{"title":"关于提升高斯贝叶斯网络的扩展观点","authors":"Mattis Hartwig , Ralf Möller , Tanya Braun","doi":"10.1016/j.artint.2024.104082","DOIUrl":null,"url":null,"abstract":"<div><p>Lifting probabilistic graphical models and developing lifted inference algorithms aim to use higher level groups of random variables instead of individual instances. In the past, many inference algorithms for discrete probabilistic graphical models have been lifted. Lifting continuous probabilistic graphical models has played a minor role. Since many real-world applications involve continuous random variables, this article turns its focus to lifting approaches for Gaussian Bayesian networks. Specifically, we present algorithms for constructing a lifted joint distribution for scenarios of sequences of overlapping and non-overlapping logical variables. We present operations that work in a fully lifted way including addition, multiplication, and inversion. We present how the operations can be used for lifted query answering algorithms and extend the existing query answering algorithm by a new way of evidence handling. The new way of evidence handling groups evidence that has the same effect on its neighboring variables in cases of partial overlap between the logical-variable sequences. In the theoretical complexity analysis and the experimental evaluation, we show under which conditions the existing lifted approach and the new lifted approach including evidence grouping lead to the most time savings compared to the grounded approach.</p></div>","PeriodicalId":8434,"journal":{"name":"Artificial Intelligence","volume":null,"pages":null},"PeriodicalIF":5.1000,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An extended view on lifting Gaussian Bayesian networks\",\"authors\":\"Mattis Hartwig , Ralf Möller , Tanya Braun\",\"doi\":\"10.1016/j.artint.2024.104082\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Lifting probabilistic graphical models and developing lifted inference algorithms aim to use higher level groups of random variables instead of individual instances. In the past, many inference algorithms for discrete probabilistic graphical models have been lifted. Lifting continuous probabilistic graphical models has played a minor role. Since many real-world applications involve continuous random variables, this article turns its focus to lifting approaches for Gaussian Bayesian networks. Specifically, we present algorithms for constructing a lifted joint distribution for scenarios of sequences of overlapping and non-overlapping logical variables. We present operations that work in a fully lifted way including addition, multiplication, and inversion. We present how the operations can be used for lifted query answering algorithms and extend the existing query answering algorithm by a new way of evidence handling. The new way of evidence handling groups evidence that has the same effect on its neighboring variables in cases of partial overlap between the logical-variable sequences. In the theoretical complexity analysis and the experimental evaluation, we show under which conditions the existing lifted approach and the new lifted approach including evidence grouping lead to the most time savings compared to the grounded approach.</p></div>\",\"PeriodicalId\":8434,\"journal\":{\"name\":\"Artificial Intelligence\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.1000,\"publicationDate\":\"2024-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Artificial Intelligence\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0004370224000183\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Artificial Intelligence","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0004370224000183","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
An extended view on lifting Gaussian Bayesian networks
Lifting probabilistic graphical models and developing lifted inference algorithms aim to use higher level groups of random variables instead of individual instances. In the past, many inference algorithms for discrete probabilistic graphical models have been lifted. Lifting continuous probabilistic graphical models has played a minor role. Since many real-world applications involve continuous random variables, this article turns its focus to lifting approaches for Gaussian Bayesian networks. Specifically, we present algorithms for constructing a lifted joint distribution for scenarios of sequences of overlapping and non-overlapping logical variables. We present operations that work in a fully lifted way including addition, multiplication, and inversion. We present how the operations can be used for lifted query answering algorithms and extend the existing query answering algorithm by a new way of evidence handling. The new way of evidence handling groups evidence that has the same effect on its neighboring variables in cases of partial overlap between the logical-variable sequences. In the theoretical complexity analysis and the experimental evaluation, we show under which conditions the existing lifted approach and the new lifted approach including evidence grouping lead to the most time savings compared to the grounded approach.
期刊介绍:
The Journal of Artificial Intelligence (AIJ) welcomes papers covering a broad spectrum of AI topics, including cognition, automated reasoning, computer vision, machine learning, and more. Papers should demonstrate advancements in AI and propose innovative approaches to AI problems. Additionally, the journal accepts papers describing AI applications, focusing on how new methods enhance performance rather than reiterating conventional approaches. In addition to regular papers, AIJ also accepts Research Notes, Research Field Reviews, Position Papers, Book Reviews, and summary papers on AI challenges and competitions.