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Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…

Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial…

The accumulation of time-series data and the absence of labels make time-series Anomaly Detection (AD) a self-supervised deep learning task. Single-normality-assumption-based methods, which reveal only a certain aspect of the whole…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

In this contribution we introduce weakly locally stationary time series through the local approximation of the non-stationary covariance structure by a stationary one. This allows us to define autoregression coefficients in a non-stationary…

High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper focuses on high-dimensional time series and on the different regularized estimation procedures proposed for…

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…

We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…

Multi-criteria Analysis (MCA) is used to rank alternatives based on various criteria. Key MCA methods, such as Multiple Criteria Decision Making (MCDM) methods, estimate parameters for criteria to compute the performance of each…

In this paper, we propose a novel variable selection approach in the framework of sparse high-dimensional GLARMA models. It consists in combining the estimation of the autoregressive moving average (ARMA) coefficients of these models with…

This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has…

We consider the estimation of the transition matrix in the high-dimensional time-varying vector autoregression (TV-VAR) models. Our model builds on a general class of locally stationary VAR processes that evolve smoothly in time. We propose…

Modern data analysis across diverse disciplines increasingly relies on time series. Many of these datasets exhibit cyclostationarity, where patterns approximately repeat in a regular manner, often across multiple time scales, such as daily,…

For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple…

We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable L\'evy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of…

Most of current anomaly detection models assume that the normal pattern remains same all the time. However, the normal patterns of Web services change dramatically and frequently. The model trained on old-distribution data is outdated after…

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p-k)-variate stationary time series. The aim is then to estimate the unmixing…

Traditional regression models assume stationary relationships between predictors and responses, failing to capture the spatial heterogeneity present in many environmental, epidemiological, and ecological processes. To address this…

We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement…

This article addresses online variational estimation in parametric state-space models. We propose a new procedure for efficiently computing the evidence lower bound and its gradient in a streaming-data setting, where observations arrive…