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In this paper we make a theoretical analysis of the convergence rates of Kaczmarz and Extended Kaczmarz projection algorithms for some of the most practically used control sequences. We first prove an at least linear convergence rate for…

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…

The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…

In this paper, we prove the validity of the Edgeworth expansion of the Discrete Fourier transforms of some linear time series. This result is applied to approach moments of non linear functionals of the periodogram. As an illustration, we…

This article considers to model large-dimensional matrix time series by introducing a regression term to the matrix factor model. This is an extension of classic matrix factor model to incorporate the information of known factors or useful…

The problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise is…

We deal with the problem of the mean square optimal estimation of linear transformations of the unobserved values of a continuous time stochastic process with periodically correlated increments. Estimates are based on observations of the…

Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…

A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…

This paper deals with the proportional hazards model proposed by D. R. Cox in a high-dimensional and sparse setting for a regression parameter. To estimate the regression parameter, the Dantzig selector is applied. The variable selection…

Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…

We propose an asympotically optimal choice of shared concentrated real poles of a family of rational approximants of time-dependent exponential functions $\exp(-tz)$ for $z \geq 0$ and $t$ in a positive time interval $T$. Our result extends…

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction…

Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…

We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This…