Related papers: A moment-matching Ferguson and Klass algorithm
Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay…
Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
Model counting is a fundamental problem which has been influential in many applications, from artificial intelligence to formal verification. Due to the intrinsic hardness of model counting, approximate techniques have been developed to…
Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have…
The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in.…
Recently there has been much interest in graph-based learning, with applications in collaborative filtering for recommender networks, link prediction for social networks and fraud detection. These networks can consist of millions of…
We combine two advanced ideas widely used in optimization for machine learning: shuffling strategy and momentum technique to develop a novel shuffling gradient-based method with momentum, coined Shuffling Momentum Gradient (SMG), for…
Let $\tau$ and $\sigma$ be two polygonal curves in $\mathbb{R}^d$ for any fixed $d$. Suppose that $\tau$ and $\sigma$ have $n$ and $m$ vertices, respectively, and $m\le n$. While conditional lower bounds prevent approximating the Fr\'echet…
The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
Since the late 1950's when quasi-Newton methods first appeared, they have become one of the most widely used and efficient algorithmic paradigms for unconstrained optimization. Despite their immense practical success, there is little theory…
Randomized algorithms are overwhelming methods for low-rank approximation that can alleviate the computational expenditure with great reliability compared to deterministic algorithms. A crucial thought is generating a standard Gaussian…
Quantum algorithms typically demand prohibitively complicated circuits to solve practical problems. Previous studies have shown that classical randomness can accelerate some specific quantum algorithms. In this work, we introduce the…
A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning problems. In practice, to ensure high quality…
This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of…
In paper I of this two-stage exposition, we introduced finite-range Coulomb gas (FRCG) models, and developed an integral-equation framework for their study. We obtained exact analytical results for $d = 0,1,2 $, where d denotes the range of…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet…