Related papers: Error bounds of constant gain least-mean-squares a…
In learning to rank area, industry-level applications have been dominated by gradient boosting framework, which fits a tree using least square error principle. While in classification area, another tree fitting principle, weighted least…
Approximate circuit design has gained significance in recent years targeting error tolerant applications. In this paper, we first demonstrate that the commonly used assumption that the inputs to the adder are uniformly distributed results…
We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory. Our upper bound relies on a generalization of…
This paper introduces a novel adaptive framework for processing dynamic flow signals over simplicial complexes, extending classical least-mean-squares (LMS) methods to high-order topological domains. Building on discrete Hodge theory, we…
The distortion-rate performance of certain randomly-designed scalar quantizers is determined. The central results are the mean-squared error distortion and output entropy for quantizing a uniform random variable with thresholds drawn…
The use of momentum in stochastic optimization algorithms has shown empirical success across a range of machine learning tasks. Recently, a new class of stochastic momentum algorithms has emerged within the Linear Minimization Oracle (LMO)…
For many inference problems in statistics and econometrics, the unknown parameter is identified by a set of moment conditions. A generic method of solving moment conditions is the Generalized Method of Moments (GMM). However, classical GMM…
We consider a distributed multi-agent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
This paper discusses the error estimation of the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of block-structured Markov chains (BSMCs) in continuous time. We first derive upper bounds…
We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalization matrices. Such a setup has important applications in…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
The article examines in some detail the convergence rate and mean-square-error performance of momentum stochastic gradient methods in the constant step-size and slow adaptation regime. The results establish that momentum methods are…
This paper presents new results on linear transceiver designs in a multiple-input-multiple-output (MIMO) link. By considering the minimal total mean-square error (MSE) criterion, we prove that the robust optimal linear transceiver design…
We consider Bayesian inference of signals with vector-valued entries. Extending concentration techniques from the mathematical physics of spin glasses, we show that the matrix-valued minimum mean-square error concentrates when the size of…
We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…
We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can…
There is growing interest in improving our algorithmic understanding of fundamental statistical problems such as mean estimation, driven by the goal of understanding the limits of what we can extract from valuable data. The state of the art…
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 considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…