Topic
Bayesian probability
About: Bayesian probability is a research topic. Over the lifetime, 26572 publications have been published within this topic receiving 817919 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data is presented, which is derived from a set of assumptions made previously as well as the assumption of likelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence.
Abstract: We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption of likelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—a prior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at most k e 1 parent. For the general case (k > 1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.
4,427 citations
Proceedings Article•
27 Nov 1995TL;DR: This paper investigates the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations.
Abstract: The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations. Two methods, using optimization and averaging (via Hybrid Monte Carlo) over hyperparameters have been tested on a number of challenging problems and have produced excellent results.
4,201 citations
TL;DR: To facilitate use of the Bayes factor, an easy-to-use, Web-based program is provided that performs the necessary calculations and has better properties than other methods of inference that have been advocated in the psychological literature.
Abstract: Progress in science often comes from discovering invariances in relationships among variables; these invariances often correspond to null hypotheses. As is commonly known, it is not possible to state evidence for the null hypothesis in conventional significance testing. Here we highlight a Bayes factor alternative to the conventional t test that will allow researchers to express preference for either the null hypothesis or the alternative. The Bayes factor has a natural and straightforward interpretation, is based on reasonable assumptions, and has better properties than other methods of inference that have been advocated in the psychological literature. To facilitate use of the Bayes factor, we provide an easy-to-use, Web-based program that performs the necessary calculations.
3,772 citations
TL;DR: A new algorithm is introduced that combines the modeling strategy of one method with the computational strategies of another and outperforms all three existing methods for inferring haplotypes from genotype data in a population sample.
Abstract: In this report, we compare and contrast three previously published Bayesian methods for inferring haplotypes from genotype data in a population sample. We review the methods, emphasizing the differences between them in terms of both the models ("priors") they use and the computational strategies they employ. We introduce a new algorithm that combines the modeling strategy of one method with the computational strategies of another. In comparisons using real and simulated data, this new algorithm outperforms all three existing methods. The new algorithm is included in the software package PHASE, version 2.0, available online (http://www.stat.washington.edu/stephens/software.html).
3,769 citations
TL;DR: It is found that on a database of more than 100 categories, the Bayesian approach produces informative models when the number of training examples is too small for other methods to operate successfully.
Abstract: Learning visual models of object categories notoriously requires hundreds or thousands of training examples. We show that it is possible to learn much information about a category from just one, or a handful, of images. The key insight is that, rather than learning from scratch, one can take advantage of knowledge coming from previously learned categories, no matter how different these categories might be. We explore a Bayesian implementation of this idea. Object categories are represented by probabilistic models. Prior knowledge is represented as a probability density function on the parameters of these models. The posterior model for an object category is obtained by updating the prior in the light of one or more observations. We test a simple implementation of our algorithm on a database of 101 diverse object categories. We compare category models learned by an implementation of our Bayesian approach to models learned from by maximum likelihood (ML) and maximum a posteriori (MAP) methods. We find that on a database of more than 100 categories, the Bayesian approach produces informative models when the number of training examples is too small for other methods to operate successfully.
3,688 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 33 |
| 2025 | 4,088 |
| 2024 | 6,206 |
| 2023 | 5,598 |
| 2022 | 9,036 |
| 2021 | 2,556 |