Large language models (LLMs) are often ensembled together to improve overall reliability and robustness, but in practice models are strongly correlated. This raises a fundamental question: which models should be selected when forming an LLM ensemble? We formulate budgeted ensemble selection as maximizing the mutual information between the true label and predictions of the selected models. Furthermore, to explain why performance can saturate even with many models, we model the correlated errors of the models using Gaussian-copula and show an information-theoretic error floor for the performance of the ensemble. Motivated by these, we propose a simple greedy mutual-information selection algorithm that estimates the required information terms directly from data and iteratively builds an ensemble under a query budget. We test our approach in two question answering datasets and one binary sentiment classification dataset: MEDMCQA, MMLU, and IMDB movie reviews. Across all datasets, we observe that our method consistently outperforms strong baselines under the same query budget.

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters are $\varepsilon$-far in total variation, the goal is to recover the partition. We establish upper and lower bounds on the sample complexity for two fundamental cases: (1) when one of the cluster's distributions is known, and (2) when both are unknown. Our upper and lower bounds characterize the sample complexity's dependence on the domain size $n$, number of distributions $k$, size $r$ of one of the clusters, and distance $\varepsilon$. In particular, we achieve tightness with respect to $(n,k,r,\varepsilon)$ (up to an $O(\log k)$ factor) for all regimes.

Every day we share our personal information through digital systems which are constantly exposed to threats. For this reason, security-oriented disciplines of signal processing have received increasing attention in the last decades: multimedia forensics, digital watermarking, biometrics, network monitoring, steganography and steganalysis are just a few examples. Even though each of these fields has its own peculiarities, they all have to deal with a common problem: the presence of one or more adversaries aiming at making the system fail. Adversarial Signal Processing lays the basis of a general theory that takes into account the impact that the presence of an adversary has on the design of effective signal processing tools. By focusing on the application side of Adversarial Signal Processing, namely adversarial information fusion in distributed sensor networks, and adopting a game-theoretic approach, this thesis contributes to the above mission by addressing four issues. First, we address decision fusion in distributed sensor networks by developing a novel soft isolation defense scheme that protect the network from adversaries, specifically, Byzantines. Second, we develop an optimum decision fusion strategy in the presence of Byzantines. In the next step, we propose a technique to reduce the complexity of the optimum fusion by relying on a novel near-optimum message passing algorithm based on factor graphs. Finally, we introduce a defense mechanism to protect decentralized networks running consensus algorithm against data falsification attacks.

In this paper, we study the pooled data problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool. In the noiseless setting, we identify an exact asymptotic threshold on the required number of tests with optimal decoding, and prove a phase transition between complete success and complete failure. In addition, we present a novel noisy variation of the problem, and provide an information-theoretic framework for characterizing the required number of tests for general random noise models. Our results reveal that noise can make the problem considerably more difficult, with strict increases in the scaling laws even at low noise levels. Finally, we demonstrate similar behavior in an approximate recovery setting, where a given number of errors is allowed in the decoded labels.

The goal is to learn a single classifier that also performs well on all the tasks.

Complementarily, we present a minimax lower bound for this problem.

The authors are listed in alphabetical order.

We are modifying and reorganizing the introduction to improve its presentation.

In this work, we show that we can better exploit the structure of the underlying computation problem by modifying the traditional bandit sampling strategy and using it in conjunction with a suitably chosen multi-armed bandit algorithm.

The goal is to learn a single classifier that also performs well on all the tasks.