Pub Date : 2024-10-29DOI: 10.1016/j.ijar.2024.109311
Qin Ma, Shikui Tu, Lei Xu
The difficulty of causal inference for small-sample-size data lies in the issue of inefficiency that the variance of the estimators may be large. Some existing weighting methods adopt the idea of bias-variance trade-off, but they require manual specification of the trade-off parameters. To overcome this drawback, in this article, we propose a Cauchy-Schwarz Bounded Trade-off Weighting (CBTW) method, in which the trade-off parameter is theoretically derived to guarantee a small Mean Square Error (MSE) in estimation. We theoretically prove that optimizing the objective function of CBTW, which is the Cauchy-Schwarz upper-bound of the MSE for causal effect estimators, contributes to minimizing the MSE. Moreover, since the upper-bound consists of the variance and the squared -norm of covariate differences, CBTW can not only estimate the causal effects efficiently, but also keep the covariates balanced. Experimental results on both simulation data and real-world data show that the CBTW outperforms most existing methods especially under small sample size scenarios.
{"title":"Cauchy-Schwarz bounded trade-off weighting for causal inference with small sample sizes","authors":"Qin Ma, Shikui Tu, Lei Xu","doi":"10.1016/j.ijar.2024.109311","DOIUrl":"10.1016/j.ijar.2024.109311","url":null,"abstract":"<div><div>The difficulty of causal inference for small-sample-size data lies in the issue of inefficiency that the variance of the estimators may be large. Some existing weighting methods adopt the idea of bias-variance trade-off, but they require manual specification of the trade-off parameters. To overcome this drawback, in this article, we propose a Cauchy-Schwarz Bounded Trade-off Weighting (CBTW) method, in which the trade-off parameter is theoretically derived to guarantee a small Mean Square Error (MSE) in estimation. We theoretically prove that optimizing the objective function of CBTW, which is the Cauchy-Schwarz upper-bound of the MSE for causal effect estimators, contributes to minimizing the MSE. Moreover, since the upper-bound consists of the variance and the squared <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-norm of covariate differences, CBTW can not only estimate the causal effects efficiently, but also keep the covariates balanced. Experimental results on both simulation data and real-world data show that the CBTW outperforms most existing methods especially under small sample size scenarios.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"176 ","pages":"Article 109311"},"PeriodicalIF":3.2,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-24DOI: 10.1016/j.ijar.2024.109309
Arun Kumar, Neha Gaur, Bisham Dewan
This paper investigates the logical structure of the 4-element chain considered as a double Stone algebra. It has been shown that any element of a double Stone algebra can be identified as monotone ordered triplet of sets. As a consequence, we obtain the 4-valued semantics for the logic of double Stone algebras. Furthermore, the rough set semantics of the logic is provided by dividing the boundary region (uncertainty) into two disjoint subregions.
{"title":"A 4-valued logic for double Stone algebras","authors":"Arun Kumar, Neha Gaur, Bisham Dewan","doi":"10.1016/j.ijar.2024.109309","DOIUrl":"10.1016/j.ijar.2024.109309","url":null,"abstract":"<div><div>This paper investigates the logical structure of the 4-element chain considered as a double Stone algebra. It has been shown that any element of a double Stone algebra can be identified as monotone ordered triplet of sets. As a consequence, we obtain the 4-valued semantics for the logic <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> of double Stone algebras. Furthermore, the rough set semantics of the logic <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> is provided by dividing the boundary region (uncertainty) into two disjoint subregions.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"176 ","pages":"Article 109309"},"PeriodicalIF":3.2,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-18DOI: 10.1016/j.ijar.2024.109308
Alexander Erreygers
This work investigates convex expectations, mainly in the setting of uncertain processes with countable state space. In the general setting it shows how, under the assumption of downward continuity, a convex expectation on a linear lattice of bounded functions can be extended to a convex expectation on the measurable extended real functions. This result is especially relevant in the setting of uncertain processes: there, an easy way to obtain a convex expectation on the linear lattice of finitary bounded functions is to combine an initial convex expectation with a convex transition semigroup. Crucially, this work presents a sufficient condition on this semigroup which guarantees that the induced convex expectation is downward continuous, so that it can be extended to the set of measurable extended real functions. To conclude, this work looks at existing results on convex transition semigroups from the point of view of the aforementioned sufficient condition, in particular to construct a sublinear Poisson process.
