arXiv research

Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either required strong technical assumptions or were limited to Gaussian distributions with …

Lower bounds on private estimation of Gaussian covariance matrices.

Researchers derived formulas for joint moments of elliptical distributions.

We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime, optimization algorithms can immensely benefit from approximate second order information.…

Estimates true Sharpe ratio of selected assets with various methods.

Paper analyzes SVGD algorithm for non-asymptotic convergence.

New applications of trace embedding lemma show exotic 4-manifolds properties.

Paper studies tensor models using random matrix theory.

Proposes a transfer learning framework for sparse SIMs without raw source data.

This paper tackles efficient and scalable estimation of a complex model involving stochastic linear combinations of non-linear regressions.

We study nonzero-sum hypothesis testing games that arise in the context of adversarial classification, in both the Bayesian as well as the Neyman-Pearson frameworks. We first show that these games admit mixed strategy Nash equilibria, and then we examine some interesting concentration phenomena of these equilibria. Our…

We develop a novel methodology based on the marriage between the Bhattacharyya distance, a measure of similarity across distributions of random variables, and the Johnson-Lindenstrauss Lemma, a technique for dimension reduction. The resulting technique is a simple yet powerful tool that allows comparisons between data-…

We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a $TT^*$ argument, simply by using the $L^2$-boundedness of the Hilbert transform on $\R$, we are able to improve the corresponding $L^2$-restriction bounds of Burq, Gérard …

We study Hamiltonian dynamics of gradient Kaehler-Ricci solitons that arise as limits of dilations of singularities of the Ricci flow on compact Kaehler manifolds. Our main result is that the underlying spaces of such gradient solitons must be Stein manifolds. Moreover, on all most all energy surfaces of the potential …

Recently, a general method for analyzing the statistical accuracy of the EM algorithm has been developed and applied to some simple latent variable models [Balakrishnan et al. 2016]. In that method, the basin of attraction for valid initialization is required to be a ball around the truth. Using Stein's Lemma, we exten…

In this paper, we study the problem of estimating smooth Generalized Linear Models (GLMs) in the Non-interactive Local Differential Privacy (NLDP) model. Different from its classical setting, our model allows the server to access some additional public but unlabeled data. In the first part of the paper we focus on GLMs…

New algorithms for private GLM estimation with minimax lower bounds.

Stein's method improves probabilistic inference and learning.

Double machine learning provides $\sqrt{n}$-consistent estimates of parameters of interest even when high-dimensional or nonparametric nuisance parameters are estimated at an $n^{-1/4}$ rate. The key is to employ Neyman-orthogonal moment equations which are first-order insensitive to perturbations in the nuisance param…

This paper investigates the model degrees of freedom in k-means clustering. An extension of Stein's lemma provides an expression for the effective degrees of freedom in the k-means model. Approximating the degrees of freedom in practice requires simplifications of this expression, however empirical studies evince the a…

GC Stein manifolds characterized with embeddings and functions.

Stochastic Stein Discrepancies improve inference efficiency.

We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected a…

Improved sampling method using regularized Stein Variational Gradient Flow.

Develops Stein's method for Riemannian manifolds using diffusion.

We propose an estimator of prediction error using an approximate message passing (AMP) algorithm that can be applied to a broad range of sparse penalties. Following Stein's lemma, the estimator of the generalized degrees of freedom, which is a key quantity for the construction of the estimator of the prediction error, …

It is shown that every subcritical Stein manifold is deformation equivalent to the product of a Stein manifold with $\C$.

Regularized Stein thinning improves MCMC output approximations.

Study Stein and Milnor fillings of links from surface singularities.

Explains the Schwarz lemma in lecture notes.

Stein transport improves Bayesian inference with faster convergence and reduced variance.

In this paper we survey results on the existence of holomorphic embeddings and immersions of Stein manifolds into complex manifolds. Most results pertain to proper maps into Stein manifolds. We include a new result saying that every continuous map $X\to Y$ between Stein manifolds is homotopic to a proper holomorphic em…

The paper improves Stein importance sampling for Markov chain samples.

Counterexample found for Stein property of certain solvable Lie groups.

A new framework improves kernel Stein discrepancy tests for validating distributions.

Author provides an alternate proof of the free ribbon lemma.

Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…

2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.

We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein 4-manifolds to have an infinite subfamily of pairwise non-diffeomorphic Stein 4-manifo…

We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…

Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.

The paper extends Schwarz's lemma to RC-positivity and complex manifolds.

For any integer $n\geq 2$, we construct an infinite family of Stein fillable contact $(4n-1)$-manifolds each of which admits infinitely many pairwise homotopy inequivalent Stein fillings.

The square root of Fredholm determinants causes numerical instabilities in option pricing models.

Survey on strong closing lemmas in Hamiltonian dynamics.

Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.

Study continuity and Hölder estimates for solutions on Stein spaces.

Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing