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We obtain two results about the proof complexity of deep inference: 1) deep-inference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin extension rule or with the substitution rule; 2) there are…
In this thesis, we develop a comprehensive account of the expressive power, modelling efficiency, and performance advantages of so-called trading agents (i.e., Deep Soft Recurrent Q-Network (DSRQN) and Mixture of Score Machines (MSM)),…
This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present in the given input formula $\phi^*$. The first enhancement…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
This paper introduces a fuzzy reinforcement learning framework, Enhanced-FQL($\lambda$), that integrates novel Fuzzified Eligibility Traces (FET) and Segmented Experience Replay (SER) into fuzzy Q-learning with the Fuzzified Bellman…
We determine the minimal number of variables $\Gamma^*(d, K)$ which guarantees a nontrivial solution for every additive form of degree $d=4$ over the four ramified quadratic extensions $\mathbb{Q}_2(\sqrt{2}), \mathbb{Q}_2(\sqrt{10}),…
Novel significance tests are proposed for the quite general additive concurrent model formulation without the need of model, error structure preliminary estimation or the use of tuning parameters. Making use of the martingale difference…
In this paper we introduce a novel procedure for improving multiple testing procedures (MTPs) under scenarios when the null hypothesis $p$-values tend to be stochastically larger than standard uniform (referred to as 'inflated'). An…
Interpretability is having an increasingly important role in the design of machine learning algorithms. However, interpretable methods tend to be less accurate than their black-box counterparts. Among others, DNFs (Disjunctive Normal Forms)…
Quantified Conflict Driven Clause Leaning (QCDCL) is one of the main approaches to solving Quantified Boolean Formulas (QBF). Cube-learning is employed in this approach to ensure that true formulas can be verified. Dependency Schemes help…
Empirical regression discontinuity (RD) studies often include covariates in their specifications to increase the precision of their estimates. In this paper, we propose a novel class of estimators that use such covariate information more…
We propose a sequential, anytime-valid method to test the conditional independence of a response $Y$ and a predictor $X$ given a random vector $Z$. The proposed test is based on e-statistics and test martingales, which generalize likelihood…
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…
Motivated by the gene co-expression pattern analysis, we propose a novel sample quantile-based contingency (squac) statistic to infer quantile associations conditioning on covariates. It features enhanced flexibility in handling variables…
This paper shows that sequential statistical analysis techniques can be generalised to the problem of selecting between alternative forecasting methods using scoring rules. A return to basic principles is necessary in order to show that…
This article presents differential equations and solution methods for the functions of the form $Q(x) = F^{-1}(G(x))$, where $F$ and $G$ are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
We develop generalized approach to obtaining Edgeworth expansions for $t$-statistics of an arbitrary order using computer algebra and combinatorial algorithms. To incorporate various versions of mean-based statistics, we introduce Adjusted…
Guided exploration with expert demonstrations improves data efficiency for reinforcement learning, but current algorithms often overuse expert information. We propose a novel algorithm to speed up Q-learning with the help of a limited…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…