International Journal of Approximate Reasoning最新文献

Feature importance is a complex issue in machine learning, as determining a superior attribute is vague, uncertain, and dependent on the model. This study introduces a rough-fuzzy hybrid (RAFAR) method that merges various techniques from rough set theory and fuzzy set theory to tackle uncertainty in attribute importance and ranking. RAFAR utilizes an interval-valued fuzzy matrix to depict preference between attribute pairs. This research focuses on constructing these matrices from datasets and identifying suitable rankings based on these matrices. The concept of interval-valued weight vectors is introduced to represent attribute importance, and their additive and multiplicative compatibility is examined. The properties of these consistency types and the efficient algorithms for solving related problems are discussed. These new theoretical findings are valuable for creating effective optimization models and algorithms within the RAFAR framework. Additionally, novel approaches for constructing pairwise comparison matrices and enhancing the scalability of RAFAR are suggested. The study also includes experimental results on benchmark datasets to demonstrate the accuracy of the proposed solutions.

The notion of trustworthiness, central to many fields of human inquiry, has recently attracted the attention of various researchers in logic, computer science, and artificial intelligence (AI). Both conceptual and formal approaches for modeling trustworthiness as a (desirable) property of AI systems are emerging in the literature. To develop logics fit for this aim means to analyze both the non-deterministic aspect of AI systems and to offer a formalization of the intended meaning of their trustworthiness. In this work we take a semantic perspective on representing such processes, and provide a measure on possible worlds for evaluating them as trustworthy. In particular, we intend trustworthiness as the correspondence within acceptable limits between a model in which the theoretical probability of a process to produce a given output is expressed and a model in which the frequency of showing such output as established during a relevant number of tests is measured. From a technical perspective, we show that our semantics characterizes the probabilistic typed natural deduction calculus introduced in D'Asaro and Primiero (2021)[12] and further extended in D'Asaro et al. (2023) [13]. This contribution connects those results on trustworthy probabilistic processes with the mainstream method in modal logic, thereby facilitating the understanding of this field of research for a larger audience of logicians, as well as setting the stage for an epistemic logic appropriate to the task.

In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast ‘on the fly’ without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the more standard approach. We take the first steps in allowing for probability intervals instead of precise probabilities on this prequential approach, based on ideas borrowed from our earlier imprecise-probabilistic, standard account of algorithmic randomness. We define what it means for an infinite sequence $(I_1,x_1,I_2,x_2,\dots )$ of successive interval forecasts $I_k$ and subsequent binary outcomes $x_k$ to be random, both in a martingale-theoretic and a test-theoretic sense. We prove that these two versions of prequential randomness coincide, we compare the resulting prequential randomness notions with the more standard ones, and we investigate where the prequential and standard randomness notions coincide.

This paper presents a novel distribution-free Inferential Model (IM) construction that provides valid probabilistic inference across a broad spectrum of distribution-free problems, even in finite sample settings. More specifically, the proposed IM has the capability to assign (imprecise) probabilities to assertions of interest about any feature of the unknown quantities under examination, and these probabilities are well-calibrated in a frequentist sense. It is also shown that finite-sample confidence regions can be derived from the IM for any such features. Particular emphasis is placed on quantile regression, a domain where uncertainty quantification often takes the form of set estimates for the regression coefficients in applications. Within this context, the IM facilitates the acquisition of these set estimates, ensuring they are finite-sample confidence regions. It also enables the provision of finite-sample valid probabilistic assignments for any assertions of interest about the regression coefficients. As a result, regardless of the type of uncertainty quantification desired, the proposed framework offers an appealing solution to quantile regression.

The neighborhood rough set model serves as an important tool for handling attribute reduction tasks involving heterogeneous attributes. However, measuring the relationship between conditional attributes and decision in the neighborhood rough set model is a crucial issue. Most studies have utilized neighborhood information entropy to measure the relationship between attributes. When using neighborhood conditional information entropy to measure the relationships between the decision and conditional attributes, it lacks monotonicity, consequently affecting the rationality of the final attribute reduction subset. In this paper, we introduce the concept of neighborhood granularity and propose a new form of relative neighborhood granularity to measure the relationship between the decision and conditional attributes, which exhibits monotonicity. Moreover, our approach for measuring neighborhood granularity avoids the logarithmic function computation involved in neighborhood information entropy. Finally, we conduct comparative experiments on 12 datasets using two classifiers to compare the results of attribute reduction with six other attribute reduction algorithms. The comparison demonstrates the advantages of our measurement approach.

