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This article is concerned with the identification of autoregressive with exogenous inputs (ARX) models. Most of the existing approaches like prediction error minimization and state-space framework are widely accepted and utilized for the…

Autoregressive (AR) approaches, which represent images as sequences of discrete tokens from a finite codebook, have achieved remarkable success in image generation. However, the quantization process and the limited codebook size inevitably…

This work aims at a challenging task: human action-reaction synthesis, i.e., generating human reactions conditioned on the action sequence of another person. Currently, autoregressive modeling approaches with vector quantization (VQ) have…

Route alignment design in surveying and transportation engineering frequently involves fixed waypoint constraints, where a path must precisely traverse specific coordinates. While existing literature primarily relies on geometric…

In this paper, we give a AR$(1)$ type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, we derive continuous time algebraic Riccati equations for the parameter matrix…

A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by…

We develop a new methodology for the fitting of nonstationary time series that exhibit nonlinearity, asymmetry, local persistence and changes in location scale and shape of the underlying distribution. In order to achieve this goal, we…

We consider the variant of stochastic homogenization theory introduced in [X. Blanc, C. Le Bris and P.-L. Lions, C. R. Acad. Sci. Serie I 2006 and Journal de Mathematiques Pures et Appliquees 2007]. The equation under consideration is a…

Class-conditional generative models have emerged as accurate and robust classifiers, with diffusion models demonstrating clear advantages over other visual generative paradigms, including autoregressive (AR) models. In this work, we revisit…

This paper studies the state estimation problem of linear discrete-time systems with stochastic unknown inputs. The unknown input is a wide-sense stationary process while no other prior informaton needs to be known. We propose an…

Deep latent variable models, trained using variational autoencoders or generative adversarial networks, are now a key technique for representation learning of continuous structures. However, applying similar methods to discrete structures,…

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…

While the Vector Autoregression (VAR) model has received extensive attention for modelling complex time series, quantile VAR analysis remains relatively underexplored for high-dimensional time series data. To address this disparity, we…

Time series of matrix-valued data are increasingly available in various areas including economics, finance, social science, among others. These data may shed light on the inter-dynamical relationships between two sets of attributes, for…

A Poisson autoregressive (PAR) model accounting for discreteness and autocorrelation of count time series data is typically estimated in the state-space modelling framework through extended Kalman filter. However, because of the complex…

We propose an approach for improving sequence modeling based on autoregressive normalizing flows. Each autoregressive transform, acting across time, serves as a moving frame of reference, removing temporal correlations, and simplifying the…

This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…

The Variational Autoencoder (VAE) is a popular and powerful model applied to text modelling to generate diverse sentences. However, an issue known as posterior collapse (or KL loss vanishing) happens when the VAE is used in text modelling,…

Tiny Recursive Models (TRMs) have recently demonstrated remarkable performance on ARC-AGI, showing that very small models can compete against large foundation models through a two-step refinement mechanism that updates an internal reasoning…

Autoregressive language modeling (ALM) have been successfully used in self-supervised pre-training in Natural language processing (NLP). However, this paradigm has not achieved comparable results with other self-supervised approach in…