Adaptive pointwise estimation of conditional density function

Adaptive pointwise estimation of conditional density function

Bottleneck Conditional Density Estimation

We propose a neural network framework for high-dimensional conditional density estimation. The Bottleneck Conditional Density Estimator (BCDE) is a variant of the conditional variational autoencoder (CVAE) that employs layer(s) of stochastic variables as the bottleneck between the input x and target y, where both are highdimensional. The key to effectively train BCDEs is the hybrid blending of ...

Pointwise adaptive estimation for quantile regression

A nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds...

Fast Nonparametric Conditional Density Estimation

Conditional density estimation. The idea of conditional density estimation is to construct a density estimate f̂(y|x) for a dependent variable y, conditional on a vector of variables x. This can be seen as a generalization of regression, where instead of estimating the expected value E(y|x) alone, we instead model the full density. This is especially important for multi-modal densities, where th...

Partition-Based Conditional Density Estimation

We propose a general partition-based strategy to estimate conditional density with candidate densities that are piecewise constant with respect to the covariate. Capitalizing on a general penalized maximum likelihood model selection result, we prove, on two specific examples, that the penalty of each model can be chosen roughly proportional to its dimension. We first study a classical strategy ...