Related papers: Learning Without Mixing: Towards A Sharp Analysis …

We consider the problem of estimating the state transition matrix of a linear time-invariant (LTI) system, given access to multiple independent trajectories sampled from the system. Several recent papers have conducted a non-asymptotic…

This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…

Data approximation is essential in fields such as geometric design, numerical PDEs, and curve modeling. Moving Least Squares (MLS) is a widely used method for data fitting; however, its accuracy degrades in the presence of discontinuities,…

For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…

This article deals with asimple issue: if we have grouped data with a binary dependent variable and want to include fixed effects (group specific intercepts) in the specification, is Ordinary Least Squares (OLS) in any way superior to a…

A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…

We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…

The autocovariance least squares (ALS) method is a computationally efficient approach for estimating noise covariances in Kalman filters without requiring specific noise models. However, conventional ALS and its variants rely on the classic…

We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs,…

This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE)…

This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…

Orthogonal least squares (OLS)-type algorithms are efficient in reconstructing sparse signals, which include the well-known OLS, multiple OLS (MOLS) and block OLS (BOLS). In this paper, we first investigate the noiseless exact recovery…

Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…

This paper proposes a method for estimating multiple change points in panel data models with unobserved individual effects via ordinary least-squares (OLS). Typically, in this setting, the OLS slope estimators are inconsistent due to the…

In large-scale data processing scenarios, data often arrive in sequential streams generated by complex systems that exhibit drifting distributions and time-varying system parameters. This nonstationarity challenges theoretical analysis, as…

We consider the question of learning in general topological vector spaces. By exploiting known (or parametrized) covariance structures, our Main Theorem demonstrates that any continuous linear map corresponds to a certain isomorphism of…

This paper develops the non-intrusive formulation of the Least-squares shadowing (LSS) method, for computing the sensitivity of long-time averaged objectives in chaotic dynamical systems. This non-intrusive formulation constrains the…

Linear fixed point equations in Hilbert spaces arise in a variety of settings, including reinforcement learning, and computational methods for solving differential and integral equations. We study methods that use a collection of random…

We propose a block least mean square (LMS) algorithm to monitor the longitudinal power profile of a fiber-optic link through receiver-based digital data from a coherent detector. Compared to the benchmark least squares (LS) method, the…