Deep neural networks with dependent weights: Gaussian process mixture limit, heavy tails, sparsity and compressibility
This article studies the infinite-width limit of deep feedforward neural networks whose
weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden …
weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden …
Heavy-Tailed NGG-Mixture Models
VP Ramírez, M de Carvalho, L Gutiérrez - Bayesian Analysis, 2024 - projecteuclid.org
Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of
mainstream random probability measures such as the Dirichlet process (DP). The first …
mainstream random probability measures such as the Dirichlet process (DP). The first …
Batch and online variational learning of hierarchical pitman-yor mixtures of multivariate beta distributions
N Manouchehri, N Bouguila… - 2021 20th IEEE …, 2021 - ieeexplore.ieee.org
In this paper, we propose hierarchical Pitman-Yor process mixtures of multivariate Beta
distributions and learn this novel clustering method by online variational inference. The …
distributions and learn this novel clustering method by online variational inference. The …
Sparse networks with core-periphery structure
We propose a statistical model for graphs with a core-periphery structure. We give a precise
notion of what it means for a graph to have this structure, based on the sparsity properties of …
notion of what it means for a graph to have this structure, based on the sparsity properties of …
Deep neural networks with dependent weights: Gaussian process mixture limit, heavy tails, sparsity and compressibility
This article studies the infinite-width limit of deep feedforward neural networks whose
weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden …
weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden …
Asymptotic behavior of the number of distinct values in a sample from the geometric stick-breaking process
Discrete random probability measures are a key ingredient of Bayesian nonparametric
inference. A sample generates ties with positive probability and a fundamental object of both …
inference. A sample generates ties with positive probability and a fundamental object of both …
On sparsity, power-law, and clustering properties of graphex processes
This paper investigates properties of the class of graphs based on exchangeable point
processes. We provide asymptotic expressions for the number of edges, number of nodes …
processes. We provide asymptotic expressions for the number of edges, number of nodes …
A General Purpose Approximation to the Ferguson-Klass Algorithm for Sampling from L\'evy Processes Without Gaussian Components
D Bernaciak, JE Griffin - arXiv preprint arXiv:2407.01483, 2024 - arxiv.org
We propose a general-purpose approximation to the Ferguson-Klass algorithm for
generating samples from L\'evy processes without Gaussian components. We show that the …
generating samples from L\'evy processes without Gaussian components. We show that the …
A unified construction for series representations and finite approximations of completely random measures
A unified construction for series representations and finite approximations of completely random
measures Page 1 Bernoulli 29(3), 2023, 2142–2166 https://doi.org/10.3150/22-BEJ1536 A …
measures Page 1 Bernoulli 29(3), 2023, 2142–2166 https://doi.org/10.3150/22-BEJ1536 A …
Similarity-based Random Partition Distribution for Clustering Functional Data
T Wakayama, S Sugasawa, G Kobayashi - arXiv preprint arXiv …, 2023 - arxiv.org
Random partitioned distribution is a powerful tool for model-based clustering. However, the
implementation in practice can be challenging for functional spatial data such as hourly …
implementation in practice can be challenging for functional spatial data such as hourly …