This paper offers a unified, model-agnostic, analogy-based framework for extracting relevant attributes and building contrastive explanations for a given classification. Analogical reasoning relies on the idea of comparing items by pairs to discern their similarities and differences, based on an observable sample S of data. First, adhering to this principle, we propose a pair-based approach to extract relevant attributes via an analogical relevance index (ARI) from Boolean or nominal datasets. We prove properties establishing the behavior of ARI with respect to available samples S. When comparing ARI against established methods such as χ2, mutual information, Shapley, or Sobol indices, empirical evidence highlights the appropriateness of ARI for synthetic datasets, where the classes are generated using specific Boolean functions. ARI also demonstrates robust performance across a diverse range of functions commonly encountered in real datasets. However, some synthetic datasets created from certain functions pose challenges for all indices. Second, we use analogical classification as a surrogate for explanation provision. Analogical classifiers are rooted on analogical proportions, involving the comparison of two pairs of items (a, b) and (c, d) through statements like “a differs from b as c differs from d”, denoted as a:b::c:d. To explain the classification of an item d, we search for an item c close to d but in a different class, forming a pair (c, d). Then, the analogical classifier extracts pairs (a, b) satisfying a:b::c:d leveraging the relevant features identified earlier. Finally we explain why d belongs to a class distinct from that of c by computing the frequency of pairs (a,b), mirroring the difference between c and d, that lead to the same class change. Standard local methods typically capitalize on examples within the item’s neighborhood for explanation. In contrast, our approach operates beyond the neighborhood, broadening the scope of explanatory power. Experiments on categorical synthetic and real datasets indicate that the proposed framework provides plausible and essentially human-understandable explanations.

This paper presents a survey of researches in analogical reasoning whose building block are analogical proportions which are statements of the form “a is to b as c is to d”. They have been developed in the last twenty years within an Artificial Intelligence perspective. After discussing their formal modeling with the associated inference mechanism, the paper reports the main results obtained in various AI domains ranging from computational linguistics to classification, including image processing, I.Q. tests, case based reasoning, preference learning, and formal concepts analysis. The last section discusses some new theoretical concerns, and the potential of analogical proportions in other areas such as argumentation, transfer learning, and XAI.

It has been observed that a particular form of analogical inference, based on analogical proportions, yields competitive results in classification tasks. Using the algebraic normal form of Boolean functions, it has been shown that analogical prediction is always exact iff the labeling function is affine. We point out that affine functions are also meaningful when using another view of analogy. We address the accuracy of analogical inference for arbitrary Boolean functions and show that if a function is epsilon-close to an affine function, then the probability of making a wrong prediction is upper bounded by 4 epsilon. This result is confirmed by an empirical study showing that the upper bound is tight. It highlights the specificity of analogical inference, also characterized in terms of the Hamming distance.

The classification of a new item may be viewed as a matter of associating it with the class where it is the least at odds w.r.t. the elements already in the class. An oddness measure of an item with respect to a multiset, applicable to Boolean features as well as to numerical ones, has been recently proposed. It has been shown that cumulating this measure over pairs or triples (rather than larger subsets) of elements in a class could provide an accurate estimate of the global oddness of an item with respect to a class. This idea is confirmed and refined in the present paper. Rather than considering all the pairs in a class, one can only deal with the pairs whose an element is one of the nearest neighbors of the item, in the target class. The oddness evaluation computed on this basis still leads to good results in terms of accuracy. One can take a step further and choose the second element in the pair also as another nearest neighbor in the class. Although the method relies on the notion of neighbors, the resulting algorithm is far from being a variant of the classical -nearest neighbors approach. The oddness with respect to a class computed only on the basis of pairs made of two nearest neighbors leads to a low complexity algorithm. Experiments on a set of UCI benchmarks show that the classifier obtained can compete with other well-known approaches.

Training set extension is an important issue in machine learning. Indeed when the examples at hand are in a limited quantity, the performances of standard classifiers may significantly decrease and it can be helpful to build additional examples. In this paper, we consider the use of analogical reasoning, and more particularly of analogical proportions for extending training sets. Here the ground truth labels are considered to be given by a (partially known) function. We examine the conditions that are required for such functions to ensure an error-free extension in a Boolean setting. To this end, we introduce the notion of Analogy Preserving (AP) functions, and we prove that their class is the class of affine Boolean functions. This noteworthy theoretical result is complemented with an empirical investigation of approximate AP functions, which suggests that they remain suitable for training set extension.

Classification can be viewed as a matter of associating a new item with the class where it is the least at odds w.r.t. the other elements. A recently proposed oddness index applied to pairs or triples (rather than larger subsets of elements in a class), when summed up over all such subsets, provides an accurate estimate of a global oddness of an item w.r.t. a class. Rather than considering all pairs in a class, one can only deal with pairs containing one of the nearest neighbors of the item in the target class. Taking a step further, we choose the second element in the pair as another nearest neighbor in the class. The oddness w.r.t. a class computed on the basis of pairs made of two nearest neighbors leads to low complexity classifiers, still competitive in terms of accuracy w.r.t. classical approaches.

