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Gibbs sampling is a workhorse for Bayesian inference but has several limitations when used for parameter estimation, and is often much slower than non-sampling inference methods. SAME (State Augmentation for Marginal Estimation)…
Bayesian hierarchical models are commonly employed for inference in count datasets, as they account for multiple levels of variation by incorporating prior distributions for parameters at different levels. Examples include Beta-Binomial,…
Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…
The Homotopy Analysis Method (HAM) is a widely used analytical approach for solving nonlinear problems, yet its theoretical foundation lacks rigorous justification, and its intrinsic correlation with perturbation theory remains ambiguous,…
In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come…
Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…
In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single time frames, followed by the application of a suitable kinetic model to time activity curves (TACs)…
An implementation of a nonparametric Bayesian approach to solving binary classification problems on graphs is described. A hierarchical Bayesian approach with a randomly scaled Gaussian prior is considered. The prior uses the graph…
A fundamental problem in modern supervised learning is computing reliable conditional prediction intervals in high-dimensional settings: existing methods often rely on restrictive modelling assumptions, do not scale as predictor dimension…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous…
Current approaches to memory in neural systems rely on similarity-based retrieval: given a query, find the most representationally similar stored state. This assumption -- that useful memories are similar memories -- fails to capture a…
We describe nonparametric deconvolution models (NDMs), a family of Bayesian nonparametric models for collections of data in which each observation is the average over the features from heterogeneous particles. For example, these types of…
Causal discovery amounts to learning a directed acyclic graph (DAG) that encodes a causal model. This model selection problem can be challenging due to its large combinatorial search space, particularly when dealing with non-parametric…
We introduce a nonparametric model for inferring time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and…
Discrete Bayesian nonparametric models whose expectation is a convex linear combination of a point mass at some point of the support and a diffuse probability distribution allow to incorporate strong prior information, while still being…
Existing language models (LMs) predict tokens with a softmax over a finite vocabulary, which can make it difficult to predict rare tokens or phrases. We introduce NPM, the first nonparametric masked language model that replaces this softmax…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…