Related papers: Bayesian Hierarchical Invariant Prediction
Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new…
Selecting powerful predictors for an outcome is a cornerstone task for machine learning. However, some types of questions can only be answered by identifying the predictors that causally affect the outcome. A recent approach to this causal…
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…
In this work, we propose a modified Bayesian Information Criterion (BIC) specifically designed for mixture models and hierarchical structures. This criterion incorporates the determinant of the Hessian matrix of the log-likelihood function,…
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…
An important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system's underlying causal structure. To this end, Invariant Causal Prediction (ICP) (Peters et…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
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…
It is common to show the confidence intervals or $p$-values of selected features, or predictor variables in regression, but they often involve selection bias. The selective inference approach solves this bias by conditioning on the…
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…
The Bayesian evidence, crucial ingredient for model selection, is arguably the most important quantity in Bayesian data analysis: at the same time, however, it is also one of the most difficult to compute. In this paper we present a…
An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…
Bayesian predictive inference analyzes a dataset to make predictions about new observations. When a model does not match the data, predictive accuracy suffers. We develop population empirical Bayes (POP-EB), a hierarchical framework that…
The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the…
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…
We propose Bayesian Conformal Prediction (BCP), a framework that combines Bayesian posterior predictive distributions with PAC-style conformal risk control to produce prediction sets with finite-sample coverage guarantees. Standard…
Predictive coding (PC) is an influential theory of information processing in the brain, providing a biologically plausible alternative to backpropagation. It is motivated in terms of Bayesian inference, as hidden states and parameters are…
We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of…
Inductive Conformal Prediction (ICP) is a set of distribution-free and model agnostic algorithms devised to predict with a user-defined confidence with coverage guarantee. Instead of having point predictions, i.e., a real number in the case…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…