Related papers: Finite time large deviations via matrix product st…

We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…

High-dimensional time series prediction is needed in applications as diverse as demand forecasting and climatology. Often, such applications require methods that are both highly scalable, and deal with noisy data in terms of corruptions or…

We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…

First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…

We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer…

We formulate a data-driven method for constructing finite volume discretizations of a dynamical system's underlying Continuity / Fokker-Planck equation. A method is employed that allows for flexibility in partitioning state space,…

We introduce a class of Bayesian matrix dynamic factor models that accommodates time-varying volatility, outliers, and cross-sectional correlation in the idiosyncratic components. For model comparison, we employ an importance-sampling…

Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult…

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…

We consider the dynamics of a linear stochastic approximation algorithm driven by Markovian noise, and derive finite-time bounds on the moments of the error, i.e., deviation of the output of the algorithm from the equilibrium point of an…

Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced…

We propose a novel framework in high-dimensional factor models to simultaneously analyse multiple tensor time series, each with potentially different tensor orders and dimensionality. The connection between different tensor time series is…

In this paper the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum seeking algorithm. We propose to use a suitable…

A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…

This paper presents extensions of finite-time stability results to some prototypical adaptive control and estimation frameworks. First, we present a novel scheme of online parameter estimation that guarantees convergence of the estimation…

Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…

We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…

In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…