Bayesian approach approximates probability functions of Gaussian mixtures.
problem Approximating probability functions of non-spherical Gaussian mixtures.
method Bayesian decomposition, spherical radial decomposition, random sampling.
result Established differentiability and integral representation of gradient for probability functions.
This paper improves learning uncertain Bayesian networks from incomplete data.
problem Learning conditional probabilities in Bayesian networks with limited data.
method Develops methods to estimate and quantify uncertainty in conditional probabilities with incomplete data.
result Improves state-of-the-art approaches for handling uncertain Bayesian networks with incomplete data.
New acquisition function improves batch Bayesian active learning.
problem BatchBALD conflates epistemic and aleatoric uncertainty, leading to suboptimal performance.
method Focus on predictive probabilities to separate epistemic uncertainty, leading to better performance and faster evaluation.
result The new acquisition function performs better and allows for larger batches.
Bayesian algorithm improves best-arm identification within fixed budget.
problem Maximizing probability of identifying optimal arm within fixed budget.
method Proposes Bayesian elimination algorithm and derives upper bound on misidentification probability.
result Upper bound on misidentification probability reflects prior quality and matches lower bound.
Bayesian approach to robust risk measures under model uncertainty.
problem Representing robust risk measures as a single probability measure.
method Introducing two types of risk measures and analyzing their relation to robust risk measures.
result Robust risk measures can be represented by a mixture probability measure, a Bayesian approach.
Efficient algorithm for Bayesian networks reduces marginal probability distribution computation.
problem Exact computation of marginal probability distribution is NP-hard for categorical variables in Bayesian networks.
method Divide-and-conquer approach exploiting graphical properties of Bayesian networks.
result Novel algorithm outperforms state-of-the-art methods in classification and cancer subtype identification.
Bayesian imaging methods deliver trustworthy probabilities in some cases but struggle with uncertainty quantification.
problem Uncertainty quantification in Bayesian imaging methods.
method Monte Carlo method to explore reliability of probabilities.
result Modern Bayesian imaging techniques deliver reliable probabilities in some cases but not for uncertainty quantification.
Convolutional Bayesian filtering generalizes state estimation by incorporating inequality conditions.
problem Standard Bayesian filtering assumes exact conditional probabilities, limiting its applicability.
method Introducing inequality conditions transforms conditional probabilities into convolutional forms, expanding the filtering framework.
result Convolutional Bayesian filtering encompasses standard Bayesian filtering and allows for more nuanced model consideration.
SOLBP extends efficient inference to uncertain Bayesian networks.
problem Inference in uncertain Bayesian networks with second-order probabilities.
method Extends Loopy Belief Propagation to second-order Bayesian networks.
result Generates inferences consistent with sum-product networks, more efficient and scalable.
Paper improves tree probability estimation using stochastic optimization and variance reduction.
problem Improving tree probability estimation in phylogenetic inference.
method Introduces computationally efficient methods for training SBNs and variance reduction for optimization.
result Methods outperform previous baseline methods in tree topology probability estimation and Bayesian phylogenetic inference.
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions based on Bayesian learning of clique tree decomposition is presented. The main contr…
Bayesian neural networks are compressed using feature and weight pruning based on posterior inclusion probabilities.
problem Efficiently compressing Bayesian neural networks to reduce computation cost and improve generalizability.
method Bayesian model selection principles are applied to obtain posterior inclusion probabilities for pruning and feature selection.
result Pruned models show better generalizability on simulated and real-world data.
Paper examines stability of Bayesian posterior measures using integral probability metrics.
problem Stability of Bayesian inference in large-scale inverse problems.
method New families of integral probability metrics for likelihood and prior perturbations.
result Constructs new stability results for Bayesian posterior measures.
