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A new definition for feature selection stability analysis 特征选择稳定性分析的新定义
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-03-01 DOI: 10.1007/s10472-024-09936-8
Teddy Lazebnik, Avi Rosenfeld
{"title":"A new definition for feature selection stability analysis","authors":"Teddy Lazebnik,&nbsp;Avi Rosenfeld","doi":"10.1007/s10472-024-09936-8","DOIUrl":"10.1007/s10472-024-09936-8","url":null,"abstract":"<div><p>Feature selection (FS) stability is an important topic of recent interest. Finding stable features is important for creating reliable, non-overfitted feature sets, which in turn can be used to generate machine learning models with better accuracy and explanations and are less prone to adversarial attacks. There are currently several definitions of FS stability that are widely used. In this paper, we demonstrate that existing stability metrics fail to quantify certain key elements of many datasets such as resilience to data drift or non-uniformly distributed missing values. To address this shortcoming, we propose a new definition for FS stability inspired by Lyapunov stability in dynamic systems. We show the proposed definition is statistically different from the classical <i>record-stability</i> on (<span>(n=90)</span>) datasets. We present the advantages and disadvantages of using Lyapunov and other stability definitions and demonstrate three scenarios in which each one of the three proposed stability metrics is best suited.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 3","pages":"753 - 770"},"PeriodicalIF":1.2,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-024-09936-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140017398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Correction: Personalized choice prediction with less user information 更正：利用较少的用户信息进行个性化选择预测
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-20 DOI: 10.1007/s10472-024-09934-w
Francine Chen, Yanxia Zhang, Minh Nguyen, Matt Klenk, Charlene Wu
{"title":"Correction: Personalized choice prediction with less user information","authors":"Francine Chen,&nbsp;Yanxia Zhang,&nbsp;Minh Nguyen,&nbsp;Matt Klenk,&nbsp;Charlene Wu","doi":"10.1007/s10472-024-09934-w","DOIUrl":"10.1007/s10472-024-09934-w","url":null,"abstract":"","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 3","pages":"771 - 771"},"PeriodicalIF":1.2,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-024-09934-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sequential composition of propositional logic programs 命题逻辑程序的顺序组合
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-15 DOI: 10.1007/s10472-024-09925-x
Christian Antić
{"title":"Sequential composition of propositional logic programs","authors":"Christian Antić","doi":"10.1007/s10472-024-09925-x","DOIUrl":"10.1007/s10472-024-09925-x","url":null,"abstract":"<div><p>This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for arbitrary programs. We show that the immediate consequence operator of a program can be represented via composition which allows us to compute its least model without any explicit reference to operators. This bridges the conceptual gap between the syntax and semantics of a propositional logic program in a mathematically satisfactory way.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 2","pages":"505 - 533"},"PeriodicalIF":1.2,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-024-09925-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analogical proportions in monounary algebras 单名代数中的类比比例
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-10 DOI: 10.1007/s10472-023-09921-7
Christian Antić
{"title":"Analogical proportions in monounary algebras","authors":"Christian Antić","doi":"10.1007/s10472-023-09921-7","DOIUrl":"10.1007/s10472-023-09921-7","url":null,"abstract":"<div><p>This paper studies analogical proportions in monounary algebras consisting only of a universe and a single unary function, where we analyze the role of congruences, and we show that the analogical proportion relation is characterized in the infinite monounary algebra formed by the natural numbers together with the successor function via difference proportions.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 6","pages":"1663 - 1677"},"PeriodicalIF":1.2,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10472-023-09921-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A category theory approach to the semiotics of machine learning 机器学习符号学的范畴理论方法
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-09 DOI: 10.1007/s10472-024-09932-y
Fernando Tohmé, Rocco Gangle, Gianluca Caterina
