linearly on the ratio of corrupted to uncorrupted samples, and show a lower bound with the same behavior, albeit with a gap of a constant factor.

cs.LG↗

arXiv2025

Robust Hypothesis Testing with Abstention

We study the binary hypothesis testing problem where an adversary may potentially corrupt a fraction of the samples. The detector is, however, permitted to abstain from making a decision if (and only if) the adversary is present. We consider a few natural "contamination models" and characterize for them the trade-off between the error exponents of the four types of errors -- errors of deciding in favour of the incorrect hypothesis when the adversary is present and errors of abstaining or deciding in favour of the wrong hypothesis when the adversary is absent, under the two hypotheses.

cs.IT↗

arXiv2024

Broadcast Channel Synthesis from Shared Randomness

We study the problem of synthesising a two-user broadcast channel using a common message, where each output terminal shares an independent source of randomness with the input terminal. This generalises two problems studied in the literature (Cuff, IEEE Trans. Inform. Theory, 2013; Kurri et.al., IEEE Trans. Inform. Theory, 2021). We give an inner bound on the tradeoff region between the rates of communication and shared randomness, and a lower bound on the minimum communication rate. Although the bounds presented here are not tight in general, they are tight for some special cases, including the aforementioned problems.

cs.IT↗