Related papers: Bayesian multinomial regression with class-specifi…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…
While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation…
Bayesian adaptive experimental design is a form of active learning, which chooses samples to maximize the information they give about uncertain parameters. Prior work has shown that other forms of active learning can suffer from active…
This article focuses on the problem of predicting a response variable based on a network-valued predictor. Our motivation is the development of interpretable and accurate predictive models for cognitive traits and neuro-psychiatric…
The aim of reduced rank regression is to connect multiple response variables to multiple predictors. This model is very popular, especially in biostatistics where multiple measurements on individuals can be re-used to predict multiple…
We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified…
Multinomial probit (mnp) models are fundamental and widely-applied regression models for categorical data. Fasano and Durante (2022) proved that the class of unified skew-normal distributions is conjugate to several mnp sampling models.…
Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and…
We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…
There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…
In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for…
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…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART). In the semi-parametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear…
Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the…
The two-level normal hierarchical model has played an important role in statistical theory and applications. In this paper, we first introduce a general adjusted maximum likelihood method for estimating the unknown variance component of the…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…