We propose a betting strategy based on Bayesian logistic regression modeling for the probability forecasting game in the framework of game-theoretic probability by Shafer and Vovk (2001). We prove some results concerning the strong law of large numbers in the probability forecasting game with side information based on …
Proposes qPO, a new acquisition strategy for batched Bayesian optimization that maximizes the probability of including the optimum.
problem Efficiently identifying top-performing compounds from a large chemical library.
method qPO (multipoint Probability of Optimality) acquisition strategy that maximizes the probability of including the true optimum.
result Empirical evidence shows that qPO is competitive with and complements other state-of-the-art methods in batched Bayesian optimization.
Bayesian and simulation methods predict credit default probabilities.
problem Assessing credit risk in large customer portfolios.
method Two-phase approach: Bayesian estimation followed by Monte Carlo simulations.
result Estimation of true default rates through simulations.
To model categorical response variables given their covariates, we propose a permuted and augmented stick-breaking (paSB) construction that one-to-one maps the observed categories to randomly permuted latent sticks. This new construction transforms multinomial regression into regression analysis of stick-specific binar…
Bayesian meta learning improves uncertainty quantification in regression.
problem Trusting uncertainty quantification in Bayesian regression.
method Trust-Bayes framework for Bayesian meta learning, optimizing for trustworthy uncertainty quantification.
result Lower bounds and sample complexity for trustworthy uncertainty quantification are characterized.
Bayesian inference engines improve density estimation accuracy and scalability.
problem Constructing accurate and scalable probability density functions.
method Bayesian inference engines (no-U-turn sampling and expectation propagation) with binning strategy.
result Density estimates have excellent comparative performance and scale well to large sample sizes.
We present a new method to approximate posterior probabilities of Bayesian Network using Deep Neural Network. Experiment results on several public Bayesian Network datasets shows that Deep Neural Network is capable of learning joint probability distri- bution of Bayesian Network by learning from a few observation and p…
Binary classification models get more efficient predictive probabilities.
problem Computing predictive probabilities in Bayesian probit models is computationally challenging.
method Use of expectation propagation (EP) to find a closed-form expression for predictive probabilities.
result Closed-form predictive probabilities improve over existing methods.
The paper reinterprets Bayesian priors and posteriors using Riemannian manifolds.
problem The dependence of maximum a posteriori estimates on parametrization.
method Assuming a Riemannian manifold with Fisher metric, the paper reinterprets priors and posteriors as distributions over probability distributions, making estimates independent of parametrization.
result A maximum a posteriori estimate independent of parametrization is defined.
This study redefines probability for finite outcomes using axioms and examples.
problem Defining probability for finite outcomes and preserving information.
method Developed three axioms for relative probability functions and provided examples and a system for their composition.
result Proved the topological closure of the relative probability space, preserving information under limits.
In this paper, we provide a method to learn the directed structure of a Bayesian network using data. The data is accessed by making conditional probability queries to a black-box model. We introduce a notion of simplicity of representation of conditional probability tables for the nodes in the Bayesian network, that we…
Bayesian method estimates coverage from sketching imperfect data.
problem Estimating coverage probabilities from compressed data.
method Bayesian nonparametric approach using Dirichlet process prior.
result Estimators accurately recover distinct counts and frequencies.
Bayesian model improves classification performance with flexible uncertainty modeling.
problem Improving classification performance with flexible uncertainty modeling.
method Combines Gaussian process and Dirichlet process priors for latent function and link function, respectively.
result Outperforms standard logistic regression on simulated data.
Two BO methods improve reliability optimization for rare failures.
problem Maximizing reliability of designs subject to random perturbations.
method Bayesian optimization with Thompson sampling and knowledge gradient.
result Proposed methods outperform existing techniques in extreme failure probability scenarios.
Enhances Bayesian model comparison with a probabilistic framework for meta-uncertainty.
problem Uncertainty in posterior model probabilities (PMPs) when derived from finite data.
method Develops a fully probabilistic approach to quantify and represent meta-uncertainty over PMPs.
result Demonstrates utility in various BMC contexts, including regression, MCMC, and neural networks.
The article introduces inferential moments for analyzing uncertain multivariable systems.
problem Handling inference tasks in uncertain multivariable systems.
method Bayesian inference and quantification of inferential moments.
result Quantification of inferential moments and their connection to mutual information.
