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High-Dimensional Probability Estimation with Deep Density Models
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High-Dimensional Probability Estimation with Deep Density Models
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One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations lie on a lower-dimensional manifold of high probability. It has been more difficult, however, to exploit this insight to build explicit, tractable density models for high-dimensional data. In this paper, we introduce the deep density model (DDM), a new approach to density estimation. We exploit insights from deep learning to construct a bijective map to a representation space, under which the transformation of the distribution of the data is approximately factorized and has identical and known marginal densities. The simplicity of the latent distribution under the model allows us to feasibly explore it, and the invertibility of the map to characterize contraction of measure across it. This enables us to compute normalized densities for out-of-sample data. This combination of tractability and flexibility allows us to tackle a variety of probabilistic tasks on high-dimensional datasets, including: rapid computation of normalized densities at test-time without evaluating a partition function; generation of samples without MCMC; and characterization of the joint entropy of the data.
Forward citations
Cited by 5 Pith papers
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Density estimation using Real NVP
Real NVP uses affine coupling layers to create invertible transformations that support exact density estimation, sampling, and latent inference without approximations.
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NICE: Non-linear Independent Components Estimation
NICE learns a composition of invertible neural-network layers that transform data into independent latent variables, enabling exact log-likelihood training and sampling for density estimation.
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Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation
LHSD uses spectral filtering on the log-density Hessian to isolate tangent directions from noise and estimate local intrinsic dimension scalably via Stochastic Lanczos Quadrature.
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High-dimensional reliability-oriented Shapley effect estimation with Normalizing Flows
A new scheme estimates high-dimensional reliability-oriented Shapley effects by fitting normalizing flows to failure-conditional densities from one sample of failure points and adds an error estimation procedure.
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Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation
LHSD estimates local intrinsic dimension in high-D spaces by spectral filtering of the log-density Hessian via SLQ to isolate zero-curvature tangent directions.
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