{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/low-rank-characteristic-tensor-density","title":"Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation","arxiv_id":"2106.10591","date":"2021-06-20","proceeding":null,"authors":["Magda Amiridi","Nikos Kargas","Nicholas D. Sidiropoulos"],"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.","url_abs":"https://arxiv.org/abs/2106.10591v1","url_pdf":"https://arxiv.org/pdf/2106.10591v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"low-rank-characteristic-tensor-density","repo_url":"https://github.com/Mgdln94/Low-rank-joint-CF---HTF","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"anomaly-detection","task_name":"Anomaly Detection"},{"task_slug":"density-estimation","task_name":"Density Estimation"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2106.10591","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}