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We propose three novel consistent specification tests for quantile regression models which generalize former tests in three ways. First, we allow the covariate effects to be quantile-dependent and nonlinear. Second, we allow parameterizing…
Quantile regression is an effective technique to quantify uncertainty, fit challenging underlying distributions, and often provide full probabilistic predictions through joint learnings over multiple quantile levels. A common drawback of…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
We study reinforcement learning (RL) for the same class of continuous-time stochastic linear--quadratic (LQ) control problems as in \cite{huang2024sublinear}, where volatilities depend on both states and controls while states are…
Alleviating overestimation bias is a critical challenge for deep reinforcement learning to achieve successful performance on more complex tasks or offline datasets containing out-of-distribution data. In order to overcome overestimation…
Several combinatorial optimization problems can be solved with NISQ devices once that a corresponding quadratic unconstrained binary optimization (QUBO) form is derived. The aim of this work is to drastically reduce the variables needed for…
The Merge Resolution proof system (M-Res) for QBFs, proposed by Beyersdorff et al. in 2019, explicitly builds partial strategies inside refutations. The original motivation for this approach was to overcome the limitations encountered in…
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…
Quantified Boolean Formula (QBF) is a notoriously hard generalization of \textsc{SAT}, especially from the point of view of parameterized complexity, where the problem remains intractable for most standard parameters. A recent work by…
The random vector of frequencies in a generalized urn model is viewed as conditionally independent random variables, given their sum. Such a representation is exploited to derive Edgeworth expansions for a sum of functions of such…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
Extensions (entropies) play a central role in the theory of hyperbolic conservation laws by providing intrinsic selection criteria for weak solutions. For a given hyperbolic system u_t+f(u)_x=0, a standard approach is to analyze directly…
Accurate band gap prediction in semiconductors is crucial for materials science and semiconductor technology advancements. This paper extends the Perdew-Burke-Ernzerhof (PBE) functional for a wide range of semiconductors, tackling the…
We describe extensions to the siesta density functional theory (dft) code [30], for the simulation of isolated molecules and their absorption spectra. The extensions allow for: - Use of a multi-grid solver for the Poisson equation on a…
Learning from human demonstrations can facilitate automation but is risky because the execution of the learned policy might lead to collisions and other failures. Adding explicit constraints to avoid unsafe states is generally not possible…
The problem of precise evaluation of the perturbative QCD predictions at moderate energies is considered. Substantial renormalization scheme dependence of the perturbative predictions obtained with the conventional renormalization group…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
Conditional independence testing is a key problem required by many machine learning and statistics tools. In particular, it is one way of evaluating the usefulness of some features on a supervised prediction problem. We propose a novel…
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…