arXiv research

Deep belief networks can approximate any multivariate density with binary hidden units.

Paper develops polynomial approximations for complex probability densities.

Adaptive neural network approximates stochastic system densities.

Novel filter uses deep BSDE for nonlinear density approximation.

Estimation of density derivatives is a versatile tool in statistical data analysis. A naive approach is to first estimate the density and then compute its derivative. However, such a two-step approach does not work well because a good density estimator does not necessarily mean a good density-derivative estimator. In t…

In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. Th…

Proposes a method for approximating transition densities of SDEs driven by gamma processes.

New method uses SoS densities and α-divergences for efficient sequential transport maps.

ADDA-KR uses KRnets for solving high-dimensional Fokker-Planck equations.

Develops efficient methods for approximating densities of financial models with jumps.

In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density ratio function by solving a convex constrained minimization problem. Approximating…

Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution comparison such as outlier detection, transfer learning, and two-sample homogeneity…

A new density model using Fourier basis achieves better approximations and compression.

Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximat…

Paper proposes approximate Stein classes for efficient truncated density estimation.

Paper proposes new costs for learning multiple centers in MDNs.

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…

VI approximates complex densities faster than classical methods.

Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accurate energies are achieved. Accurate {\em constrained optimal densitie…

New method approximates high-dimensional probability densities efficiently.

Paper formulates particle flow using variational inference and Fisher-Rao gradient flow.

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point…

Paper explores variable skipping to speed up range density estimation.

AdaAnn optimizes annealing for efficient probability density approximation.

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

Modal regression is aimed at estimating the global mode (i.e., global maximum) of the conditional density function of the output variable given input variables, and has led to regression methods robust against heavy-tailed or skewed noises. The conditional mode is often estimated through maximization of the modal regre…

Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this problem is tractable in the following sense: there exists an algorithm that use…

New method efficiently interpolates nonparametric density estimators.

Dual-ISL improves implicit generative model training with convex optimization and explicit density approximation.

The paper approximates CARMA models for option pricing.

Estimates expected information gain using density approximations and dimension reduction.

Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive den…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we write the joint density approximately as a product of an approximate posterior dens…

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique o…

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is …

The problem of inhomogeneous cluster densities has been a long-standing issue for distance-based and density-based algorithms in clustering and anomaly detection. These algorithms implicitly assume that all clusters have approximately the same density. As a result, they often exhibit a bias towards dense clusters in th…

FourNet approximates financial transition densities using Fourier transforms.

Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run independent MCMC algorithms targeting the corresponding subposterior, can spread…

Normalising flows (NFS) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural autoregressive flow (NAF) which is a universal approximator for density functions. Their fl…

Proposes a method to estimate time-dependent probability density functions using binary classifiers.

Proposes log density gradient to improve reinforcement learning sample complexity.

Novel method recursively partitions sample space for density estimation.

This survey explores various optimality concepts in importance sampling.

A new method improves density ratio estimation efficiency and accuracy.

A new method inflates and deflates data manifolds to estimate densities without losing universality.

Efficient clustering in high dimensions with Quick Shift and LSH.

Study refracted skew Brownian motion, find densities and asymptotics.

SDG uses optimal control to improve classifier guidance in low-density regions.