Exact Bayesian inference for discrete models using probability generating functions.
problem Discrete statistical models with infinite support and continuous priors.
method Probabilistic programming language with automatic differentiation and probability generating functions.
result Genfer tool provides exact solutions for a wide range of inference problems.
Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, re…
This article introduces a Bayesian nonparametric method for quantifying the relative evidence in a dataset in favour of the dependence or independence of two variables conditional on a third. The approach uses Polya tree priors on spaces of conditional probability densities, accounting for uncertainty in the form of th…
Bayesian learning improves reliability of molecular predictions for hit compound discovery.
problem Improving reliability of machine learning predictions for virtual screening.
method Bayesian learning algorithms applied to graph neural networks.
result Bayesian learning leads to well-calibrated predictions and higher hit compound success.
New method optimizes multiple points in Bayesian optimization efficiently.
problem Optimizing multiple points in expensive black-box functions.
method Reformulated BO as probability measure optimization, using convex gradient flows.
result Demonstrated effectiveness on various benchmarks compared to state-of-the-art methods.
This paper calculates the exact probability distribution of hypervolume improvement for bi-objective problems.
problem Calculating the exact probability distribution of hypervolume improvement in bi-objective problems.
method Cell partition-based method to derive the probability distribution of hypervolume improvement from a bi-variate Gaussian random variable.
result The proposed ε-PoHVI acquisition function outperforms other related functions in Bayesian optimization. Bayesian approach improves neural network classification accuracy and uncertainty.
problem Overconfidence and lack of uncertainty in softmax for classification tasks.
method Model categorical probability using a random variable with a prior distribution.
result Consistent gains in generalization performance across multiple tasks.
Bayesian optimization stops when a solution is within ε of the optimum with high probability.
problem Stopping Bayesian optimization prematurely based on a probabilistic criterion.
method Introducing a (ε,δ)-criterion for stopping Bayesian optimization. result Bayesian optimization satisfies the (ε,δ)-criterion under mild assumptions. We review and illustrate how the volatility smile translates into a probability distribution, the market-implied probability distribution representing believes priced in. The effects of changes in the smile are examined. Special attention is given to the effects of slope, which might appear at first counter-intuitive. …
New method improves ABC for Bayesian model comparison.
problem Comparing complex models with observed data.
method Approximate Bayesian Computation with posterior density estimation.
result Efficiently assigns high posterior probabilities to ground-truth models.
Bayesian model averaging improves causal effect estimation by averaging over multiple models.
problem Estimating causal effects under linear Structural Causal Models (SCMs).
method Bayesian model averaging using Gaussian scale mixture distributions for computational efficiency.
result Bayesian model averaging is optimal for causal effect estimation.
Bayesian Power Steering fine-tunes large diffusion models for domain adaptation.
problem Fine-tuning pre-trained diffusion models for tasks in a smaller probability space.
method Bayesian framework with a novel network structure (Bayesian Power Steering).
result Bayesian Power Steering achieves an FID score of 10.49 on the COCO17 dataset.
Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by dr…
Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we call an embedded Bayesian network classifier or EBNC. The model for a node Y g…
We study the problem of learning Bayesian network structures from data. We develop an algorithm for finding the k-best Bayesian network structures. We propose to compute the posterior probabilities of hypotheses of interest by Bayesian model averaging over the k-best Bayesian networks. We present empirical results on s…
This paper optimizes Bayesian acquisition functions in Gaussian Processes for better optimization.
problem Improving the efficiency of Bayesian optimization methods.
method Analysis of different acquisition functions and optimizers for optimizing Bayesian acquisition functions.
result Optimization of acquisition functions leads to faster and more accurate sampling points.
The need to estimate smooth probability distributions (a.k.a. probability densities) from finite sampled data is ubiquitous in science. Many approaches to this problem have been described, but none is yet regarded as providing a definitive solution. Maximum entropy estimation and Bayesian field theory are two such appr…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and many other parametric and nonparametric Bayesian models fall within the remit of …
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained d…