Related papers: Conditional Dirichlet Processes and Functional Con…

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach…

We introduce a simple and intuitive framework that provides quantitative explanations of statistical models through the probabilistic assessment of input feature importance. The core idea comes from utilizing the Dirichlet distribution to…

Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

The beta distribution serves as a canonical tool for modeling probabilities in statistics and machine learning. However, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent…

For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum…

The functional delta-method has a wide range of applications in statistics. Applications on functionals of empirical processes yield various limit results for classical statistics. To improve the finite sample properties of statistical…

Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical…

We study the problem of topic modeling in corpora whose documents are organized in a multi-level hierarchy. We explore a parametric approach to this problem, assuming that the number of topics is known or can be estimated by…

Random partition distribution is a crucial tool for model-based clustering. This study advances the field of random partition in the context of functional spatial data, focusing on the challenges posed by hourly population data across…

We propose a novel Bayesian nonparametric classification model that combines a Gaussian process prior for the latent function with a Dirichlet process prior for the link function, extending the interpretative framework of de Finetti…

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…

We study Dirichlet process-based models for sets of predictor-dependent probability distributions, where the domain and predictor space are general Polish spaces. We generalize the definition of dependent Dirichlet processes, originally…

Contextual Markov decision processes (CMDPs) describe a class of reinforcement learning problems in which the transition kernels and reward functions can change over time with different MDPs indexed by a context variable. While CMDPs serve…

We study discrete-time discounted constrained Markov decision processes (CMDPs) on Borel spaces with unbounded reward functions. In our approach the transition probability functions are weakly or set-wise continuous. The reward functions…

Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…

In many cases it makes sense to model a relationship symmetrically, not implying any particular directionality. Consider the classical example of a recommendation system where the rating of an item by a user should symmetrically be…

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

Conditional density estimation (CDE) is a fundamental task in machine learning that aims to model the full conditional law $\mathbb{P}(\mathbf{y} \mid \mathbf{x})$, beyond mere point prediction (e.g., mean, mode). A core challenge is…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…