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This work investigates binary hypothesis testing between $H_0\sim P_0$ and $H_1\sim P_1$ in the finite-sample regime under asymmetric error constraints. By employing the ``reverse" R\'enyi divergence, we derive novel non-asymptotic bounds…
Two new proofs of the Fisher information inequality (FII) using data processing inequalities for mutual information and conditional variance are presented.
Counterfactual explanations are usually obtained by identifying the smallest change made to an input to change a prediction made by a fixed model (hereafter called sparse methods). Recent work, however, has revitalized an old insight: there…
We study from the proof complexity perspective the (informal) proof search problem: Is there an optimal way to search for propositional proofs? We note that for any fixed proof system there exists a time-optimal proof search algorithm.…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
This paper presents a new classifier combination technique based on the Dempster-Shafer theory of evidence. The Dempster-Shafer theory of evidence is a powerful method for combining measures of evidence from different classifiers. However,…
Let $(X,T,\mu,d)$ be a metric measure-preserving system for which $3$-fold correlations decay exponentially for Lipschitz continuous observables. Suppose that $(M_k)$ is a sequence satisfying some weak decay conditions and suppose there…
Neural symbolic processing aims to combine the generalization of logical learning approaches and the performance of neural networks. The Neural Theorem Proving (NTP) model by Rocktaschel et al (2017) learns embeddings for concepts and…
Multi-hop Question Answering (QA) is a challenging task since it requires an accurate aggregation of information from multiple context paragraphs and a thorough understanding of the underlying reasoning chains. Recent work in multi-hop QA…
Verification methods based on SAT, SMT, and Theorem Proving often rely on proofs of unsatisfiability as a powerful tool to extract information in order to reduce the overall effort. For example a proof may be traversed to identify a minimal…
Counterfactual explanations and adversarial attacks have a related goal: flipping output labels with minimal perturbations regardless of their characteristics. Yet, adversarial attacks cannot be used directly in a counterfactual explanation…
We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.
We compare two different techniques for proving non-Shannon-type information inequalities. The first one is the original Zhang-Yeung's method, commonly referred to as the copy/pasting lemma/trick. The copy lemma was used to derive the first…
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for…
Misinformation such as fake news is one of the big challenges of our society. Research on automated fact-checking has proposed methods based on supervised learning, but these approaches do not consider external evidence apart from labeled…
In two-prover one-round interactive proof systems, no-signaling provers are those who are allowed to use arbitrary strategies, not limited to local operations, as long as their strategies cannot be used for communication between them. Study…
Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…
Pre-trained multimodal models have achieved significant success in retrieval-based question answering. However, current multimodal retrieval question-answering models face two main challenges. Firstly, utilizing compressed evidence features…
We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized…