World-class interpretable poker

Machine Learning - We address the problem of interpretability in iterative game solving for imperfect-information games such as poker. This lack of interpretability has two main sources: first, the...     

Special issue on interpretable fuzzy systems

Interpretability is acknowledged as one of the most appreciated advantages of fuzzy systems in many applications, especially in those with high human interaction where it actually becomes a strong requirement. However, it is important to remark that there is a somehow misleading but widely extended belief, even in part of the fuzzy community, regarding fuzzy systems as interpretable no matter how they were designed. Of course, we are aware the use of fuzzy logic favors the interpretability of designed models. Thanks to their semantic expressivity, close to natural language, fuzzy variables and rules can be used to formalize linguistic propositions which are likely to be easily understandood by human beings. Obviously, this fact makes easier the knowledge extraction and representation tasks carried out when modeling real-world complex systems. Notwithstanding, fuzzy logic is not enough by itself to guarantee the interpretability of the final model. As it is thoroughly illustrated in this special issue, achieving interpretable fuzzy systems is a matter of careful design because fuzzy systems cannot be deemed as interpretable per se. Thus, several constraints have to be imposed along the whole design process with the aim of producing really interpretable fuzzy systems, in the sense that every element of the whole system may be checked and understood by a human being. Otherwise, fuzzy systems may even become black-boxes.     

Automatic discovery of interpretable planning strategies

Machine Learning - When making decisions, people often overlook critical information or are overly swayed by irrelevant information. A common approach to mitigate these biases is to provide...     

An effective and interpretable method for document classification

As the number of documents has been rapidly increasing in recent time, automatic text categorization is becoming a more important and fundamental task in information retrieval and text mining. Accuracy and interpretability are two important aspects of a text classifier. While the accuracy of a classifier measures the ability to correctly classify unseen data, interpretability is the ability of the classifier to be understood by humans and provide reasons why each data instance is assigned to a label. This paper proposes an interpretable classification method by exploiting the Dirichlet process mixture model of von Mises–Fisher distributions for directional data. By using the labeled information of the training data explicitly and determining automatically the number of topics for each class, the learned topics are coherent, relevant and discriminative. They help interpret as well as distinguish classes. Our experimental results showed the advantages of our approach in terms of separability, interpretability and effectiveness in classification task of datasets with high dimension and complex distribution. Our method is highly competitive with state-of-the-art approaches.     

A highly interpretable form of Sugeno inference systems

We present a form of fuzzy inference systems (FISs) that is highly interpretable and easy to manipulate. The form is based on a judicious choice of membership functions that have strong locality and differentiability properties and on a modification of the Sugeno and generalized Sugeno forms of the consequent polynomials so as to make them rule centered. Under these conditions, the coefficients in the consequent polynomials can be exactly interpreted as Taylor series coefficients. Besides the intuitive interpretation thus bestowed on the coefficients, we show that the new form allows easy design, manipulation, testing, training, and combination of the resulting fuzzy inference systems. The rudiments of a calculus of fuzzy inference systems are then introduced     

Learning interpretable fuzzy inference systems with FisPro

Fuzzy inference systems (FIS) are likely to play a significant part in system modeling, provided that they remain interpretable following learning from data. The aim of this paper is to set up some guidelines for interpretable FIS learning, based on practical experience with fuzzy modeling in various fields. An open source software system called FisPro has been specifically designed to provide generic tools for interpretable FIS design and learning. It can then be extended with the addition of new contributions. This work presents a global approach to design data-driven FIS that satisfy certain interpretability and accuracy criteria. It includes fuzzy partition generation, rule learning, input space reduction and rule base simplification. The FisPro implementation is discussed and illustrated through several detailed case studies.     

BLasso for object categorization and retrieval: Towards interpretable visual models

We propose a new supervised object retrieval method based on the selection of local visual features learned with the BLasso algorithm. BLasso is a boosting-like procedure that efficiently approximates the Lasso path through backward regularization steps. The advantage compared to a classical boosting strategy is that it produces a sparser selection of visual features. This allows us to improve the efficiency of the retrieval and, as discussed in the paper, it facilitates human visual interpretation of the models generated. We carried out our experiments on the Caltech-256 dataset with state-of-the-art local visual features. We show that our method outperforms AdaBoost in effectiveness while significantly reducing the model complexity and the prediction time. We discuss the evaluation of the visual models obtained in terms of human interpretability.     

Computation is just interpretable symbol manipulation; cognition isn't

Computation is interpretable symbol manipulation. Symbols are objects that are manipulated on the basis of rules operating only on theirshapes, which are arbitrary in relation to what they can be interpreted as meaning. Even if one accepts the Church/Turing Thesis that computation is unique, universal and very near omnipotent, not everything is a computer, because not everything can be given a systematic interpretation; and certainly everything can't be givenevery systematic interpretation. But even after computers and computation have been successfully distinguished from other kinds of things, mental states will not just be the implementations of the right symbol systems, because of the symbol grounding problem: The interpretation of a symbol system is not intrinsic to the system; it is projected onto it by the interpreter. This is not true of our thoughts. We must accordingly be more than just computers. My guess is that the meanings of our symbols are grounded in the substrate of our robotic capacity to interact with that real world of objects, events and states of affairs that our symbols are systematically interpretable as being about.     

Identification of interpretable and accurate fuzzy classifiers and function estimators with hybrid methods

This paper studies the identification of fuzzy classifiers and function estimators focusing on improving their interpretability while maintaining their accuracy. Advances of various methods, such as, input variable selection, appropriate initialization algorithms, evolutionary algorithms and simplification techniques are hybridized to form a framework capable of identifying interpretable and accurate fuzzy models (FMs). FMs are initialized by two algorithms. Modified Gath–Geva (MGG) is used for function estimation and C4.5 for classification problems. The initialized FMs go through a three-step GA-based optimization, in which the adequate structure and parameters of FMs are searched. The proposed fitness function makes the favoring of simple FMs possible. Furthermore, the rule base is made more comprehensible by reducing the number of conditions in the rules. The validity of FMs is verified through studying several well-known benchmark problems. The results indicate, that by means of the proposed framework, interpretable, yet accurate FMs are obtained.     

Generating an interpretable family of fuzzy partitions from data

In this paper, we propose a new method to construct fuzzy partitions from data. The procedure generates a hierarchy including best partitions of all sizes from n to two fuzzy sets. The maximum size n is determined according to the data distribution and corresponds to the finest resolution level. We use an ascending method for which a merging criterion is needed. This criterion is based on the definition of a special metric distance suitable for fuzzy partitioning, and the merging is done under semantic constraints. The distance we define does not handle the point coordinates, but directly their membership degrees to the fuzzy sets of the partition. This leads to the introduction of the notions of internal and external distances. The hierarchical fuzzy partitioning is carried independently over each dimension, and, to demonstrate the partition potential, they are used to build fuzzy inference system using a simple selection mechanism. Due to the merging technique, all the fuzzy sets in the various partitions are interpretable as linguistic labels. The tradeoff between accuracy and interpretability constitutes the most promising aspect in our approach. Well known data sets are investigated and the results are compared with those obtained by other authors using different techniques. The method is also applied to real world agricultural data, the results are analyzed and weighed against those achieved by other methods, such as fuzzy clustering or discriminant analysis.     

CaDET: interpretable parametric conditional density estimation with decision trees and forests

Machine Learning - We introduce CaDET, an algorithm for parametric Conditional Density Estimation (CDE) based on decision trees and random forests. CaDET uses the empirical cross entropy impurity...     

CATSMLP: toward a robust and interpretable multilayer perceptron with sigmoid activation functions.

Enhancing the robustness and interpretability of a multilayer perceptron (MLP) with a sigmoid activation function is a challenging topic. As a particular MLP, additive TS-type MLP (ATSMLP) can be interpreted based on single-stage fuzzy IF-THEN rules, but its robustness will be degraded with the increase in the number of intermediate layers. This paper presents a new MLP model called cascaded ATSMLP (CATSMLP), where the ATSMLPs are organized in a cascaded way. The proposed CATSMLP is a universal approximator and is also proven to be functionally equivalent to a fuzzy inference system based on syllogistic fuzzy reasoning. Therefore, the CATSMLP may be interpreted based on syllogistic fuzzy reasoning in a theoretical sense. Meanwhile, due to the fact that syllogistic fuzzy reasoning has distinctive advantage over single-stage IF-THEN fuzzy reasoning in robustness, this paper proves in an indirect way that the CATSMLP is more robust than the ATSMLP in an upper-bound sense. Several experiments were conducted to confirm such a claim.     

Evolving compact and interpretable Takagi-Sugeno fuzzy models with a new encoding scheme.

Developing Takagi-Sugeno fuzzy models by evolutionary algorithms mainly requires three factors: an encoding scheme, an evaluation method, and appropriate evolutionary operations. At the same time, these three factors should be designed so that they can consider three important aspects of fuzzy modeling: modeling accuracy, compactness, and interpretability. This paper proposes a new evolutionary algorithm that fulfills such requirements and solves fuzzy modeling problems. Two major ideas proposed in this paper lie in a new encoding scheme and a new fitness function, respectively. The proposed encoding scheme consists of three chromosomes, one of which uses unique chained possibilistic representation of rule structure. The proposed encoding scheme can achieve simultaneous optimization of parameters of antecedent membership functions and rule structures with the new fitness function developed in this paper. The proposed fitness function consists of five functions that consider three evaluation criteria in fuzzy modeling problems. The proposed fitness function guides evolutionary search direction so that the proposed algorithm can find more accurate compact fuzzy models with interpretable antecedent membership functions. Several evolutionary operators that are appropriate for the proposed encoding scheme are carefully designed. Simulation results on three modeling problems show that the proposed encoding scheme and the proposed fitness functions are effective in finding accurate, compact, and interpretable Takagi-Sugeno fuzzy models. From the simulation results, it is shown that the proposed algorithm can successfully find fuzzy models that approximate the given unknown function accurately with a compact number of fuzzy rules and membership functions. At the same time, the fuzzy models use interpretable antecedent membership functions, which are helpful in understanding the underlying behavior of the obtained fuzzy models.     

Developing interpretable models with optimized set reduction foridentifying high-risk software components

Applying equal testing and verification effort to all parts of a software system is not very efficient, especially when resources are tight. Therefore, one needs to low/high fault frequency components so that testing/verification effort can be concentrated where needed. Such a strategy is expected to detect more faults and thus improve the resulting reliability of the overall system. The authors present the optimized set reduction approach for constructing such models, which is intended to fulfill specific software engineering needs. The approach to classification is to measure the software system and build multivariate stochastic models for predicting high-risk system components. Experimental results obtained by classifying Ada components into two classes (is, or is not likely to generate faults during system and acceptance rest) are presented. The accuracy of the model and the insights it provides into the error-making process are evaluated     

A robust design criterion for interpretable fuzzy models with uncertain data

We believe that nonlinear fuzzy filtering techniques may be turned out to give better robustness performance than the existing linear methods of estimation (H/sup 2/ and H/sup /spl infin// filtering techniques), because of the fact that not only linear parameters (consequents), but also the nonlinear parameters (membership functions) attempt to identify the uncertain behavior of the unknown system. However, the fuzzy identification methods must be robust to data uncertainties and modeling errors to ensure that the fuzzy approximation of unknown system's behavior is optimal in some sense. This study presents a deterministic approach to the robust design of fuzzy models in the presence of unknown but finite uncertainties in the identification data. We consider online identification of an interpretable fuzzy model, based on the robust solution of a regularized least-squares fuzzy parameters estimation problem. The aim is to resolve the difficulties associated with the robust fuzzy identification method due to lack of a priori knowledge about upper bounds on the data uncertainties. The study derives an optimal level of regularization that should be provided to ensure the robustness of fuzzy identification strategy by achieving an upper bound on the value of energy gain from data uncertainties and modeling errors to the estimation errors. A time-domain feedback analysis of the proposed identification approach is carried out with emphasis on stability, robustness, and steady-state issues. The simulation studies are provided to show the superiority of the proposed fuzzy estimation over the classical estimation methods.     

Stacking-based ensemble learning of decision trees for interpretable prostate cancer detection

Prostate cancer is a highly incident malignant cancer among men. Early detection of prostate cancer is necessary for deciding whether a patient should receive costly and invasive biopsy with possible serious complications. However, existing cancer diagnosis methods based on data mining only focus on diagnostic accuracy, while neglecting the interpretability of the diagnosis model that is necessary for helping doctors make clinical decisions. To take both accuracy and interpretability into consideration, we propose a stacking-based ensemble learning method that simultaneously constructs the diagnostic model and extracts interpretable diagnostic rules. For this purpose, a multi-objective optimization algorithm is devised to maximize the classification accuracy and minimize the ensemble complexity for model selection. As for model combination, a random forest classifier-based stacking technique is explored for the integration of base learners, i.e., decision trees. Empirical results on real-world data from the General Hospital of PLA demonstrate that the classification performance of the proposed method outperforms that of several state-of-the-art methods in terms of the classification accuracy, sensitivity and specificity. Moreover, the results reveal that several diagnostic rules extracted from the constructed ensemble learning model are accurate and interpretable.