Related papers: A New Method for Multinomial Inference using Demps…
The mixture of Dirichlet process (MDP) defines a flexible prior distribution on the space of probability measures. This study shows that ordinary least-squares (OLS) estimator, as a functional of the MDP posterior distribution, has…
This paper is concerned with the reliable inference of optimal tree-approximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between…
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…
The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special…
We propose Dirichlet Simplex Nest, a class of probabilistic models suitable for a variety of data types, and develop fast and provably accurate inference algorithms by accounting for the model's convex geometry and low dimensional…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…
We introduce an innovative method for incremental nonparametric probabilistic inference in high-dimensional state spaces. Our approach leverages \slices from high-dimensional surfaces to efficiently approximate posterior distributions of…
We propose Diffusion Model Variational Inference (DMVI), a novel method for automated approximate inference in probabilistic programming languages (PPLs). DMVI utilizes diffusion models as variational approximations to the true posterior…
In this paper we extend an earlier result within Dempster-Shafer theory ["Fast Dempster-Shafer Clustering Using a Neural Network Structure," in Proc. Seventh Int. Conf. Information Processing and Management of Uncertainty in Knowledge-Based…
Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…
Bayesian inference involves two main computational challenges. First, in estimating the parameters of some model for the data, the posterior distribution may well be highly multi-modal: a regime in which the convergence to stationarity of…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
Existing multi-view classification and clustering methods typically improve task accuracy by leveraging and fusing information from different views. However, ensuring the reliability of multi-view integration and final decisions is crucial,…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
A common assumption in the fitting of unordered multinomial response models for $J$ mutually exclusive categories is that the responses arise from the same set of $J$ categories across subjects. However, when responses measure a choice made…
Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…