{"title":"A category theory approach to the semiotics of machine learning","authors":"Fernando Tohmé,&nbsp;Rocco Gangle,&nbsp;Gianluca Caterina","doi":"10.1007/s10472-024-09932-y","DOIUrl":"10.1007/s10472-024-09932-y","url":null,"abstract":"<div><p>The successes of Machine Learning, and in particular of Deep Learning systems, have led to a reformulation of the Artificial Intelligence agenda. One of the pressing issues in the field is the extraction of knowledge out of the behavior of those systems. In this paper we propose a semiotic analysis of that behavior, based on the formal model of <i>learners</i>. We analyze the topos-theoretic properties that ensure the logical expressivity of the knowledge embodied by learners. Furthermore, we show that there exists an ideal <i>universal learner</i>, able to interpret the knowledge gained about any possible function as well as about itself, which can be monotonically approximated by networks of increasing size.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 3","pages":"733 - 751"},"PeriodicalIF":1.2,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds on depth of decision trees derived from decision rule systems with discrete attributes 从具有离散属性的决策规则系统得出的决策树深度的界限
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-08 DOI: 10.1007/s10472-024-09933-x
Kerven Durdymyradov, Mikhail Moshkov
{"title":"Bounds on depth of decision trees derived from decision rule systems with discrete attributes","authors":"Kerven Durdymyradov,&nbsp;Mikhail Moshkov","doi":"10.1007/s10472-024-09933-x","DOIUrl":"10.1007/s10472-024-09933-x","url":null,"abstract":"<div><p>Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of relationships between these two models is an important task of computer science. It is easy to transform a decision tree into a decision rule system. The inverse transformation is a more difficult task. In this paper, we study unimprovable upper and lower bounds on the minimum depth of decision trees derived from decision rule systems with discrete attributes depending on the various parameters of these systems. To illustrate the process of transformation of decision rule systems into decision trees, we generalize well known result for Boolean functions to the case of functions of <i>k</i>-valued logic.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 3","pages":"703 - 732"},"PeriodicalIF":1.2,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Theoretical aspects of robust SVM optimization in Banach spaces and Nash equilibrium interpretation 巴拿赫空间中稳健 SVM 优化的理论问题和纳什均衡解释
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-08 DOI: 10.1007/s10472-024-09931-z
Mohammed Sbihi, Nicolas Couellan
{"title":"Theoretical aspects of robust SVM optimization in Banach spaces and Nash equilibrium interpretation","authors":"Mohammed Sbihi,&nbsp;Nicolas Couellan","doi":"10.1007/s10472-024-09931-z","DOIUrl":"10.1007/s10472-024-09931-z","url":null,"abstract":"<div><p>There are many real life applications where data can not be effectively represented in Hilbert spaces and/or where the data points are uncertain. In this context, we address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalized to their robust counterpart in Banach spaces. These include the representer theorem, strong duality for the associated optimization problem as well as their geometrical interpretation. Furthermore, we propose a game theoretical interpretation of the class separation problem when the underlying space is reflexive and smooth. The proposed Nash equilibrium formulation draws connections and emphasizes the interplay between class separation in machine learning and game theory in the general setting of Banach spaces.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 5","pages":"1273 - 1293"},"PeriodicalIF":1.2,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Learning preference representations based on Choquet integrals for multicriteria decision making 基于乔奎特积分的偏好表征学习用于多标准决策
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-07 DOI: 10.1007/s10472-024-09930-0
Margot Herin, Patrice Perny, Nataliya Sokolovska
{"title":"Learning preference representations based on Choquet integrals for multicriteria decision making","authors":"Margot Herin,&nbsp;Patrice Perny,&nbsp;Nataliya Sokolovska","doi":"10.1007/s10472-024-09930-0","DOIUrl":"10.1007/s10472-024-09930-0","url":null,"abstract":"<div><p>This paper concerns preference elicitation and learning of decision models in the context of multicriteria decision making. We propose an approach to learn a representation of preferences by a non-additive multiattribute utility function, namely a Choquet or bi-Choquet integral. This preference model is parameterized by one-dimensional utility functions measuring the attractiveness of consequences w.r.t. various point of views and one or two set functions (capacities) used to weight the coalitions and control the intensity of interactions among criteria, on the positive and possibly the negative sides of the utility scale. Our aim is to show how we can successively learn marginal utilities from properly chosen preference examples and then learn where the interactions matter in the overall model. We first present a preference elicitation method to learn spline representations of marginal utilities on every component of the model. Then we propose a sparse learning approach based on adaptive <span>(L_1)</span>-regularization for determining a compact Möbius representation fitted to the observed preferences. We present numerical tests to compare different regularization methods. We also show the advantages of our approach compared to basic methods that do not seek sparsity or that force sparsity a priori by requiring <i>k</i>-additivity.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 6","pages":"1511 - 1544"},"PeriodicalIF":1.2,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A metaheuristic for inferring a ranking model based on multiple reference profiles 基于多个参考剖面推断排序模型的元智程
