Related papers: A Generalized Markov-Chain Modelling Approach to $…

Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a…

We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…

This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification,…

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of…

Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…

This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…

We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…

We extend Hoeffding's lemma to general-state-space and not necessarily reversible Markov chains. Let $\{X_i\}_{i \ge 1}$ be a stationary Markov chain with invariant measure $\pi$ and absolute spectral gap $1-\lambda$, where $\lambda$ is…

This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…

We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…

In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…

Online (also called "recursive" or "adaptive") estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modelling. In this work, we propose an online parameter estimation algorithm that…

Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…

We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, relying on recent results of gradient flow systems. These…

We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient…

In this paper some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias…

In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains…

We study stochastic approximation procedures for approximately solving a $d$-dimensional linear fixed point equation based on observing a trajectory of length $n$ from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the…

In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention…

Evolution Strategies (ES) are stochastic derivative-free optimization algorithms whose most prominent representative, the CMA-ES algorithm, is widely used to solve difficult numerical optimization problems. We provide the first rigorous…