Related papers: A moment-matching Ferguson and Klass algorithm
Low-rank approximation and column subset selection are two fundamental and related problems that are applied across a wealth of machine learning applications. In this paper, we study the question of socially fair low-rank approximation and…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
We report on a global CKM matrix analysis taking into account most recent experimental and theoretical results. The statistical framework (Rfit) developed in this paper advocates formal frequentist statistics. Other approaches, such as…
Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…
Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the…
In finite samples, the use of a slightly endogenous but highly relevant instrument can reduce mean-squared error (MSE). Building on this observation, I propose a novel moment selection procedure for GMM -- the Focused Moment Selection…
We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard…
Classification is a common task in machine learning. Random features (RFs) stand as a central technique for scalable learning algorithms based on kernel methods, and more recently proposed optimized random features, sampled depending on the…
This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments…
Stochastic approximation algorithms are iterative procedures which are used to approximate a target value in an environment where the target is unknown and direct observations are corrupted by noise. These algorithms are useful, for…
Time series foundation models (TSFMs) have recently gained significant attention due to their strong zero-shot capabilities and widespread real-world applications. Such models typically require a computationally costly pre-training on…
Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where…
It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…
We introduce a notion of vague convergence for random marked metric measure spaces. Our main result shows that convergence of the moments of order $k \ge 1$ of a random marked metric measure space is sufficient to obtain its vague…
We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional…
Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…
This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
We present flow matching for reaction coordinates (FMRC), a novel deep learning algorithm designed to identify optimal reaction coordinates (RC) in biomolecular reversible dynamics. FMRC is based on the mathematical principles of…