Related papers: Autoregressive Optimal Transport Models
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
In time-series analyses, particularly for finance, generalized autoregressive conditional heteroscedasticity (GARCH) models are widely applied statistical tools for modelling volatility clusters (i.e., periods of increased or decreased…
Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range…
Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…
We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…
We propose a framework for constructing microscopic traffic models from microscopic acceleration patterns that can in principle be experimental measured and proper averaged. The exact model thus obtained can be used to justify the…
This paper presents a decentralized control framework for distribution matching in multi-agent systems (MAS), where agents collectively achieve a prescribed terminal spatial distribution. The problem is formulated using optimal transport…
This paper presents an innovative extension of spatial autoregressive (SAR) models, introducing spatial coefficients specific to each spatial region that evolve over time. The proposed estimation methodology covers both homoscedastic and…
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability…
Generative modeling of high-dimensional data is a key problem in machine learning. Successful approaches include latent variable models and autoregressive models. The complementary strengths of these approaches, to model global and local…
We propose Significance-Offset Convolutional Neural Network, a deep convolutional network architecture for regression of multivariate asynchronous time series. The model is inspired by standard autoregressive (AR) models and gating…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
We review autoregressive models for the analysis of multivariate count time series. In doing so, we discuss the choice of a suitable distribution for a vectors of count random variables. This review focus on three main approaches taken for…
Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting…
We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The…
Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature…
This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…
In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…
The univariate integer-valued time series has been extensively studied, but literature on multivariate integer-valued time series models is quite limited and the complex correlation structure among the multivariate integer-valued time…