Related papers: Supplementary material for Uncorrected least-squar…

Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…

In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear)…

Let $\mathbf{P}=\{ p_1, p_2, \ldots p_n \}$ and $\mathbf{Q} = \{ q_1, q_2 \ldots q_m \}$ be two point sets in an arbitrary metric space. Let $\mathbf{A}$ represent the $m\times n$ pairwise distance matrix with $\mathbf{A}_{i,j} = d(p_i,…

The least trimmed squares (LTS) estimator is a renowned robust alternative to the classic least squares estimator and is popular in location, regression, machine learning, and AI literature. Many studies exist on LTS, including its…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…

We present an algorithm for skill discovery from expert demonstrations. The algorithm first utilizes Large Language Models (LLMs) to propose an initial segmentation of the trajectories. Following that, a hierarchical variational inference…

We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.

This paper presents a real-time computational framework for multi-node distributed optimization by extending the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. Our approach integrates adjoint sequential…

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.

We amend the statement of point~(i) in Theorem~1.3 in arxiv:0901.1022 and supply the additional arguments and minor changes for the results that depend on it. We also seize the occasion and generalize to non-finitely generated lattices.

This paper revisits the temporal difference (TD) learning algorithm for the policy evaluation tasks in reinforcement learning. Typically, the performance of TD(0) and TD($\lambda$) is very sensitive to the choice of stepsizes. Oftentimes,…

In this paper, we propose a new nonparametric estimator of time-varying forecast combination weights. When the number of individual forecasts is small, we study the asymptotic properties of the local linear estimator. When the number of…

We study inhomogeneous heat equation with inverse square potential, namely, \[\partial_tu + \mathcal{L}_a u= \pm |\cdot|^{-b} |u|^{\alpha}u,\] where $\mathcal{L}_a=-\Delta + a |x|^{-2}.$ We establish some fixed-time decay estimate for…

In this paper, we propose a new algorithm for the estimation of multiple time delays (TDs). Since a TD is a fundamental spatial cue for sensor array signal processing techniques, many methods for estimating it have been studied. Most of…

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models,…

This article considers the error analysis of finite element discretizations and adaptive mesh refinement procedures for nonlocal dynamic contact and friction, both in the domain and on the boundary. For a large class of parabolic…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

The threshold estimate derived in previous versions of this paper was incorrect; this note explains the flaw. A new proof is discussed in arXiv:0809.5063.

The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a…

The temporal-difference methods TD($\lambda$) and Sarsa($\lambda$) form a core part of modern reinforcement learning. Their appeal comes from their good performance, low computational cost, and their simple interpretation, given by their…