Related papers: Linear Prediction of Long-Range Dependent Time Ser…

An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated.…

Despite recent advances in training recurrent neural networks (RNNs), capturing long-term dependencies in sequences remains a fundamental challenge. Most approaches use backpropagation through time (BPTT), which is difficult to scale to…

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the…

To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…

LLMs are statistical models of language learning through stochastic gradient descent with a next token prediction objective. Prompting a popular view among AI modelers: LLMs are just next token predictors. While LLMs are engineered using…

We aim at improving reasoning on inconsistent and uncertain data. We focus on knowledge-graph data, extended with time intervals to specify their validity, as regularly found in historical sciences. We propose principles on semantics for…

Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…

We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models.…

We apply methods from randomized numerical linear algebra (RandNLA) to develop improved algorithms for the analysis of large-scale time series data. We first develop a new fast algorithm to estimate the leverage scores of an autoregressive…

We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…

In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the…

Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a "next-generation"…

Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…

In prevalent cohort studies with follow-up, the time-to-event outcome is subject to left truncation leading to selection bias. For estimation of the distribution of time-to-event, conventional methods adjusting for left truncation tend to…

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…

Sequence modeling faces challenges in capturing long-range dependencies across diverse tasks. Recent linear and transformer-based forecasters have shown superior performance in time series forecasting. However, they are constrained by their…

This paper introduces a semiparametric regression estimator of the memory parameter for long-memory time series process. It is based on the regression in a neighborhood of the zero-frequency of the periodogram averaged over epochs. The…