arXiv research

Paper analyzes normal approximation for two-timescale stochastic algorithms, revealing interaction between fast and slow timescales.

Proposes a new normalization method using convolutional neural networks.

Flexible approach for normal approximations in geometric and topological statistics.

PLN-Nets with two linear layers and parallel LN achieve universal approximation.

This paper uses normalizing flows to approximate transport maps between densities.

The study examines the limitations of bi-Lipschitz Normalizing Flows in approximating certain distributions.

Residual flows are shown to approximate MMD well.

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

This paper develops the exact linear relationship between the leading eigenvector of the unnormalized modularity matrix and the eigenvectors of the adjacency matrix. We propose a method for approximating the leading eigenvector of the modularity matrix, and we derive the error of the approximation. There is also a comp…

Stochastic approximation proves asymptotic normality for non-smooth problems.

The paper uses transformed ANOVA to identify important fire detection variables.

Normalizing flow regression approximates posterior distributions without additional sampling.

A new method learns latent space normalizing flow for approximate inference in generator models.

The paper connects least area surfaces to quasi-normal surfaces in 3-manifolds.

We present a new approximation to the normal distribution quantile function. It has a similar form to the approximation of Beasley and Springer [3], providing a maximum absolute error of less than $2.5 \cdot 10^{-5}$. This is less accurate than [3], but still sufficient for many applications. However it is faster than …

Bi-Lipschitz flows approximate a wide range of distributions.

Copula-based normalizing flows improve flexibility and stability for heavy-tailed data.

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restricti…

This paper presents a general framework for norm-based capacity control for $L_{p,q}$ weight normalized deep neural networks. We establish the upper bound on the Rademacher complexities of this family. With an $L_{p,q}$ normalization where $q\le p^*$, and $1/p+1/p^{*}=1$, we discuss properties of a width-independent ca…

Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.

In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami…

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.

New Hermite approximations accelerate convergence with adaptive coordinate transformations.

Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are considered. The use of variational Bayes approximations here is a substantial departure fr…

Stochastic algo learns from evolving data, achieving optimal performance.

In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using…

We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward to improve the approximation by employing normalizing flows…

This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The formula is neat and holds for deterministic matrix perturbations. Second, we calculate…

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single…

The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.

Two new rational formulae for normal implied volatility are presented.

Study random walks on sub-Riemannian manifolds using retractions.

This paper shows how to approximate any log-concave distribution using well-conditioned affine coupling flows.

We construct a formal normal form for a real 2-codimensional submanifold $M\subset\mathbb{C}^{N+1}$ near a CR singularity approximating the sphere. This result gives a higher dimensional extension of Huang-Yin's normal form in $\mathbb{C}^{2}$.

ELF simplifies normalizing flows, making them more efficient and universal.

New approximations for Asian basket spread options using stochastic Taylor expansions.

Self Normalizing Flows improve normalizing flows by reducing computational complexity.

Paper improves CLT and bootstrap approximations for LSA with decreasing step size.

A new base distribution for normalizing flows allows modeling complex distributions without sacrificing invertibility.

In the LIBOR market model, forward interest rates are log-normal under their respective forward measures. This note shows that their distributions under the other forward measures of the tenor structure have approximately log-normal tails.

Methods for prediction and tolerance intervals in non-normal models.

The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-Röllin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition of Reinert-Röllin allows for wider applicability of the method, while the method of…

Posterior refinement improves sample efficiency in Bayesian neural networks.

Study improves BN TTA under distribution shift using higher-order asymptotics.

Many statistical models are given in the form of non-normalized densities with an intractable normalization constant. Since maximum likelihood estimation is computationally intensive for these models, several estimation methods have been developed which do not require explicit computation of the normalization constant,…

Develops an oblique projection technique to approximate a foliation for non-normal dynamics.

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them…

ACNML method improves uncertainty estimation for deep networks.