Related papers: Rademacher complexity of stationary sequences

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

We extend well-known comparative results under expected utility to models of non-expected utility by providing novel conditions on local utility functions. We illustrate how our results parallel, and are distinct from, existing results for…

A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…

This paper presents an approach to modeling progressive event-history data when the overall objective is prediction based on time-dependent covariates. This approach does not model the hazard function directly. Instead, it models the…

We study the sequential empirical process indexed by general function classes and its smoothed set-indexed analogue. Sufficient conditions for asymptotic equicontinuity are provided for nonstationary arrays of time series. This yields…

This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance…

Producing probabilistic forecasts for large collections of similar and/or dependent time series is a practically relevant and challenging task. Classical time series models fail to capture complex patterns in the data, and multivariate…

The question whether a time series behaves as a random walk or as a station- ary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This paper studies the problem to…

Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…

In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample (e.g., metric learning, ranking). We…

While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by non-stationarity. We develop a fast and effective approach to allow for non-stationarity in the…

Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…

Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…

We consider the problem of uncertainty quantification for prediction in a time series: if we use past data to forecast the next time point, can we provide valid prediction intervals around our forecasts? To avoid placing distributional…

One of the fundamental challenges in the deep learning community is to theoretically understand how well a deep neural network generalizes to unseen data. However, current approaches often yield generalization bounds that are either too…

In this paper I provide simple and easily verifiable conditions under which a strong form of stochastic equicontinuity holds in a wide variety of modern time series models. In contrast to most results currently available in the literature,…

We develop an anomaly-detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly-free inputs (i.e., those…

While we are usually focused on forecasting future values of time series, it is often valuable to additionally predict their entire probability distributions, e.g. to evaluate risk, Monte Carlo simulations. On example of time series of…

In several real world applications, machine learning models are deployed to make predictions on data whose distribution changes gradually along time, leading to a drift between the train and test distributions. Such models are often…

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…