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-02-06 DOI: 10.1007/s10472-024-09926-w
Arwa Khannoussi, Alexandru-Liviu Olteanu, Patrick Meyer, Bastien Pasdeloup
{"title":"A metaheuristic for inferring a ranking model based on multiple reference profiles","authors":"Arwa Khannoussi,&nbsp;Alexandru-Liviu Olteanu,&nbsp;Patrick Meyer,&nbsp;Bastien Pasdeloup","doi":"10.1007/s10472-024-09926-w","DOIUrl":"10.1007/s10472-024-09926-w","url":null,"abstract":"<div><p>In the context of Multiple Criteria Decision Aiding, decision makers often face problems with multiple conflicting criteria that justify the use of preference models to help advancing towards a decision. In order to determine the parameters of these preference models, preference elicitation makes use of preference learning algorithms, usually taking as input holistic judgments, i.e., overall preferences on some of the alternatives, expressed by the decision maker. Tools to achieve this goal in the context of a ranking model based on multiple reference profiles are usually based on mixed-integer linear programming, Boolean satisfiability formulation or metaheuristics. However, they are usually unable to handle realistic problems involving many criteria and a large amount of input information. We propose here an evolutionary metaheuristic in order to address this issue. Extensive experiments illustrate its ability to handle problem instances that previous proposals cannot.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 6","pages":"1467 - 1488"},"PeriodicalIF":1.2,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139767244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A knowledge compilation perspective on queries and transformations for belief tracking 从知识汇编角度看信念跟踪的查询和转换
IF 1.2 4区 计算机科学
Annals of Mathematics and Artificial Intelligence Pub Date : 2024-01-31 DOI: 10.1007/s10472-023-09908-4
Alexandre Niveau, Hector Palacios, Sergej Scheck, Bruno Zanuttini
{"title":"A knowledge compilation perspective on queries and transformations for belief tracking","authors":"Alexandre Niveau,&nbsp;Hector Palacios,&nbsp;Sergej Scheck,&nbsp;Bruno Zanuttini","doi":"10.1007/s10472-023-09908-4","DOIUrl":"10.1007/s10472-023-09908-4","url":null,"abstract":"<div><p>Nondeterministic planning is the process of computing plans or policies of actions achieving given goals, when there is nondeterministic uncertainty about the initial state and/or the outcomes of actions. This process encompasses many precise computational problems, from classical planning, where there is no uncertainty, to contingent planning, where the agent has access to observations about the current state. Fundamental to these problems is belief tracking, that is, obtaining information about the current state after a history of actions and observations. At an abstract level, belief tracking can be seen as maintaining and querying the current belief state, that is, the set of states consistent with the history. We take a knowledge compilation perspective on these processes, by defining the queries and transformations which pertain to belief tracking. We study them for propositional domains, considering a number of representations for belief states, actions, observations, and goals. In particular, for belief states, we consider explicit propositional representations with and without auxiliary variables, as well as implicit representations by the history itself; and for actions, we consider propositional action theories as well as ground PDDL and conditional STRIPS. For all combinations, we investigate the complexity of relevant queries (for instance, whether an action is applicable at a belief state) and transformations (for instance, revising a belief state by an observation); we also discuss the relative succinctness of representations. Though many results show an expected tradeoff between succinctness and tractability, we identify some interesting combinations. We also discuss the choice of representations by existing planners in light of our study.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 5","pages":"1113 - 1159"},"PeriodicalIF":1.2,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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