Related papers: Hellinger Distance and Bayesian Non-Parametrics: H…
We propose a model of inference and heuristic decision-making in groups that is rooted in the Bayes rule but avoids the complexities of rational inference in partially observed environments with incomplete information, which are…
Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…
Hierarchical Bayesian networks and neural networks with stochastic hidden units are commonly perceived as two separate types of models. We show that either of these types of models can often be transformed into an instance of the other, by…
Bayesian network classifiers (BNCs) possess a number of properties desirable for a modern classifier: They are easily interpretable, highly scalable, and offer adaptable complexity. However, traditional methods for learning BNCs have…
There are many issues that can cause problems when attempting to infer model parameters from data. Data and models are both imperfect, and as such there are multiple scenarios in which standard methods of inference will lead to misleading…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
We propose a new statistical approach to obtain differential gene expression of non-detects in quantitative real-time PCR (qPCR) experiments through Bayesian hierarchical modeling. We propose to treat non-detects as non-random missing data,…
When the likelihood is analytically unavailable and computationally intractable, approximate Bayesian computation (ABC) has emerged as a widely used methodology for approximate posterior inference; however, it suffers from severe…
The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…
This paper focuses on the problem of hierarchical non-overlapping clustering of a dataset. In such a clustering, each data item is associated with exactly one leaf node and each internal node is associated with all the data items stored in…
Employing nonparametric methods for density estimation has become routine in Bayesian statistical practice. Models based on discrete nonparametric priors such as Dirichlet Process Mixture (DPM) models are very attractive choices due to…
Gaussian processes constitute a very powerful and well-understood method for non-parametric regression and classification. In the classical framework, the training data consists of deterministic vector-valued inputs and the corresponding…
We propose a novel Riemannian geometric framework for variational inference in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold of probability density functions. Under the square-root density representation, the…
The increasing availability of multiple network data has highlighted the need for statistical models for heterogeneous populations of networks. A convenient framework makes use of metrics to measure similarity between networks. In this…
Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we…
This paper analyzes hierarchical Bayesian inverse problems using techniques from high-dimensional statistics. Our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain…
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…
Multi-level normal hierarchical models, also interpreted as mixed effects models, play an important role in developing statistical theory in multi-parameter estimation for a wide range of applications. In this article, we propose a novel…
Bayesian hierarchical modeling is a natural framework to effectively integrate data and borrow information across groups. In this paper, we address problems related to density estimation and identifying clusters across related groups, by…