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This work extends the analysis of the theoretical results presented within the paper Is Q-Learning Provably Efficient? by Jin et al. We include a survey of related research to contextualize the need for strengthening the theoretical…
Diffusion models are powerful generative models that allow for precise control over the characteristics of the generated samples. While these diffusion models trained on large datasets have achieved success, there is often a need to…
In this dissertation, we show that the Central Limit Theorem and the Invariance Principle for Discrete Fourier Transforms discovered by Peligrad and Wu can be extended to the quenched setting. We show that the random normalization…
Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
Query Expansion (QE) improves retrieval performance by enriching queries with related terms. Recently, Large Language Models (LLMs) have been used for QE, but existing methods face a trade-off: generating diverse terms boosts performance…
This paper proposes an extension of regression trees by quadratic unconstrained binary optimization (QUBO). Regression trees are very popular prediction models that are trainable with tabular datasets, but their accuracy is insufficient…
Craig interpolation has emerged as an effective means of generating candidate program invariants. We present interpolation procedures for the theories of Presburger arithmetic combined with (i) uninterpreted predicates (QPA+UP), (ii)…
We study the complexity of proof systems augmenting resolution with inference rules that allow, given a formula $\Gamma$ in conjunctive normal form, deriving clauses that are not necessarily logically implied by $\Gamma$ but whose addition…
Fisher Discriminant Analysis (FDA) is one of the essential tools for feature extraction and classification. In addition, it motivates the development of many improved techniques based on the FDA to adapt to different problems or data types.…
This note discusses the problem of choosing between hypotheses in a situation with many, correlated non-normal variables. A new method is introduced to shrink the many variables into a smaller subset of variables with zero mean, unit…
This paper extends the work of Gottlob, Lee, and Valiant (PODS 2009)[GLV], and considers worst-case bounds for the size of the result Q(D) of a conjunctive query Q to a database D given an arbitrary set of functional dependencies. The…
Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the…
Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications. In recent years, multivariate false discovery rate (FDR) controlling methods have emerged,…
We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…
In this paper we extend the new family of (quantitative) Belief Conditioning Rules (BCR) recently developed in the Dezert-Smarandache Theory (DSmT) to their qualitative counterpart for belief revision. Since the revision of quantitative as…
In this paper we extend the notion of ``filtration-consistent nonlinear expectation" (or "${\cal F}$-consistent nonlinear expectation") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We…
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence…
Dispersive sum rules constitute long-standing tools for extracting hadron features from QCD. We estimate the systematic uncertainties induced by assuming quark-hadron duality and improve the accuracy of the resulting predictions by…
Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for post-training large language models (LLMs) on complex reasoning tasks. Yet, the conditions under which RLVR yields robust generalization remain…