Farhad Mirkarimi

Farhad Mirkarimi, Stefano Rini, Nariman Farsad

Recently, several methods have been proposed for estimating the mutual information from sample data using deep neural networks. These estimators ar referred to as neural mutual information estimation (NMIE)s. NMIEs differ from other approaches as they are data-driven estimators. As such, they have the potential to perform well on a large class of capacity problems. In order to test the performance across various NMIEs, it is desirable to establish a benchmark encompassing the different challenges of capacity estimation. This is the objective of this paper. In particular, we consider three scenarios for benchmarking:i the classic AWGN channel, ii channels continuous inputs optical intensity and peak-power constrained AWGN channel iii channels with a discrete output, i.e., Poisson channel. We also consider the extension to the multi-terminal case with iv the AWGN and optical MAC models. We argue that benchmarking a certain NMIE across these four scenarios provides a substantive test of performance. In this paper we study the performance of mutual information neural estimator (MINE), smoothed mutual information lower-bound estimator (SMILE), and directed information neural estimator (DINE). and provide insights on the performance of other methods as well. To summarize our benchmarking results, MINE provides the most reliable performance.

Farhad Mirkarimi

Many real-world tasks require optimizing expensive black-box functions accessible only through noisy evaluations, a setting commonly addressed with Bayesian optimization (BO). While Bayesian neural networks (BNNs) have recently emerged as scalable alternatives to Gaussian Processes (GPs), traditional BNN-BO frameworks remain burdened by expensive posterior sampling and acquisition function optimization. In this work, we propose {VBO-MI} (Variational Bayesian Optimization with Mutual Information), a fully gradient-based BO framework that leverages recent advances in variational mutual information estimation. To enable end-to-end gradient flow, we employ an actor-critic architecture consisting of an {action-net} to navigate the input space and a {variational critic} to estimate information gain. This formulation effectively eliminates the traditional inner-loop acquisition optimization bottleneck, achieving up to a {$10^2 \times$ reduction in FLOPs} compared to BNN-BO baselines. We evaluate our method on a diverse suite of benchmarks, including high-dimensional synthetic functions and complex real-world tasks such as PDE optimization, the Lunar Lander control problem, and categorical Pest Control. Our experiments demonstrate that VBO-MI consistently provides the same or superior optimization performance and computational scalability over the baselines.

Farhad Mirkarimi, Stefano Rini, Nariman Farsad

Recently, several methods have been proposed for estimating the mutual information from sample data using deep neural networks and without the knowing closed form distribution of the data. This class of estimators is referred to as neural mutual information estimators. Although very promising, such techniques have yet to be rigorously bench-marked so as to establish their efficacy, ease of implementation, and stability for capacity estimation which is joint maximization frame-work. In this paper, we compare the different techniques proposed in the literature for estimating capacity and provide a practitioner perspective on their effectiveness. In particular, we study the performance of mutual information neural estimator (MINE), smoothed mutual information lower-bound estimator (SMILE), and directed information neural estimator (DINE) and provide insights on InfoNCE. We evaluated these algorithms in terms of their ability to learn the input distributions that are capacity approaching for the AWGN channel, the optical intensity channel, and peak power-constrained AWGN channel. For both scenarios, we provide insightful comments on various aspects of the training process, such as stability, sensitivity to initialization.