With the growing adoption of machine learning techniques, there is a surge of research interest towards making machine learning systems more transparent and interpretable. Various visualizations have been developed to help model developers understand, diagnose, and refine machine learning models. However, a large number of potential but neglected users are the domain experts with little knowledge of machine learning but are expected to work with machine learning systems. In this paper, we present an interactive visualization technique to help users with little expertise in machine learning to understand, explore and validate predictive models. By viewing the model as a black box, we extract a standardized rule-based knowledge representation from its input-output behavior. We design RuleMatrix, a matrix-based visualization of rules to help users navigate and verify the rules and the black-box model. We evaluate the effectiveness of RuleMatrix via two use cases and a usability study.
Model induction is a technique that infers an approximate and interpretable model from any machine learning model. The inferred model can be a linear classifier @cite_10 , a decision tree @cite_26 , or a rule set @cite_13 @cite_32 . It has been increasingly applied to create human-comprehensible proxy models that help users make sense of the behavior of complex models, such as artificial neural networks and support vector machines (SVMs). One most desirable advantage of model induction is that it provides interpretability by treating any complex model as a black box without compromising the performance.
@cite_13 @cite_26 @cite_10 @cite_32
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A new form of SAT-based symbolic model checking is described. Instead of unrolling the transition relation, it incrementally generates clauses that are inductive relative to (and augment) stepwise approximate reachability information. In this way, the algorithm gradually refines the property, eventually producing either an inductive strengthening of the property or a counterexample trace. Our experimental studies show that induction is a powerful tool for generalizing the unreachability of given error states: it can refine away many states at once, and it is effective at focusing the proof search on aspects of the transition system relevant to the property. Furthermore, the incremental structure of the algorithm lends itself to a parallel implementation. The rapid advance in information processing systems in recent decades had directed engineering research towards the development of intelligent systems that can evolve models of natural phenomena automatically—“by themselves,” so to speak. In this respect, a wide range of machine learning techniques like decision trees, artificial neural networks (ANNs), Bayesian methods, fuzzy-rule based systems, and evolutionary algorithms have been successfully applied to model different civil engineering systems. In this study, the possibility of using yet another machine learning paradigm that is firmly based on the theory of statistical learning, namely that of the support vector machine (SVM), is investigated. An interesting property of this approach is that it is an approximate implementation of a structural risk minimization (SRM) induction principle that aims at minimizing a bound on the generalization error of a model, rather than minimizing only the mean square error over the data set. In this paper, the basic ... 1. Summary In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction. Almost all, if not all problems in induction can be put in this form. Some strong heuristic arguments have been obtained for the equivalence of the last three models. One of these models is equivalent to a Bayes formulation, in which a priori probabilities are assigned to sequences of symbols on the basis of the lengths of inputs to a universal Turing machine that are required to produce the sequence of interest as output. Though it seems likely, it is not certain whether the first of the four models is equivalent to the other three. Few rigorous results are presented. Informal investigations are made of the properties of these models. There are discussions of their consistency and meaningfulness, of their degree of independence of the exact nature of the Turing machine used, and of the accuracy of their predictions in comparison to those of other induction methods. In Part II these models are applied to the solution of three problems—prediction of the Bernoulli sequence, extrapolation of a certain kind of Markov chain, and the use of phrase structure grammars for induction. Though some approximations are used, the first of these problems is treated most rigorously. The result is Laplace's rule of succession. The solution to the second problem uses less certain approximations, but the properties of the solution that are discussed, are fairly independent of these approximations. The third application, using phrase structure grammars, is least exact of the three. First a formal solution is presented. Though it appears to have certain deficiencies, it is hoped that presentation of this admittedly inadequate model will suggest acceptable improvements in it. This formal solution is then applied in an approximate way to the determination of the “optimum” phrase structure grammar for a given set of strings. The results that are obtained are plausible, but subject to the uncertainties of the approximation used. We present combined-case k-induction, a novel technique for verifying software programs. This technique draws on the strengths of the classical inductive-invariant method and a recent application of k-induction to program verification. In previous work, correctness of programs was established by separately proving a base case and inductive step. We present a new k-induction rule that takes an unstructured, reducible control flow graph (CFG), a natural loop occurring in the CFG, and a positive integer k, and constructs a single CFG in which the given loop is eliminated via an unwinding proportional to k. Recursively applying the proof rule eventually yields a loop-free CFG, which can be checked using SAT- SMT-based techniques. We state soundness of the rule, and investigate its theoretical properties. We then present two implementations of our technique: K-INDUCTOR, a verifier for C programs built on top of the CBMC model checker, and K-BOOGIE, an extension of the Boogie tool. Our experiments, using a large set of benchmarks, demonstrate that our k-induction technique frequently allows program verification to succeed using significantly weaker loop invariants than are required with the standard inductive invariant approach.