Generalized Naive Bayes

• URL: http://arxiv.org/abs/2408.15923v1
• Date: Wed, 28 Aug 2024 16:36:18 GMT
• Title: Generalized Naive Bayes
• Authors: Edith Alice Kovács, Anna Ország, Dániel Pfeifer, András Benczúr,
• Abstract summary: We introduce the so-called Generalized Naive Bayes structure as an extension of the Naive Bayes structure. We prove that this fits the data at least as well as the probability distribution determined by the classical Naive Bayes (NB)
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: In this paper we introduce the so-called Generalized Naive Bayes structure as an extension of the Naive Bayes structure. We give a new greedy algorithm that finds a good fitting Generalized Naive Bayes (GNB) probability distribution. We prove that this fits the data at least as well as the probability distribution determined by the classical Naive Bayes (NB). Then, under a not very restrictive condition, we give a second algorithm for which we can prove that it finds the optimal GNB probability distribution, i.e. best fitting structure in the sense of KL divergence. Both algorithms are constructed to maximize the information content and aim to minimize redundancy. Based on these algorithms, new methods for feature selection are introduced. We discuss the similarities and differences to other related algorithms in terms of structure, methodology, and complexity. Experimental results show, that the algorithms introduced outperform the related algorithms in many cases.

Related papers

• On Policy Evaluation Algorithms in Distributional Reinforcement Learning [0.0]
  We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL) For a plain instance of our proposed class of algorithms we prove error bounds, both within Wasserstein and Kolmogorov--Smirnov distances. For return distributions having probability density functions the algorithms yield approximations for these densities; error bounds are given within supremum norm.
  arXiv  Detail & Related papers  (2024-07-19T10:06:01Z)
• Optimal estimation of Gaussian (poly)trees [25.02920605955238]
  We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery) The first approach is based on the Chow-Liu algorithm, and learns an optimal tree-structured distribution efficiently. The second approach is a modification of the PC algorithm for polytrees that uses partial correlation as a conditional independence tester for constraint-based structure learning.
  arXiv  Detail & Related papers  (2024-02-09T12:58:36Z)
• Generalized Schrödinger Bridge Matching [54.171931505066]
  Generalized Schr"odinger Bridge (GSB) problem setup is prevalent in many scientific areas both within and without machine learning. We propose Generalized Schr"odinger Bridge Matching (GSBM), a new matching algorithm inspired by recent advances. We show that such a generalization can be cast as solving conditional optimal control, for which variational approximations can be used.
  arXiv  Detail & Related papers  (2023-10-03T17:42:11Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Hybrid Bayesian network discovery with latent variables by scoring multiple interventions [5.994412766684843]
  We present the hybrid mFGS-BS (majority rule and Fast Greedy equivalence Search with Bayesian Scoring) algorithm for structure learning from discrete data. The algorithm assumes causal insufficiency in the presence of latent variables and produces a Partial Ancestral Graph (PAG) Experimental results show that mFGS-BS improves structure learning accuracy relative to the state-of-the-art and it is computationally efficient.
  arXiv  Detail & Related papers  (2021-12-20T14:54:41Z)
• Bayesian decision-making under misspecified priors with applications to meta-learning [64.38020203019013]
  Thompson sampling and other sequential decision-making algorithms are popular approaches to tackle explore/exploit trade-offs in contextual bandits. We show that performance degrades gracefully with misspecified priors.
  arXiv  Detail & Related papers  (2021-07-03T23:17:26Z)
• Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information [78.78486761923855]
  In many real world problems, we want to infer some property of an expensive black-box function f, given a budget of T function evaluations. We present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm's output. On these problems, InfoBAX uses up to 500 times fewer queries to f than required by the original algorithm.
  arXiv  Detail & Related papers  (2021-04-19T17:22:11Z)
• Distributed Variational Bayesian Algorithms Over Sensor Networks [6.572330981878818]
  We propose two novel distributed VB algorithms for general Bayesian inference problem. The proposed algorithms have excellent performance, which are almost as good as the corresponding centralized VB algorithm relying on all data available in a fusion center.
  arXiv  Detail & Related papers  (2020-11-27T08:12:18Z)
• Efficient Computation of Expectations under Spanning Tree Distributions [67.71280539312536]
  We propose unified algorithms for the important cases of first-order expectations and second-order expectations in edge-factored, non-projective spanning-tree models. Our algorithms exploit a fundamental connection between gradients and expectations, which allows us to derive efficient algorithms.
  arXiv  Detail & Related papers  (2020-08-29T14:58:26Z)
• Differentiable TAN Structure Learning for Bayesian Network Classifiers [19.30562170076368]
  We consider learning of tree-augmented naive Bayes (TAN) structures for Bayesian network classifiers with discrete input features. Instead of performing a optimization over the space of possible graph structures, the proposed method learns a distribution over graph structures. Our method consistently outperforms random TAN structures and Chow-Liu TAN structures.
  arXiv  Detail & Related papers  (2020-08-21T16:22:47Z)
• Learning to Accelerate Heuristic Searching for Large-Scale Maximum Weighted b-Matching Problems in Online Advertising [51.97494906131859]
  Bipartite b-matching is fundamental in algorithm design, and has been widely applied into economic markets, labor markets, etc. Existing exact and approximate algorithms usually fail in such settings due to either requiring intolerable running time or too much computation resource. We propose textttNeuSearcher which leverages the knowledge learned from previously instances to solve new problem instances.
  arXiv  Detail & Related papers  (2020-05-09T02:48:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.