Martina Cardone

Mine Gokce Dogan, Martina Cardone, Christina Fragouli

This paper aims to develop resilient transmission mechanisms to suitably distribute traffic across multiple paths in an arbitrary millimeter-wave (mmWave) network. The main contributions include: (a) the development of proactive transmission mechanisms that build resilience against network disruptions in advance, while achieving a high end-to-end packet rate; (b) the design of a heuristic path selection algorithm that efficiently selects (in polynomial time in the network size) multiple proactively resilient paths with high packet rates; and (c) the development of a hybrid scheduling algorithm that combines the proposed path selection algorithm with a deep reinforcement learning (DRL) based online approach for decentralized adaptation to blocked links and failed paths. To achieve resilience to link failures, a state-of-the-art Soft Actor-Critic DRL algorithm, which adapts the information flow through the network, is investigated. The proposed scheduling algorithm robustly adapts to link failures over different topologies, channel and blockage realizations while offering a superior performance to alternative algorithms.

Mohammad Milanian, Alex Dytso, Martina Cardone

In this paper, we study Sibson's $α$-mutual information in the context of the additive Gaussian noise channel. While the classical case $α= 1$ is well understood and admits deep connections to estimation-theoretic quantities, such as the minimum mean-square error (MMSE) and Fisher information, many of the corresponding structural properties for general $α$ remain less explored. Our goal is to develop a systematic understanding of $α$-mutual information in the Gaussian noise setting and to identify which properties extend beyond the Shannon case. To this end, we establish several regularity properties, including finiteness conditions, continuity with respect to the signal-to-noise ratio (SNR) and the input distribution, and strict concavity/convexity properties that ensure uniqueness in associated optimization problems. A central contribution is the development of an $α$-I-MMSE relationship, generalizing the classical identity by relating the derivative of $α$-mutual information with respect to SNR to the MMSE evaluated under appropriately tilted distributions. This connection further leads to a generalized de Bruijn identity and new estimation-theoretic representations of Rényi entropy and differential Rényi entropy. We also characterize the low- and high-SNR behavior. In the low-SNR regime, the first-order behavior depends only on the input variance. In the high-SNR regime, for discrete inputs, $α$-mutual information converges to the Rényi entropy of order $1/α$, while for general inputs we connect it to $α$-information dimension. Overall, our results show that many fundamental relationships between information and estimation extend beyond the Shannon setting, in a form involving $α$-tilted distributions.

Minoh Jeong, Martina Cardone, Alex Dytso

Classification is a fundamental task in many applications on which data-driven methods have shown outstanding performances. However, it is challenging to determine whether such methods have achieved the optimal performance. This is mainly because the best achievable performance is typically unknown and hence, effectively estimating it is of prime importance. In this paper, we consider binary classification problems and we propose an estimator for the false positive rate (FPR) of the Bayes classifier, that is, the optimal classifier with respect to accuracy, from a given dataset. Our method utilizes soft labels, or real-valued labels, which are gaining significant traction thanks to their properties. We thoroughly examine various theoretical properties of our estimator, including its consistency, unbiasedness, rate of convergence, and variance. To enhance the versatility of our estimator beyond soft labels, we also consider noisy labels, which encompass binary labels. For noisy labels, we develop effective FPR estimators by leveraging a denoising technique and the Nadaraya-Watson estimator. Due to the symmetry of the problem, our results can be readily applied to estimate the false negative rate of the Bayes classifier.