相关论文: Hierarchical Methods of Moments

Mixture models are a fundamental tool in applied statistics and machine learning for treating data taken from multiple subpopulations. The current practice for estimating the parameters of such models relies on local search heuristics…

Fluid dynamical simulations are often performed using cheap macroscopic models like the Euler equations. For rarefied gases under near-equilibrium conditions, however, macroscopic models are not sufficiently accurate and a simulation using…

Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this paper. The hybrid methods are particularly efficient when describing the…

Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…

Network-theoretic tools contribute to understanding real-world system dynamics, e.g., in wildlife conservation, epidemics, and power outages. Network visualization helps illustrate structural heterogeneity; however, details about…

Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, motif finding algorithms of increasingly high performance are required to process the big…

We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…

Hierarchical models allow for heterogeneous behaviours in a population while simultaneously borrowing estimation strength across all subpopulations. Unfortunately, existing likelihood-based methods for fitting hierarchical models have high…

We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an…

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

While Spectral Methods have long been used for Principal Component Analysis, this survey focusses on work over the last 15 years with three salient features: (i) Spectral methods are useful not only for numerical problems, but also discrete…

We present a novel algorithm for learning the parameters of hidden Markov models (HMMs) in a geometric setting where the observations take values in Riemannian manifolds. In particular, we elevate a recent second-order method of moments…

Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…

Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately…

This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…

Motivated by the sampling problems and heterogeneity issues common in high- dimensional big datasets, we consider a class of discordant additive index models. We propose method of moments based procedures for estimating the indices of such…

Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…

In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…