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Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter…
We establish area theorems for iterative detection over coded linear systems (including multiple-input multipleoutput (MIMO) channels, inter-symbol-interference (ISI) channels, and orthogonal frequency-division multiplexing (OFDM) systems).…
This paper presents a system identification framework -- inspired by multi-task learning -- to estimate the dynamics of a given number of linear time-invariant (LTI) systems jointly by leveraging structural similarities across the systems.…
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…
We study algorithms for online linear optimization in Hilbert spaces, focusing on the case where the player is unconstrained. We develop a novel characterization of a large class of minimax algorithms, recovering, and even improving,…
We tackle the Few-Shot Open-Set Recognition (FSOSR) problem, i.e. classifying instances among a set of classes for which we only have a few labeled samples, while simultaneously detecting instances that do not belong to any known class. We…
System identification is a fundamental problem in reinforcement learning, control theory and signal processing, and the non-asymptotic analysis of the corresponding sample complexity is challenging and elusive, even for linear time-varying…
This paper considers the problem of system identification (ID) of linear and nonlinear non-autonomous systems from noisy and sparse data. We propose and analyze an objective function derived from a Bayesian formulation for learning a hidden…
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
This paper establishes problem-specific sample complexity lower bounds for linear system identification problems. The sample complexity is defined in the PAC framework: it corresponds to the time it takes to identify the system parameters…
In this paper, a low complexity time domain semi-blind algorithm is proposed to estimate and track the time varying MIMO OFDM channels. First, the proposed least mean squares (LMS) based algorithm is developed for the training mode and then…
The partial least squares (PLS) is a popular modeling technique commonly used in social sciences. The traditional PLS algorithm deals with variables measured on interval scales while data are often collected on ordinal scales: a…
Systems with stochastic time delay between the input and output present a number of unique challenges. Time domain noise leads to irregular alignments, obfuscates relationships and attenuates inferred coefficients. To handle these…
The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical…
An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the…
In the linear minimum mean square error (LMMSE) estimation for orthogonal frequency division multiplexing (OFDM) systems, the problem about the determination of the algorithm's parameters, especially those related with channel frequency…
Linear least squares (LLS) is perhaps the most common method of data analysis, dating back to Legendre, Gauss and Laplace. Framed as linear regression, LLS is also a backbone of mathematical statistics. Here we report on an unexpected new…
We propose a rate optimal estimator for the linear regression model on network data with interacted (unobservable) individual effects. The estimator achieves a faster rate of convergence $N$ compared to the standard estimators' $\sqrt{N}$…
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…