Signal Recovery from Time and Frequency Samples

We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either domain alone are insufficient because of sensing, storage, or bandwidth constraints. We formulate the resulting recovery problem in finite-dimensional spaces and reproducing kernel Hilbert spaces, and illustrate the infinite-dimensional setting in a Fourier-symmetric Sobolev space. Numerical experiments with sinc- and Hermite-based schemes indicate that, under a fixed sampling budget, two-sided sampling often yields better conditioned systems than one-sided approaches. A simplified spectrum-monitoring example further demonstrates improved reconstruction when limited time samples are supplemented with frequency-domain information.

Opinion Consensus Formation Among Networked Large Language Models

Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse communication graphs. To track opinion evolution, we map each message to an opinion score via sentiment analysis. We find that agents typically reach consensus and the disagreement between the agents decays exponentially. However, the limiting opinion departs from DeGroot's network-centrality-weighted forecast. The consensus between LLM agents turns out to be largely insensitive to initial conditions and instead depends strongly on the discussion subject and inherent biases. Nevertheless, transient dynamics align with classical graph theory and the convergence rate of opinions is closely related to the second-largest eigenvalue of the graph's combination matrix. Together, these findings can be useful for LLM-driven social-network simulations and the design of resource-efficient multi-agent LLM applications.

Causal Influence in Federated Edge Inference

In this paper, we consider a setting where heterogeneous agents with connectivity are performing inference using unlabeled streaming data. Observed data are only partially informative about the target variable of interest. In order to overcome the uncertainty, agents cooperate with each other by exchanging their local inferences with and through a fusion center. To evaluate how each agent influences the overall decision, we adopt a causal framework in order to distinguish the actual influence of agents from mere correlations within the decision-making process. Various scenarios reflecting different agent participation patterns and fusion center policies are investigated. We derive expressions to quantify the causal impact of each agent on the joint decision, which could be beneficial for anticipating and addressing atypical scenarios, such as adversarial attacks or system malfunctions. We validate our theoretical results with numerical simulations and a real-world application of multi-camera crowd counting.

Detection of Malicious Agents in Social Learning

Social learning is a non-Bayesian framework for distributed hypothesis testing aimed at learning the true state of the environment. Traditionally, the agents are assumed to receive observations conditioned on the same true state, although it is also possible to examine the case of heterogeneous models across the graph. One important special case is when heterogeneity is caused by the presence of malicious agents whose goal is to move the agents towards a wrong hypothesis. In this work, we propose an algorithm that allows to discover the true state of every individual agent based on the sequence of their beliefs. In so doing, the methodology is also able to locate malicious behavior.

Social Learning in Community Structured Graphs

Traditional social learning frameworks consider environments with a homogeneous state, where each agent receives observations conditioned on that true state of nature. In this work, we relax this assumption and study the distributed hypothesis testing problem in a heterogeneous environment, where each agent can receive observations conditioned on their own personalized state of nature (or truth). This situation arises in many scenarios, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. In these heterogeneous contexts, the graph topology admits a block structure. We study social learning under personalized (or multitask) models and examine their convergence behavior.

Causal Influences over Social Learning Networks

This paper investigates causal influences between agents linked by a social graph and interacting over time. In particular, the work examines the dynamics of social learning models and distributed decision-making protocols, and derives expressions that reveal the causal relations between pairs of agents and explain the flow of influence over the network. The results turn out to be dependent on the graph topology and the level of information that each agent has about the inference problem they are trying to solve. Using these conclusions, the paper proposes an algorithm to rank the overall influence between agents to discover highly influential agents. It also provides a method to learn the necessary model parameters from raw observational data. The results and the proposed algorithm are illustrated by considering both synthetic data and real Twitter data.

Non-Asymptotic Performance of Social Machine Learning Under Limited Data

This paper studies the probability of error associated with the social machine learning framework, which involves an independent training phase followed by a cooperative decision-making phase over a graph. This framework addresses the problem of classifying a stream of unlabeled data in a distributed manner. We consider two kinds of classification tasks with limited observations in the prediction phase, namely, the statistical classification task and the single-sample classification task. For each task, we describe the distributed learning rule and analyze the probability of error accordingly. To do so, we first introduce a stronger consistent training condition that involves the margin distributions generated by the trained classifiers. Based on this condition, we derive an upper bound on the probability of error for both tasks, which depends on the statistical properties of the data and the combination policy used to combine the distributed classifiers. For the statistical classification problem, we employ the geometric social learning rule and conduct a non-asymptotic performance analysis. An exponential decay of the probability of error with respect to the number of unlabeled samples is observed in the upper bound. For the single-sample classification task, a distributed learning rule that functions as an ensemble classifier is constructed. An upper bound on the probability of error of this ensemble classifier is established.

On the Fusion Strategies for Federated Decision Making

We consider the problem of information aggregation in federated decision making, where a group of agents collaborate to infer the underlying state of nature without sharing their private data with the central processor or each other. We analyze the non-Bayesian social learning strategy in which agents incorporate their individual observations into their opinions (i.e., soft-decisions) with Bayes rule, and the central processor aggregates these opinions by arithmetic or geometric averaging. Building on our previous work, we establish that both pooling strategies result in asymptotic normality characterization of the system, which, for instance, can be utilized in order to give approximate expressions for the error probability. We verify the theoretical findings with simulations and compare both strategies.

Policy Evaluation in Decentralized POMDPs with Belief Sharing

Most works on multi-agent reinforcement learning focus on scenarios where the state of the environment is fully observable. In this work, we consider a cooperative policy evaluation task in which agents are not assumed to observe the environment state directly. Instead, agents can only have access to noisy observations and to belief vectors. It is well-known that finding global posterior distributions under multi-agent settings is generally NP-hard. As a remedy, we propose a fully decentralized belief forming strategy that relies on individual updates and on localized interactions over a communication network. In addition to the exchange of the beliefs, agents exploit the communication network by exchanging value function parameter estimates as well. We analytically show that the proposed strategy allows information to diffuse over the network, which in turn allows the agents' parameters to have a bounded difference with a centralized baseline. A multi-sensor target tracking application is considered in the simulations.

Distributed Bayesian Learning of Dynamic States

This work studies networked agents cooperating to track a dynamical state of nature under partial information. The proposed algorithm is a distributed Bayesian filtering algorithm for finite-state hidden Markov models (HMMs). It can be used for sequential state estimation tasks, as well as for modeling opinion formation over social networks under dynamic environments. We show that the disagreement with the optimal centralized solution is asymptotically bounded for the class of geometrically ergodic state transition models, which includes rapidly changing models. We also derive recursions for calculating the probability of error and establish convergence under Gaussian observation models. Simulations are provided to illustrate the theory and to compare against alternative approaches.