Quantitative Universal Approximation Bounds for Deep Belief Networks
Authors: Julian Sieber, Johann Gehringer
ICML 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the Lq-norm for q [1, ] (q = corresponding to the supremum norm) and in Kullback Leibler divergence. Furthermore, we establish sharp quantitative bounds on the approximation error in terms of the number of hidden units. and For each q [1, ) we show that DBNs with two binary hidden layers and parental density : Rd R+ can approximate any probability density f : Rd R+ in the Lq-norm, solely under the condition that Lq(Rd) and f W 1,q(Rd) |
| Researcher Affiliation | Collaboration | Julian Sieber 1 2 Johann Gehringer 2 1Zalando Ireland Limited, 2WML, Windmill Quarter, Dublin 2, D02 F206, Ireland 2Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom. Correspondence to: Julian Sieber <julian.sieber@zalando.ie>. |
| Pseudocode | No | The paper does not contain any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any statement about open-source code availability or links to code repositories for the methodology. |
| Open Datasets | No | The paper focuses on theoretical analysis and does not involve empirical training on a dataset. |
| Dataset Splits | No | The paper is theoretical and does not describe experimental data splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not report on experiments, thus no hardware specifications are mentioned. |
| Software Dependencies | No | The paper describes theoretical mathematical results and does not specify software dependencies with version numbers for experimental reproduction. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup, including hyperparameters or system-level training settings. |