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Inference methods in traditional statistics, machine learning and data mining assume that data is generated from an independent and identically distributed (iid) process. Spatial data exhibits behavior for which the iid assumption must be…
We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time…
Spatial correlation in areal unit count data is typically modelled by a set of random effects that are assigned a conditional autoregressive (CAR) prior distribution. The spatial correlation structure implied by this model depends on a…
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…
Generative recommendation (GR) typically encodes behavioral or semantic aspects of item information into discrete tokens, leveraging the standard autoregressive (AR) generation paradigm to make predictions. However, existing methods tend to…
This paper introduces a Threshold Asymmetric Conditional Autoregressive Range (TACARR) formulation for modeling the daily price ranges of financial assets. It is assumed that the process generating the conditional expected ranges at each…
Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such…
Recent technological advances have enabled researchers in a variety of fields to collect accurately geocoded data for several variables simultaneously. In many cases it may be most appropriate to jointly model these multivariate spatial…
The conditional autoregressive model is a routinely used statistical model for areal data that arise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have…
Recent advances in autoregressive (AR) generative models have produced increasingly powerful systems for media synthesis. Among them, next-scale prediction has emerged as a popular paradigm, where models generate images in a coarse-to-fine…
Hierarchical spatial models are very flexible and popular for a vast array of applications in areas such as ecology, social science, public health, and atmospheric science. It is common to carry out Bayesian inference for these models via…
Large sample statistical analysis of threshold autoregressive (TAR) models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we consider a model, driven by Gaussian noise with geometric…
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.…
We show that the mixed causal-noncausal Vector Autoregressive (VAR) processes satisfy the Markov property in both calendar and reverse time. Based on that property, we introduce closed-form formulas of forward and backward predictive…
Conventional wisdom suggests that autoregressive models are used to process discrete data. When applied to continuous modalities such as visual data, Visual AutoRegressive modeling (VAR) typically resorts to quantization-based approaches to…
The classical multilevel model fails to capture the proximity effect in epidemiological studies, where subjects are nested within geographical units. Multilevel Conditional Autoregressive models are alternatives to help explain the spatial…
We present Spanning Tree Autoregressive (STAR) modeling, which can incorporate prior knowledge of images, such as center bias and locality, to maintain sampling performance while also providing sufficiently flexible sequence orders to…
Modeling high-dimensional time series with simple structures is a challenging problem. This paper proposes a network double autoregression (NDAR) model, which combines the advantages of network structure and the double autoregression (DAR)…
Mixed spatial autoregressive (SAR) models with numerical covariates have been well studied. However, as non-numerical data, such as functional data and compositional data, receive substantial amounts of attention and are applied to…
Regression is a fundamental task in machine learning that has garnered extensive attention over the past decades. The conventional approach for regression involves employing loss functions that primarily concentrate on aligning model…