Related papers: Data-driven Algorithms for signal processing with …
The paper presents linear integral predictors for continuous time high-frequency signals with a a finite spectrum gap. The predictors are based on approximation of a complex valued periodic exponential (complex sinusoid) by rational…
In 2023, the U.S. Food and Drug Administration issued guidance for adjustment of covariates in randomized clinical trials, emphasizing its role in enhancing precision and power through prognostic baseline variables. Despite its potential,…
A unified linear algebraic approach to adaptive signal processing (ASP) is presented. Starting from just Ax=b, key ASP algorithms are derived in a simple, systematic, and integrated manner without requiring any background knowledge to the…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
Adaptive algorithms belong to an important class of algorithms used in radar target detection to overcome prior uncertainty of interference covariance. The contamination of the empirical covariance matrix by the useful signal leads to…
Methods have previously been developed for the approximation of Lyapunov functions using radial basis functions. However these methods assume that the evolution equations are known. We consider the problem of approximating a given Lyapunov…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…
Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like…
Recent research demonstrate that prediction of time series by recurrent neural networks (RNNs) based on the noisy input generates a smooth anticipated trajectory. We examine the internal dynamics of RNNs and establish a set of conditions…
We introduce Active Tuning, a novel paradigm for optimizing the internal dynamics of recurrent neural networks (RNNs) on the fly. In contrast to the conventional sequence-to-sequence mapping scheme, Active Tuning decouples the RNN's…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system's dynamics from experimental data remains a…
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
We propose a data-driven algorithm for the maximum a posteriori (MAP) estimation of stochastic processes from noisy observations. The primary statistical properties of the sought signal is specified by the penalty function (i.e., negative…
In this work, we propose a time-varying wave-shape extraction algorithm based on a modified version of the adaptive non-harmonic model for non-stationary signals. The model codifies the time-varying wave-shape information in the relative…
Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…