[2212.02987] Generative random latent features models and statistics of natural images Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Disordered Systems and Neural Networks arXiv:2212.02987 (cond-mat) [Submitted on 6 Dec 2022 ( v1 ), last revised 13 Jun 2024 (this version, v2)] Title: Generative random latent features models and statistics of natural images Authors: Philipp Fleig , Ilya Nemenman View a PDF of the paper titled Generative random latent features models and statistics of natural images, by Philipp Fleig and Ilya Nemenman View PDF HTML (experimental) Abstract: Complex, multivariable systems are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of latent features and data decompositions can be defined, and one typically uses a trial and error approach to determine a decomposition that is natural to the system and its data. It is highly desirable to develop principled understanding of which decomposition is appropriate for given a data set. In this work, we take a step in this direction and argue that sample-sample correlations in the data carry important information to this effect. For this we construct a generative random latent feature matrix model of large data based on linear mixing of latent features. Key ingredient of our model is that we allow for statistical dependence between the mixing coefficients and argue that the model captures characteristic properties found in many types of natural data. Latent dimensionality and correlation patterns of the data are controlled by only two model parameters. The model's data patterns include (overlapping) clusters, sparse mixing, and constrained (non-negative) mixing. We describe the characteristic correlation and eigenvalue distributions of each pattern. Finally, we fit the model on correlation data from natural images and find a near perfect match with the sparse mixing regime of our model. This finding is in line with the well-known sparse coding structure in natural scene images and provides information about the appropriate data decomposition, namely a sparse coding scheme. We believe that our work will deliver similar insights for diverse data of biological systems. Comments: 15 pages, 8 figures Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn) Cite as: arXiv:2212.02987 [cond-mat.dis-nn] (or arXiv:2212.02987v2 [cond-mat.dis-nn] for this version) https://doi.org/10.48550/arXiv.2212.02987 Focus to learn more arXiv-issued DOI via DataCite Journal reference: PRX Life 3, 023014 (2025) Related DOI : https://doi.org/10.1103/8xd4-6hsr Focus to learn more DOI(s) linking to related resources Submission history From: Philipp Fleig [ view email ] [v1] Tue, 6 Dec 2022 13:55:58 UTC (10,902 KB) [v2] Thu, 13 Jun 2024 20:19:18 UTC (13,649 KB) Full-text links: Access Paper: View a PDF of the paper titled Generative random latent features models and statistics of natural images, by Philipp Fleig and Ilya Nemenman View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.dis-nn < prev | next > new | recent | 2022-12 Change to browse by: cond-mat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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