Related papers: On Distributional Autoregression and Iterated Tran…
This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
We characterize recurrence and transience of nonnegative multivariate autoregressive processes of order one with random contractive coefficient matrix, of subcritical multitype Galton-Watson branching processes in random environment with…
We present here a general framework and a specific algorithm for predicting the destination, route, or more generally a pattern, of an ongoing journey, building on the recent work of [Y. Lassoued, J. Monteil, Y. Gu, G. Russo, R. Shorten,…
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…
A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…
Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…
Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…
We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Inference-time scaling methods rely on Process Reward Models (PRMs), which are often poorly calibrated and overestimate success probabilities. We propose, to our knowledge, the first use of conditional optimal transport for calibrating…
We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is H\"{o}lder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
Stochastic optimization methods such as mirror descent have wide applications due to low computational cost. Those methods have been well studied under assumption of the independent and identical distribution, and usually achieve sublinear…
We consider a classical First-order Vector AutoRegressive (VAR(1)) model, where we interpret the autoregressive interaction matrix as influence relationships among the components of the VAR(1) process that can be encoded by a weighted…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
In this paper we study the bicausal optimal transport problem for Markov chains, an optimal transport formulation suitable for stochastic processes which takes into consideration the accumulation of information as time evolves. Our analysis…
In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion…