Fault Detection Effectiveness of Metamorphic Relations Developed for Testing Supervised Classifiers

In machine learning, supervised classifiers are used to obtain predictions for unlabeled data by inferring prediction functions using labeled data. Supervised classifiers are widely applied in domains such as computational biology, computational physics and healthcare to make critical decisions. However, it is often hard to test supervised classifiers since the expected answers are unknown. This is commonly known as the \emph{oracle problem} and metamorphic testing (MT) has been used to test such programs. In MT, metamorphic relations (MRs) are developed from intrinsic characteristics of the software under test (SUT). These MRs are used to generate test data and to verify the correctness of the test results without the presence of a test oracle. Effectiveness of MT heavily depends on the MRs used for testing. In this paper we have conducted an extensive empirical study to evaluate the fault detection effectiveness of MRs that have been used in multiple previous studies to test supervised classifiers. Our study uses a total of 709 reachable mutants generated by multiple mutation engines and uses data sets with varying characteristics to test the SUT. Our results reveal that only 14.8\% of these mutants are detected using the MRs and that the fault detection effectiveness of these MRs do not scale with the increased number of mutants when compared to what was reported in previous studies.Comment: 8 pages, AITesting 201

Covariate-assisted ranking and screening for large-scale two-sample inference

Two-sample multiple testing has a wide range of applications. The conventionalpractice first reduces the original observations to a vector of p-values and then chooses a cutoffto adjust for multiplicity. However, this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures.We introduce a new framework fortwo-sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power. A data-driven multiple-testing procedure is developed by employinga covariate-assisted ranking and screening (CARS) approach that optimally combines the informationfrom both the primary and the auxiliary variables. The proposed CARS procedureis shown to be asymptotically valid and optimal for false discovery rate control. The procedureis implemented in the R package CARS. Numerical results confirm the effectiveness of CARSin false discovery rate control and show that it achieves substantial power gain over existingmethods. CARS is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection

Automated metamorphic testing on the analyses of feature models

Copyright © 2010 Elsevier B.V. All rights reserved.Context: A feature model (FM) represents the valid combinations of features in a domain. The automated extraction of information from FMs is a complex task that involves numerous analysis operations, techniques and tools. Current testing methods in this context are manual and rely on the ability of the tester to decide whether the output of an analysis is correct. However, this is acknowledged to be time-consuming, error-prone and in most cases infeasible due to the combinatorial complexity of the analyses, this is known as the oracle problem.Objective: In this paper, we propose using metamorphic testing to automate the generation of test data for feature model analysis tools overcoming the oracle problem. An automated test data generator is presented and evaluated to show the feasibility of our approach.Method: We present a set of relations (so-called metamorphic relations) between input FMs and the set of products they represent. Based on these relations and given a FM and its known set of products, a set of neighbouring FMs together with their corresponding set of products are automatically generated and used for testing multiple analyses. Complex FMs representing millions of products can be efficiently created by applying this process iteratively.Results: Our evaluation results using mutation testing and real faults reveal that most faults can be automatically detected within a few seconds. Two defects were found in FaMa and another two in SPLOT, two real tools for the automated analysis of feature models. Also, we show how our generator outperforms a related manual suite for the automated analysis of feature models and how this suite can be used to guide the automated generation of test cases obtaining important gains in efficiency.Conclusion: Our results show that the application of metamorphic testing in the domain of automated analysis of feature models is efficient and effective in detecting most faults in a few seconds without the need for a human oracle.This work has been partially supported by the European Commission(FEDER)and Spanish Government under CICYT project SETI(TIN2009-07366)and the Andalusian Government project ISABEL(TIC-2533)

The fused Kolmogorov filter: A nonparametric model-free screening method

A new model-free screening method called the fused Kolmogorov filter is proposed for high-dimensional data analysis. This new method is fully nonparametric and can work with many types of covariates and response variables, including continuous, discrete and categorical variables. We apply the fused Kolmogorov filter to deal with variable screening problems emerging from a wide range of applications, such as multiclass classification, nonparametric regression and Poisson regression, among others. It is shown that the fused Kolmogorov filter enjoys the sure screening property under weak regularity conditions that are much milder than those required for many existing nonparametric screening methods. In particular, the fused Kolmogorov filter can still be powerful when covariates are strongly dependent on each other. We further demonstrate the superior performance of the fused Kolmogorov filter over existing screening methods by simulations and real data examples.Comment: Published at http://dx.doi.org/10.1214/14-AOS1303 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Abduction-Based Explanations for Machine Learning Models