During the last years, the study of fuzzy database query languages has attracted the attention of many researchers. In this line of research, our group has proposed and developed FSA-SPARQL (Fuzzy Sets and Aggregators based SPARQL), which is a fuzzy extension of the Semantic Web query language SPARQL. FSA-SPARQL works with fuzzy RDF datasets and allows the definition of fuzzy queries involving fuzzy conditions through fuzzy connectives and aggregators. However, there are two main challenges to be solved for the practical applicability of FSA-SPARQL. The first problem is the lack of fuzzy RDF data sources. The second is how to customize fuzzy queries on fuzzy RDF data sources. Our research group has also recently proposed a fuzzy logic programming language called $FASILL$ that offers powerful tuning capabilities that can accept applications in many fields. The purpose of this paper is to show how the $FASILL$ tuning capabilities serve to accomplish in a unified framework both challenges in FSA-SPARQL: data fuzzification and query customization. More concretely, from a FSA-SPARQL to $FASILL$ transformation, data fuzzification and query customization in FSA-SPARQL become $FASILL$ tuning problems. We have validated the approach with queries against datasets from online communities.

Collapsibility refers to the property that, when marginalizing over some variables that are not of interest from the full model, the resulting marginal model of the remaining variables is equivalent to the local model induced by the subgraph on these variables. This means that when the marginal model satisfies collapsibility, statistical inference results based on the marginal model and the local model are consistent. This has significant implications for small-sample data, modeling latent variable data, and reducing the computational complexity of statistical inference. This paper focuses on studying the conditional independence collapsibility of acyclic directed mixed graph (ADMG) models. By introducing the concept of inducing paths in ADMGs and exploring its properties, the conditional independence collapsibility of ADMGs is characterized equivalently from both graph theory and statistical perspectives.

In this paper we propose a Bayesian approach for inferring Bayesian network (BN) structures from ordinal data. Our approach can be seen as the Bayesian counterpart of a recently proposed frequentist approach, referred to as the ‘ordinal structure expectation maximization’ (OSEM) method. Like for the OSEM method, the key idea is to assume that each ordinal variable originates from a Gaussian variable that can only be observed in discretized form, and that the dependencies in the latent Gaussian space can be modeled by BNs; i.e. by directed acyclic graphs (DAGs). Our Bayesian method combines the ‘structure MCMC sampler’ for DAG posterior sampling, a slightly modified version of the ‘Bayesian metric for Gaussian networks having score equivalence’ (BGe score), the concept of the ‘extended rank likelihood’, and a recently proposed algorithm for posterior sampling the parameters of Gaussian BNs. In simulation studies we compare the new Bayesian approach and the OSEM method in terms of the network reconstruction accuracy. The empirical results show that the new Bayesian approach leads to significantly improved network reconstruction accuracies.

This paper proposes a tentative and original survey of meeting points between Knowledge Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have been developed quite separately in the last four decades. First, some common concerns are identified and discussed such as the types of representation used, the roles of knowledge and data, the lack or the excess of information, or the need for explanations and causal understanding. Then, the survey is organised in seven sections covering most of the territory where KRR and ML meet. We start with a section dealing with prototypical approaches from the literature on learning and reasoning: Inductive Logic Programming, Statistical Relational Learning, and Neurosymbolic AI, where ideas from rule-based reasoning are combined with ML. Then we focus on the use of various forms of background knowledge in learning, ranging from additional regularisation terms in loss functions, to the problem of aligning symbolic and vector space representations, or the use of knowledge graphs for learning. Then, the next section describes how KRR notions may benefit to learning tasks. For instance, constraints can be used as in declarative data mining for influencing the learned patterns; or semantic features are exploited in low-shot learning to compensate for the lack of data; or yet we can take advantage of analogies for learning purposes. Conversely, another section investigates how ML methods may serve KRR goals. For instance, one may learn special kinds of rules such as default rules, fuzzy rules or threshold rules, or special types of information such as constraints, or preferences. The section also covers formal concept analysis and rough sets-based methods. Yet another section reviews various interactions between Automated Reasoning and ML, such as the use of ML methods in SAT solving to make reasoning faster. Then a section deals with works related to model accountability, including explainability and interpretability, fairness and robustness. Finally, a section covers works on handling imperfect or incomplete data, including the problem of learning from uncertain or coarse data, the use of belief functions for regression, a revision-based view of the EM algorithm, the use of possibility theory in statistics, or the learning of imprecise models. This paper thus aims at a better mutual understanding of research in KRR and ML, and how they can cooperate. The paper is completed by an abundant bibliography.