arXiv research

Improved spectral methods of moments for robust latent variable model learning.

In this paper, we study the confounder detection problem in the linear model, where the target variable $Y$ is predicted using its $n$ potential causes $X_n=(x_1,...,x_n)^T$. Based on an assumption of rotation invariant generating process of the model, recent study shows that the spectral measure induced by the regress…

A method learns representations for conditional moment models with controlled ill-posedness.

Paper provides unbiased spectral moment estimates from finite data.

Spectral learning extends matrix methods to tensors for better latent variable modeling.

Optimizes graph spectral density learning for large networks.

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 technique yields consistent parameter estimates from low-order observable moments, wit…

Graph spectra have been successfully used to classify network types, compute the similarity between graphs, and determine the number of communities in a network. For large graphs, where an eigen-decomposition is infeasible, iterative moment matched approximations to the spectra and kernel smoothing are typically used. …

New method estimates log-determinant using trace powers, avoiding classical limitations.

In this paper, we propose guaranteed spectral methods for learning a broad range of topic models, which generalize the popular Latent Dirichlet Allocation (LDA). We overcome the limitation of LDA to incorporate arbitrary topic correlations, by assuming that the hidden topic proportions are drawn from a flexible class o…

Nonparametric models are versatile, albeit computationally expensive, tool for modeling mixture models. In this paper, we introduce spectral methods for the two most popular nonparametric models: the Indian Buffet Process (IBP) and the Hierarchical Dirichlet Process (HDP). We show that using spectral methods for the in…

We propose a method of moments (MoM) algorithm for training large-scale implicit generative models. Moment estimation in this setting encounters two problems: it is often difficult to define the millions of moments needed to learn the model parameters, and it is hard to determine which properties are useful when specif…

Study heavy-tailed weights' impact on neural network's spectral distribution.

Study spectral density of neural networks using resolvent method.

New model detects communities in network data from edge nominations.

We describe the cohomology of a specific type of foliation on complex manifolds.

New algorithm for robust regression with subgaussian error bound.

Study finds the minimum number of finite Gaussian mixtures for best approximation.

New method identifies latent treatment effects from proxy models.

New algorithm learns two-layer neural networks under symmetric input distributions.

Study on estimating rank-one tensors in noisy data with heavy tails.

Empirical moment matrix reveals properties of point clouds.

Random walks on hyperbolic spaces show linear growth in translation lengths.

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 problem, based on the eigenvectors of both the second order moment matrix and t…

Spectral methods simplify data analysis, improving accuracy and stability.

We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing, recommendation systems, and learning Boolean functions. The existing solutions e…

Spectral method speeds fitting of binary time series models.

Corrected moment-based methods improve inference in topic model regression.

New estimator tackles multi-task linear regression with outliers, avoiding eigenvalue lower bounds.

We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the…

Paper improves spectral learning of HMMs to avoid local optima and improve robustness.

New Fourier transform method handles missing data and asynchronous observations.

We consider the problem of training input-output recurrent neural networks (RNN) for sequence labeling tasks. We propose a novel spectral approach for learning the network parameters. It is based on decomposition of the cross-moment tensor between the output and a non-linear transformation of the input, based on score …

Estimates MLDS using tensor decomposition, improving upon existing methods.

The paper calculates quantum cohomology for coadjoint orbits and Hamiltonian groups.

Develops a new method to compare data distributions on manifolds.

Develops MENT for interpreting and detecting changes in network trajectories.

Study of multi-armed bandits with state-switching rewards using Markov models.

New insights into spectral statistics of sample covariance matrix for stable linear systems.

Efficiently factorize tensors in streaming data with coreset selection.

We give an identification of the triple reduced product of three coadjoint orbits in SU(3) with a space of Hitchin pairs over a genus 0 curve with three punctures, where the residues of the Higgs field at the punctures are constrained to lie in fixed coadjoint orbits. Using spectral curves for the corresponding Hitchin…

Study examines large deviations in random walks on hyperbolic spaces.

The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power …

Study of asymmetric rank-one tensor models with non-Gaussian noise.

In this paper we consider dividend problem for an insurance company whose risk evolves as a spectrally negative Lévy process (in the absence of dividend payments) when Parisian delay is applied. The objective function is given by the cumulative discounted dividends received until the moment of ruin when so-called barri…

We discuss a certain Riemannian metric, related to the toric Kahler-Einstein equation, that is associated in a linearly-invariant manner with a given log-concave measure in R^n. We use this metric in order to bound the second derivatives of the solution to the toric Kahler-Einstein equation, and in order to obtain spec…

Fast simulates Volterra processes using RFF, focusing on S-fBM.

Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant spectrum of the Laplace operator acting on smooth functions on (O,g) determines the moment polytope of O, and hence by Delzant's theorem det…