2017/02/28 by Jean Daunizeau, Daunizeau, Jean · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Biological sciences #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Neurons and Cognition (q-bio.NC) #Statistical Methods and Bayesian Inference #q-bio.NC #stat.ML
paper · pdf · doi:10.48550/arxiv.1703.00091
openalex publication_date 2017/03/01 · arxiv created 2017/03/03 · arxiv updated 2017/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note is concerned with accurate and computationally efficient approximations of moments of Gaussian random variables passed through sigmoid or softmax mappings. These approximations are semi-analytical (i.e. they involve the numerical adjustment of parametric forms) and highly accurate (they yield 5% error at most). We also highlight a few niche applications of these approximations, which arise in the context of, e.g., drift-diffusion models of decision making or non-parametric data clustering approaches. We provide these as examples of efficient alternatives to more tedious derivations that would be needed if one was to approach the underlying mathematical issues in a more formal way. We hope that this technical note will be helpful to modellers facing similar mathematical issues, although maybe stemming from different academic prospects.