Related papers: A skew true INAR(1) process with application
We present the first algorithm for computing class groups and unit groups of arbitrary number fields that provably runs in probabilistic subexponential time, assuming the Extended Riemann Hypothesis (ERH). Previous subexponential algorithms…
We consider a class of step skew product systems of interval diffeomorphisms over shift operators, as a means to study random compositions of interval diffeomorphisms. The class is chosen to present in a simplified setting intriguing…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…
We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularization. While related inequalities appear in the literature, we…
Stochastic processes defined on integer valued state spaces are popular within the physical and biological sciences. These models are necessary for capturing the dynamics of small systems where the individual nature of the populations…
We consider the problem of threshold estimation for autoregressive time series with a "space switching" in the situation, when the regression is nonlinear and the innovations have a smooth, possibly non Gaussian, probability density.…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
We introduce a neural network architecture to solve inverse problems linked to a one-dimensional integral operator. This architecture is built by unfolding a forward-backward algorithm derived from the minimization of an objective function…
The paper focuses on the numerical approximation of nabla fractional order systems with the conditions of nonzero initial instant and nonzero initial state. First, the inverse nabla Laplace transform is developed and the equivalent infinite…
In [C.W. Gear, T.J. Kaper, I.G. Kevrekidis, and A. Zagaris, Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, SIAM J. Appl. Dyn. Syst. 4 (2005) 711-732], we developed a class of iterative algorithms within the…
By considering an empirical approximation, and a new class of operators that we will call walking operators, we construct, for any positive ND-toeplitz matrix, an infinite in all dimensions matrix, for which the inverse approximates the…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…
Latency and efficiency issues are often overlooked when evaluating IR models based on Pretrained Language Models (PLMs) in reason of multiple hardware and software testing scenarios. Nevertheless, efficiency is an important part of such…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
The purpose of this paper is to study the dynamical behavior of the sequence produced by a forward-backward algorithm involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
We formulate a coherent approach to signals and systems theory on time scales. The two derivatives from the time-scale calculus are used, i.e., nabla (forward) and delta (backward), and the corresponding eigenfunctions, the so-called nabla…
A method for nonlinear topology identification is proposed, based on the assumption that a collection of time series are generated in two steps: i) a vector autoregressive process in a latent space, and ii) a nonlinear, component-wise,…