{"title":"Convex expectations for countable-state uncertain processes with càdlàg sample paths","authors":"Alexander Erreygers","doi":"10.1016/j.ijar.2024.109308","DOIUrl":"10.1016/j.ijar.2024.109308","url":null,"abstract":"<div><div>This work investigates convex expectations, mainly in the setting of uncertain processes with countable state space. In the general setting it shows how, under the assumption of downward continuity, a convex expectation on a linear lattice of bounded functions can be extended to a convex expectation on the measurable extended real functions. This result is especially relevant in the setting of uncertain processes: there, an easy way to obtain a convex expectation on the linear lattice of finitary bounded functions is to combine an initial convex expectation with a convex transition semigroup. Crucially, this work presents a sufficient condition on this semigroup which guarantees that the induced convex expectation is downward continuous, so that it can be extended to the set of measurable extended real functions. To conclude, this work looks at existing results on convex transition semigroups from the point of view of the aforementioned sufficient condition, in particular to construct a sublinear Poisson process.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109308"},"PeriodicalIF":3.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-17DOI: 10.1016/j.ijar.2024.109307
Walid Fathallah , Nahla Ben Amor , Philippe Leray
In recent years, there has been a significant upsurge in the interest surrounding Quantum machine learning, with researchers actively developing methods to leverage the power of quantum technology for solving highly complex problems across various domains. However, implementing gate-based quantum algorithms on noisy intermediate quantum devices (NISQ) presents notable challenges due to limited quantum resources and inherent noise. In this paper, we propose an innovative approach for representing Bayesian networks on quantum circuits, specifically designed to address these challenges and highlight the potential of combining optimized circuits with quantum hybrid algorithms for Bayesian network inference. Our aim is to minimize the required quantum resource needed to implement a Quantum Bayesian network (QBN) and implement quantum approximate inference algorithm on a quantum computer. Through simulations and experiments on IBM Quantum computers, we show that our circuit representation significantly reduces the resource requirements without decreasing the performance of the model. These findings underscore how our approach can better enable practical applications of QBN on currently available quantum hardware.
近年来，人们对量子机器学习的兴趣大增，研究人员积极开发各种方法，利用量子技术的力量解决各个领域的高度复杂问题。然而，由于有限的量子资源和固有的噪声，在噪声中间量子器件（NISQ）上实现基于门的量子算法面临着显著的挑战。在本文中，我们提出了一种在量子电路上表示贝叶斯网络的创新方法，专门用于应对这些挑战，并强调了将优化电路与用于贝叶斯网络推理的量子混合算法相结合的潜力。我们的目标是最大限度地减少实现量子贝叶斯网络（QBN）所需的量子资源，并在量子计算机上实现量子近似推理算法。通过在 IBM 量子计算机上进行模拟和实验，我们表明，我们的电路表示法在不降低模型性能的情况下大大降低了资源需求。这些发现强调了我们的方法如何能更好地在现有量子硬件上实现 QBN 的实际应用。
{"title":"Approximate inference on optimized quantum Bayesian networks","authors":"Walid Fathallah , Nahla Ben Amor , Philippe Leray","doi":"10.1016/j.ijar.2024.109307","DOIUrl":"10.1016/j.ijar.2024.109307","url":null,"abstract":"<div><div>In recent years, there has been a significant upsurge in the interest surrounding Quantum machine learning, with researchers actively developing methods to leverage the power of quantum technology for solving highly complex problems across various domains. However, implementing gate-based quantum algorithms on noisy intermediate quantum devices (NISQ) presents notable challenges due to limited quantum resources and inherent noise. In this paper, we propose an innovative approach for representing Bayesian networks on quantum circuits, specifically designed to address these challenges and highlight the potential of combining optimized circuits with quantum hybrid algorithms for Bayesian network inference. Our aim is to minimize the required quantum resource needed to implement a Quantum Bayesian network (QBN) and implement quantum approximate inference algorithm on a quantum computer. Through simulations and experiments on IBM Quantum computers, we show that our circuit representation significantly reduces the resource requirements without decreasing the performance of the model. These findings underscore how our approach can better enable practical applications of QBN on currently available quantum hardware.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109307"},"PeriodicalIF":3.2,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.ijar.2024.109304
Yuntian Wang , Lemnaouar Zedam , Bao Qing Hu , Bernard De Baets
In this paper, we expound weaker forms of increasingness of binary operations on a lattice by reducing the number of variables involved in the classical formulation of the increasingness property as seen from the viewpoint of dominance between binary operations. We investigate the relationships among these weaker forms. Furthermore, we demonstrate the role of these weaker forms in characterizing the meet and join operations of a lattice and a chain in particular. Finally, we provide ample generic examples.
{"title":"A dissection of the monotonicity property of binary operations from a dominance point of view","authors":"Yuntian Wang , Lemnaouar Zedam , Bao Qing Hu , Bernard De Baets","doi":"10.1016/j.ijar.2024.109304","DOIUrl":"10.1016/j.ijar.2024.109304","url":null,"abstract":"<div><div>In this paper, we expound weaker forms of increasingness of binary operations on a lattice by reducing the number of variables involved in the classical formulation of the increasingness property as seen from the viewpoint of dominance between binary operations. We investigate the relationships among these weaker forms. Furthermore, we demonstrate the role of these weaker forms in characterizing the meet and join operations of a lattice and a chain in particular. Finally, we provide ample generic examples.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109304"},"PeriodicalIF":3.2,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142446030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.ijar.2024.109303
Inma P. Cabrera, Sébastien Ferré, Sergei Obiedkov
{"title":"Selected papers from the First International Joint Conference on Conceptual Knowledge Structures","authors":"Inma P. Cabrera, Sébastien Ferré, Sergei Obiedkov","doi":"10.1016/j.ijar.2024.109303","DOIUrl":"10.1016/j.ijar.2024.109303","url":null,"abstract":"","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109303"},"PeriodicalIF":3.2,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.ijar.2024.109297
Petr Tomášek, Karel Horák, Branislav Bošanský
Real-world scenarios often involve dynamic interactions among competing agents, where decisions are made considering actions taken by others. These situations can be modeled as partially observable stochastic games (POSGs), with zero-sum variants capturing strictly competitive interactions (e.g., security scenarios). While such models address a broad range of problems, they commonly focus on infinite-horizon scenarios with discounted-sum objectives. Using the discounted-sum objective, however, can lead to suboptimal solutions in cases where the length of the interaction does not directly affect the gained rewards of the players.
We thus focus on games with undiscounted objective and an indefinite horizon where every realization of the game is guaranteed to terminate after some unspecified number of turns. To manage the computational complexity of solving POSGs in general, we restrict to games with one-sided partial observability where only one player has imperfect information while their opponent is provided with full information about the current situation. We introduce two novel algorithms based on the heuristic search value iteration (HSVI) algorithm that iteratively solve sequences of easier-to-solve approximations of the game using fundamentally different approaches for constructing the sequences: (1) in GoalHorizon, the game approximations are based on a limited number of turns in which players can change their actions, (2) in GoalDiscount, the game approximations are constructed using an increasing discount factor. We provide theoretical qualitative guarantees for algorithms, and we also experimentally demonstrate that these algorithms are able to find near-optimal solutions on pursuit-evasion games and a game modeling privilege escalation problem from computer security.
{"title":"Iterative algorithms for solving one-sided partially observable stochastic shortest path games","authors":"Petr Tomášek, Karel Horák, Branislav Bošanský","doi":"10.1016/j.ijar.2024.109297","DOIUrl":"10.1016/j.ijar.2024.109297","url":null,"abstract":"<div><div>Real-world scenarios often involve dynamic interactions among competing agents, where decisions are made considering actions taken by others. These situations can be modeled as partially observable stochastic games (<span>POSG</span>s), with zero-sum variants capturing strictly competitive interactions (e.g., security scenarios). While such models address a broad range of problems, they commonly focus on infinite-horizon scenarios with discounted-sum objectives. Using the discounted-sum objective, however, can lead to suboptimal solutions in cases where the length of the interaction does not directly affect the gained rewards of the players.</div><div>We thus focus on games with undiscounted objective and an indefinite horizon where every realization of the game is guaranteed to terminate after some unspecified number of turns. To manage the computational complexity of solving <span>POSG</span>s in general, we restrict to games with one-sided partial observability where only one player has imperfect information while their opponent is provided with full information about the current situation. We introduce two novel algorithms based on the heuristic search value iteration (<span>HSVI</span>) algorithm that iteratively solve sequences of easier-to-solve approximations of the game using fundamentally different approaches for constructing the sequences: (1) in <span>GoalHorizon</span>, the game approximations are based on a limited number of turns in which players can change their actions, (2) in <span>GoalDiscount</span>, the game approximations are constructed using an increasing discount factor. We provide theoretical qualitative guarantees for algorithms, and we also experimentally demonstrate that these algorithms are able to find near-optimal solutions on pursuit-evasion games and a game modeling privilege escalation problem from computer security.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109297"},"PeriodicalIF":3.2,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.ijar.2024.109301
Mina Hemmatian , Ali Shahzadi , Saeed Mozaffari
