Related papers: On Distributional Autoregression and Iterated Tran…
Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
We consider high-dimensional distribution estimation through autoregressive networks. By combining the concepts of sparsity, mixtures and parameter sharing we obtain a simple model which is fast to train and which achieves state-of-the-art…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
Autoregressive models use chain rule to define a joint probability distribution as a product of conditionals. These conditionals need to be normalized, imposing constraints on the functional families that can be used. To increase…
Reversible Markov chains play a central role in stochastic modelling and in algorithms such as Markov chain Monte Carlo (MCMC). Motivated by the fundamental importance of reversibility in classical settings, this paper develops a…
In this paper we investigate the use of staged tree models for discrete longitudinal data. Staged trees are a type of probabilistic graphical model for finite sample space processes. They are a natural fit for longitudinal data because a…
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the…
Analyzing, understanding, and describing human behavior is advantageous in different settings, such as web browsing or traffic navigation. Understanding human behavior naturally helps to improve and optimize the underlying infrastructure or…
In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study stationarity and ergodicity of nonlinear time series models. Subgeometric ergodicity means that the transition probability…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…
We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many…
This paper considers the problem of randomized influence maximization over a Markovian graph process: given a fixed set of nodes whose connectivity graph is evolving as a Markov chain, estimate the probability distribution (over this fixed…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network…
Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…
The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods…
We investigate the transportation cost-information inequalities for bifurcating Markov chains which are a class of processes indexed by binary tree. These processes provide models for cell growth when each individual in one generation gives…