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

Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality . This paper proposes joint dimensionality reduction and non-parametric density estimation framework, using novel estimator that can explicitly capture underlying distribution appropriate reduced-dimension representations input data. The idea jointly design nonlinear reducing auto-encoder model training data terms parsimonious set latent random variables, learn xmlns:xlink="http://www.w3.org/1999/xlink">canonical low-rank tensor variables Fourier domain. proposed “universal,” as opposed predefined prior xmlns:xlink="http://www.w3.org/1999/xlink">assumed variational auto-encoders. Joint optimization pursued via formulation learns both by minimizing combination negative log-likelihood domain reconstruction loss. We demonstrate achieves very promising results on toy, tabular, image datasets regression tasks, sampling, anomaly detection.