Deep learning models have been widely employed across various fields. In real-world scenarios, especially safety-critical applications, quantifying uncertainty is as crucial as achieving high accuracy. To address this concern, Bayesian deep neural networks (BDNNs) emerged to estimate two different types of uncertainty: Aleatoric and Epistemic. Nevertheless, implementing a BDNN on resource-constrained devices poses challenges due to the substantial computational and storage costs imposed by approximation inference techniques. Thus, efficient compression methods should be utilized. We propose an uncertainty-based knowledge distillation method to compress BDNNs. Knowledge distillation is a model compression technique that involves transferring knowledge from a complex network, known as the teacher network, to a simpler one, referred to as the student network. Our method incorporates uncertainty into knowledge distillation to address situations where inappropriate teacher supervision undermines compression performance. We utilize the Epistemic uncertainty of teacher predictions to tailor supervision for each sample individually to take into account teacher's limited knowledge. Additionally, we adjust the temperature parameter of the distillation process for each sample based on the Aleatoric uncertainty of the teacher predictions, ensuring that the student receives appropriate supervision even in the presence of ambiguous data. As a result, the proposed method enables the Bayesian student network to be trained under both appropriate supervision of the Bayesian teacher network and ground truth labels. We evaluated our method on the CIFAR-10, CIFAR-100, and RAF-DB datasets, demonstrating notable improvements in accuracy over state-of-the-art knowledge distillation-based methods. Furthermore, the robustness of our approach was assessed through testing weakly trained teacher networks and the analysis of blurred and low-resolution data, which have high uncertainty. Experimental results show that the proposed method outperformed existing methods.
{"title":"Uncertainty-based knowledge distillation for Bayesian deep neural network compression","authors":"Mina Hemmatian , Ali Shahzadi , Saeed Mozaffari","doi":"10.1016/j.ijar.2024.109301","DOIUrl":"10.1016/j.ijar.2024.109301","url":null,"abstract":"<div><div>Deep learning models have been widely employed across various fields. In real-world scenarios, especially safety-critical applications, quantifying uncertainty is as crucial as achieving high accuracy. To address this concern, Bayesian deep neural networks (BDNNs) emerged to estimate two different types of uncertainty: Aleatoric and Epistemic. Nevertheless, implementing a BDNN on resource-constrained devices poses challenges due to the substantial computational and storage costs imposed by approximation inference techniques. Thus, efficient compression methods should be utilized. We propose an uncertainty-based knowledge distillation method to compress BDNNs. Knowledge distillation is a model compression technique that involves transferring knowledge from a complex network, known as the teacher network, to a simpler one, referred to as the student network. Our method incorporates uncertainty into knowledge distillation to address situations where inappropriate teacher supervision undermines compression performance. We utilize the Epistemic uncertainty of teacher predictions to tailor supervision for each sample individually to take into account teacher's limited knowledge. Additionally, we adjust the temperature parameter of the distillation process for each sample based on the Aleatoric uncertainty of the teacher predictions, ensuring that the student receives appropriate supervision even in the presence of ambiguous data. As a result, the proposed method enables the Bayesian student network to be trained under both appropriate supervision of the Bayesian teacher network and ground truth labels. We evaluated our method on the CIFAR-10, CIFAR-100, and RAF-DB datasets, demonstrating notable improvements in accuracy over state-of-the-art knowledge distillation-based methods. Furthermore, the robustness of our approach was assessed through testing weakly trained teacher networks and the analysis of blurred and low-resolution data, which have high uncertainty. Experimental results show that the proposed method outperformed existing methods.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109301"},"PeriodicalIF":3.2,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-27DOI: 10.1016/j.ijar.2024.109302
Jorge D. Laborda , Pablo Torrijos , José M. Puerta , José A. Gámez
Learning Bayesian Networks (BNs) from high-dimensional data is a complex and time-consuming task. Although there are approaches based on horizontal (instances) or vertical (variables) partitioning in the literature, none can guarantee the same theoretical properties as the Greedy Equivalence Search (GES) algorithm, except those based on the GES algorithm itself. This paper proposes a parallel distributed framework that uses GES as its local learning algorithm, obtaining results similar to those of GES and guaranteeing its theoretical properties but requiring less execution time. The framework involves splitting the set of all possible edges into clusters and constraining each framework node to only work with the received subset of edges. The global learning process is an iterative algorithm that carries out rounds until a convergence criterion is met. We have designed a ring and a star topology to distribute node connections. Regardless of the topology, each node receives a BN as input; it then fuses it with its own BN model and uses the result as the starting point for a local learning process, limited to its own subset of edges. Once finished, the result is then sent to another node as input. Experiments were carried out on a large repertory of domains, including large BNs up to more than 1000 variables. Our results demonstrate our proposal's effectiveness compared to GES and its fast version (fGES), generating high-quality BNs in less execution time.