The growing range of applications of Machine Learning (ML) in a multitude of settings motivates the ability of computing small explanations for predictions made. Small explanations are generally accepted as easier for human decision makers to understand. Most earlier work on computing explanations is based on heuristic approaches, providing no guarantees of quality, in terms of how close such solutions are from cardinality- or subset-minimal explanations. This paper develops a constraint-agnostic solution for computing explanations for any ML model. The proposed solution exploits abductive reasoning, and imposes the requirement that the ML model can be represented as sets of constraints using some target constraint reasoning system for which the decision problem can be answered with some oracle. The experimental results, obtained on well-known datasets, validate the scalability of the proposed approach as well as the quality of the computed solutions

Partial Consistency with Sparse Incidental Parameters

Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this penalization principle to a linear regression model with a finite-dimensional vector of structural parameters and a high-dimensional vector of sparse incidental parameters. For the estimators of the structural parameters, we derive their consistency and asymptotic normality, which reveals an oracle property. However, the penalized estimators for the incidental parameters possess only partial selection consistency but not consistency. This is an interesting partial consistency phenomenon: the structural parameters are consistently estimated while the incidental ones cannot. For the structural parameters, also considered is an alternative two-step penalized estimator, which has fewer possible asymptotic distributions and thus is more suitable for statistical inferences. We further extend the methods and results to the case where the dimension of the structural parameter vector diverges with but slower than the sample size. A data-driven approach for selecting a penalty regularization parameter is provided. The finite-sample performance of the penalized estimators for the structural parameters is evaluated by simulations and a real data set is analyzed

Engineering model transformations with transML

The final publication is available at Springer via http://dx.doi.org/10.1007%2Fs10270-011-0211-2Model transformation is one of the pillars of model-driven engineering (MDE). The increasing complexity of systems and modelling languages has dramatically raised the complexity and size of model transformations as well. Even though many transformation languages and tools have been proposed in the last few years, most of them are directed to the implementation phase of transformation development. In this way, even though transformations should be built using sound engineering principles—just like any other kind of software—there is currently a lack of cohesive support for the other phases of the transformation development, like requirements, analysis, design and testing. In this paper, we propose a unified family of languages to cover the life cycle of transformation development enabling the engineering of transformations. Moreover, following an MDE approach, we provide tools to partially automate the progressive refinement of models between the different phases and the generation of code for several transformation implementation languages.This work has been sponsored by the Spanish Ministry of Science and Innovation with project METEORIC (TIN2008-02081), and by the R&D program of the Community of Madrid with projects “e-Madrid" (S2009/TIC-1650). Parts of this work were done during the research stays of Esther and Juan at the University of York, with financial support from the Spanish Ministry of Science and Innovation (grant refs. JC2009-00015, PR2009-0019 and PR2008-0185)

Automated verification of model transformations based on visual contracts

The final publication is available at Springer via http://dx.doi.org/10.1007/s10515-012-0102-yModel-Driven Engineering promotes the use of models to conduct the different phases of the software development. In this way, models are transformed between different languages and notations until code is generated for the final application. Hence, the construction of correct Model-to-Model (M2M) transformations becomes a crucial aspect in this approach. Even though many languages and tools have been proposed to build and execute M2M transformations, there is scarce support to specify correctness requirements for such transformations in an implementation-independent way, i.e., irrespective of the actual transformation language used. In this paper we fill this gap by proposing a declarative language for the specification of visual contracts, enabling the verification of transformations defined with any transformation language. The verification is performed by compiling the contracts into QVT to detect disconformities of transformation results with respect to the contracts. As a proof of concept, we also report on a graphical modeling environment for the specification of contracts, and on its use for the verification of transformations in several case studies.This work has been funded by the Austrian Science Fund (FWF) under grant P21374-N13, the Spanish Ministry of Science under grants TIN2008-02081 and TIN2011-24139, and the R&D programme of the Madrid Region under project S2009/TIC-1650