Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation

• URL: http://arxiv.org/abs/2106.10591v1
• Date: Sun, 20 Jun 2021 00:38:56 GMT
• Title: Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation
• Authors: Magda Amiridi, Nikos Kargas, and Nicholas D. Sidiropoulos
• Abstract summary: Learning generative probabilistic models is a core problem in machine learning. This paper proposes a joint dimensionality reduction and non-parametric density estimation framework. We demonstrate that the proposed model achieves very promising results on regression tasks, sampling, and anomaly detection.
• Score: 31.631861197477185
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density estimation framework, using a novel estimator that can explicitly capture the underlying distribution of appropriate reduced-dimension representations of the input data. The idea is to jointly design a nonlinear dimensionality reducing auto-encoder to model the training data in terms of a parsimonious set of latent random variables, and learn a canonical low-rank tensor model of the joint distribution of the latent variables in the Fourier domain. The proposed latent density model is non-parametric and universal, as opposed to the predefined prior that is assumed in variational auto-encoders. Joint optimization of the auto-encoder and the latent density estimator is pursued via a formulation which learns both by minimizing a combination of the negative log-likelihood in the latent domain and the auto-encoder reconstruction loss. We demonstrate that the proposed model achieves very promising results on toy, tabular, and image datasets on regression tasks, sampling, and anomaly detection.

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