{"title":"Distributed fusion-based algorithms for learning high-dimensional Bayesian Networks: Testing ring and star topologies","authors":"Jorge D. Laborda , Pablo Torrijos , José M. Puerta , José A. Gámez","doi":"10.1016/j.ijar.2024.109302","DOIUrl":"10.1016/j.ijar.2024.109302","url":null,"abstract":"<div><div>Learning Bayesian Networks (BNs) from high-dimensional data is a complex and time-consuming task. Although there are approaches based on horizontal (instances) or vertical (variables) partitioning in the literature, none can guarantee the same theoretical properties as the Greedy Equivalence Search (GES) algorithm, except those based on the GES algorithm itself. This paper proposes a parallel distributed framework that uses GES as its local learning algorithm, obtaining results similar to those of GES and guaranteeing its theoretical properties but requiring less execution time. The framework involves splitting the set of all possible edges into clusters and constraining each framework node to only work with the received subset of edges. The global learning process is an iterative algorithm that carries out rounds until a convergence criterion is met. We have designed a ring and a star topology to distribute node connections. Regardless of the topology, each node receives a BN as input; it then fuses it with its own BN model and uses the result as the starting point for a local learning process, limited to its own subset of edges. Once finished, the result is then sent to another node as input. Experiments were carried out on a large repertory of domains, including large BNs up to more than 1000 variables. Our results demonstrate our proposal's effectiveness compared to GES and its fast version (fGES), generating high-quality BNs in less execution time.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109302"},"PeriodicalIF":3.2,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-26DOI: 10.1016/j.ijar.2024.109300
Lianmeng Jiao , Han Zhang , Xiaojiao Geng , Quan Pan
The belief rules which extend the classical fuzzy IF-THEN rules with belief consequent parts have been widely used for classifier design due to their capabilities of building linguistic models interpretable to users and addressing various types of uncertainty. However, in the rule learning process, a high number of features generally results in a belief rule base with large size, which degrades both the classification accuracy and the model interpretability. Motivated by this challenge, the decision tree building technique which implements feature selection and model construction jointly is introduced in this paper to learn a compact and accurate belief rule base. To this end, a new fuzzy belief decision tree (FBDT) with fuzzy feature partitions and belief leaf nodes is designed: a fuzzy information gain ratio is first defined as the feature selection criterion for node fuzzy splitting and then the belief distributions are introduced to the leaf nodes to characterize the class uncertainty. Based on the initial rules extracted from the constructed FBDT, a joint optimization objective considering both classification accuracy and model interpretability is then designed to further reduce the rule redundancy. Experimental results based on real datasets show that the proposed FBDT-based classification method has much smaller rule base and better interpretability than other rule-based methods on the premise of competitive accuracy.
{"title":"Belief rule learning and reasoning for classification based on fuzzy belief decision tree","authors":"Lianmeng Jiao , Han Zhang , Xiaojiao Geng , Quan Pan","doi":"10.1016/j.ijar.2024.109300","DOIUrl":"10.1016/j.ijar.2024.109300","url":null,"abstract":"<div><div>The belief rules which extend the classical fuzzy IF-THEN rules with belief consequent parts have been widely used for classifier design due to their capabilities of building linguistic models interpretable to users and addressing various types of uncertainty. However, in the rule learning process, a high number of features generally results in a belief rule base with large size, which degrades both the classification accuracy and the model interpretability. Motivated by this challenge, the decision tree building technique which implements feature selection and model construction jointly is introduced in this paper to learn a compact and accurate belief rule base. To this end, a new fuzzy belief decision tree (FBDT) with fuzzy feature partitions and belief leaf nodes is designed: a fuzzy information gain ratio is first defined as the feature selection criterion for node fuzzy splitting and then the belief distributions are introduced to the leaf nodes to characterize the class uncertainty. Based on the initial rules extracted from the constructed FBDT, a joint optimization objective considering both classification accuracy and model interpretability is then designed to further reduce the rule redundancy. Experimental results based on real datasets show that the proposed FBDT-based classification method has much smaller rule base and better interpretability than other rule-based methods on the premise of competitive accuracy.</div></div>","PeriodicalId":13842,"journal":{"name":"International Journal of Approximate Reasoning","volume":"175 ","pages":"Article 109300"},"PeriodicalIF":3.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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