arXiv research

Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. Th…

Develops consistent approximations for composite optimization problems.

The paper studies the consistency of mean curvature flow via volumetric varifolds.

Dynamic submodular maximization with consistency constraints.

New framework for consistent submodular maximization with insertions and deletions.

This paper establishes the asymptotic consistency of the {\it loss-calibrated variational Bayes} (LCVB) method. LCVB was proposed in~\cite{LaSiGh2011} as a method for approximately computing Bayesian posteriors in a `loss aware' manner. This methodology is also highly relevant in general data-driven decision-making con…

Strict Minimum Message Length (SMML) is an information-theoretic statistical inference method widely cited (but only with informal arguments) as providing estimations that are consistent for general estimation problems. It is, however, almost invariably intractable to compute, for which reason only approximations of it…

It is shown that bootstrap approximations of support vector machines (SVMs) based on a general convex and smooth loss function and on a general kernel are consistent. This result is useful to approximate the unknown finite sample distribution of SVMs by the bootstrap approach.

Investigates the impact of finite VC dimension on neural network approximation and learning.

In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the…

Analyzes feature learning in neural networks using a self-consistent dynamical field theory.

The paper analyzes CycleGAN's error components for unpaired data generation.

We study the asymptotic consistency properties of $α$-Rényi approximate posteriors, a class of variational Bayesian methods that approximate an intractable Bayesian posterior with a member of a tractable family of distributions, the member chosen to minimize the $α$-Rényi divergence from the true posterior. Unique to o…

ConQUR tackles delusional bias in deep Q-learning, improving performance in Atari games.

Novel bounds improve TD learning consistency in RL.

We propose a novel estimation approach for the covariance matrix based on the $l_1$-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard approximate factor…

This paper analyzes VAE approximation errors in conditional exponential families.

GES algorithm improves consistency for nonparametric DAG models.

Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistic…

Paper proposes a new method for WDRO with local perturbations, achieving better accuracy.

The computer program SnapPea can approximate whether or not a three manifold whose boundary consists of tori has a complete hyperbolic structure, but it can not prove conclusively that this is so. This article provides a method for proving that such a manifold has a complete hyperbolic structure based on the approximat…

Non-parametric approaches for analyzing network data based on exchangeable graph models (ExGM) have recently gained interest. The key object that defines an ExGM is often referred to as a graphon. This non-parametric perspective on network modeling poses challenging questions on how to make inference on the graphon und…

We propose K-TanH, a novel, highly accurate, hardware efficient approximation of popular activation function TanH for Deep Learning. K-TanH consists of parameterized low-precision integer operations, such as, shift and add/subtract (no floating point operation needed) where parameters are stored in very small look-up t…

We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm. Specifically, the penalties we approach are convex on a linear transformation of the…

We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new covariance-based dissimilarity measure is introduced, from which we obtain the approxima…

Geometric Gaussian approximations capture any distribution.

New method for scalable set encoding with unbiased gradient approximation.

A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) methods. VB methods tend to be faster while achieving comparabl…

Self-consistent models improve reinforcement learning by aligning predictions with future values.

SC improves robustness in model comparison for misspecified models.

ALO-CV approximates leave-one-out error in proportional regime.

This work examines consistency issues in Gaussian Mixture Model reduction algorithms.

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing constraints on covariance, one can ensure consistency of linear response with the var…

This paper describes a new method for low rank kernel approximation called IKA. The main advantage of IKA is that it produces a function $ψ(x)$ defined as a linear combination of arbitrarily chosen functions. In contrast the approximation produced by Nyström method is a linear combination of kernel evaluations. The pro…

Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but lacks important anytime properties such as: 1) providing accurate and consistent mar…

Proposes sampling from reverse diffusion posteriors for contextual bandits.

Structured Nonparametric Variational Inference for Dependent Latent Modeling

New algorithms improve likelihood of finding global optima in Bayesian inference.

In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning on the remaining underlying assets and calculating the mixed exponential-power mo…

The variational framework for learning inducing variables (Titsias, 2009a) has had a large impact on the Gaussian process literature. The framework may be interpreted as minimizing a rigorously defined Kullback-Leibler divergence between the approximating and posterior processes. To our knowledge this connection has th…

Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate inference strategies. In such cases, taking the eventual decision-making task i…

Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is c…

This paper introduces a spline-based method for nonparametric ADVI that handles complex posterior distributions.

Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.

Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading eigenvectors, where $k$ is the desired number of clusters among $n$ objects. This is pro…

The paper introduces Bellman-consistent pessimism to improve offline reinforcement learning without overly pessimistic bias.

We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional total variation, leading to piecewise-constant approximations. Fast algorithms are …

This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$ constraint, a pairwise $\ell^\infty$ constraint, or a pairwise $\ell^1$ constraint. …