In recent works, analogy-based classifiers have been proved quite successful. They exhibit good accuracy rates when compared with standard classification methods. Nevertheless, a theoretical study of their predictive power has not been done so far. One of the main barriers has been the lack of functional definition: analogical learners have only algorithmic definitions. The aim of our paper is to complement the empirical studies with a theoretical perspective. Using a simplified framework, we first provide a concise functional definition of the output of an analogical learner. Two versions of the definition are considered, a strict and a relaxed one. As far as we know, this is the first definition of this kind for analogical learner. Then, taking inspiration from results in k-NN studies, we examine some analytic properties such as convergence and VC-dimension, which are among the basic markers in terms of machine learning expressiveness. We then look at what could be expected in terms of theoretical accuracy from such a learner, in a Boolean setting. We examine learning curves for artificial domains, providing experimental results that illustrate our formulas, and empirically validate our functional definition of analogical classifiers.

The paper investigates the use of analogical reasoning for recommendation purposes. More particularly, we address the problem of predicting missing ratings on the basis of known ones. After discussing the differences with another recently experimented approach based on analogical proportions, a new analogical approach is proposed. It relies on the intuition that “the rating of user u for item i is to the rating of user v for item i as the rating of user u for item j is to the rating of user v for item j”. This leads to algorithms yielding results close to the ones of state-of-the art approaches, when the ratings are regarded as numerical quantities. This is due to the fact that these latter approaches embed an estimation process that is implicitly close to analogy, as discussed in this paper. An analogical approach is also outlined and briefly discussed when the ratings are supposed to have an ordinal meaning only.

The paper shows that a Boolean logic modeling of analogical proportions can serve as a basis for solving quizzes as well as a common and popular type of IQ tests, namely Raven's progressive matrices. They are nonverbal tests supposedly measuring general intelligence. A 3 × 3 Raven matrix exhibits eight geometric pictures displayed as its eight first cells: the remaining ninth cell is empty. In these tests, a set of candidate pictures is also given among which the subject is asked to identify the solution. In this paper, we investigate a general approach allowing to automatically solve Raven's progressive matrices tests. The approach is based on a logical view of analogical proportions, i.e., statements of the form “A is to B as C is to D.” We assume that analogical proportions hold between the rows and between the columns of the Raven's matrix. This view can be applied to a feature-based description of the pictures but also, in a number of cases, to a very low level representation, i.e., the pixel level. It appears that the analogical proportion reading just amounts here to a recopy of patterns of feature values that already appear in the data, after checking that there is no conflicting patterns. Implementing this principle, our algorithm builds up the ninth picture, without the help of any set of candidate solutions, and only on the basis of the eight known cells of the Raven matrices. A comparison with other approaches is provided. The ability to construct the missing picture without relying on candidate solutions is a distinctive feature of our work. Moreover, we emphasize the general principle underlying the approach that offers a simple and uniform mechanism applicable to the tests. At this step, the paper makes no claim about the cognitive validity of the approach with respect to the way humans solve such tests.

Introduced a few years ago, analogy-based classification methods are a noticeable addition to the set of lazy learning techniques. They provide amazing results (in terms of accuracy) on many classical datasets. They look for all triples of examples in the training set that are in analogical proportion with the item to be classified on a maximal number of attributes and for which the corresponding analogical proportion equation on the class has a solution. In this paper when classifying a new item, we demonstrate a new approach where we focus on a small part of the triples available. To restrict the scope of the search, we first look for examples that are as similar as possible to the new item to be classified. We then only consider the pairs of examples presenting the same dissimilarity as between the new item and one of its closest neighbors. Thus we implicitly build triples that are in analogical proportion on all attributes with the new item. Then the classification is made on the basis of a majority vote on the pairs leading to a solvable class equation. This new algorithm provides results as good as other analogical classifiers with a lower average complexity.

Reasoning deductively under incomplete information is nonmonotonic in nature since the arrival of additional information may invalidate or reverse previously obtained conclusions. It amounts to apply generic default rules in an appropriate way to a particular (partially described) situation. This type of nonmonotonic reasoning can only provide plausible conclusions. Analogical reasoning is another form of commonly used reasoning that yields brittle conclusions. It is nondeductive in nature and proceeds by putting particular situations in parallel. Analogical reasoning also exhibits nonmonotonic features, as investigated in this paper when particular situations may be incompletely stated. The paper reconsiders the pattern of plausible reasoning proposed by Polya, “a and b are analogous, a is true, then b true is more credible,'' from a nonmonotonic reasoning point of view. A representation of the statement “a and b are analogous” in terms of nonmonotonic consequences relations is presented. This representation is then related to a logical definition of analogical proportions, i.e. statements of the form “a is to b as c is to d” that has been recently proposed and extended to other types of proportions. Remarkably enough, semantic equivalence between conditional objects of the form “b given a,” which have been shown as being at the root of nonmonotonic reasoning, constitutes another type of noticeable proportions. By offering a parallel between two important forms of commonsense reasoning, this paper enriches the comparison between nonmonotonic reasoning and analogical reasoning that is not often made. © 2011 Wiley Periodicals, Inc.

Cells are able to use the bottom-up information (genome versus metabolic pathway) but also top-down environment/gene mutation. Our approach considers the information emergency from the sub-systems to the whole system. In these conditions an unified analytical model is very difficult to build up. Therefore an abstract model can be very helpful for prognosis diagnostic in medical science. We enhance the pertinence analysis of the information which is primordially to find out relationship between experimental data and biological knowledge.

In this paper, we present a current cooperative work involving different Institutes around the world. Our aim is to provide an online inductive logic programming tool. This is the first step in a more complete structure for enabling e-technology for machine learning and bio-informatics. We describe the main architecture of the project and how the data will be formatted for being sent to the ILP machinery. We focus on a biological application (yeast fermentation process) due to its importance for high added value end products.

No abstract available.