Software Product Lines (SPLs) are inherently difficult to test due to the combinatorial explosion of the number of products to consider. To reduce the number of products to test, sampling techniques such as combinatorial interaction testing have been proposed. They usually start from a feature model and apply a coverage criterion (e.g. pairwise feature interaction or dissimilarity) to generate tractable, fault-finding, lists of configurations to be tested. Prioritization can also be used to sort generate such lists, optimizing coverage criteria or weights assigned to features. However, current sampling prioritization techniques barely take product behaviour into account. We explore how ideas of statistical testing, based on a usage model (a Markov chain), can be used to extract configurations of interest according to the likelihood of their executions. These executions are gathered in featured transition systems, compact representation of SPL behaviour. We discuss possible scenarios and give a prioritization procedure validated on a web-based learning management software.
Our will is to apply ideas stemming from statistical testing and adapt them in an SPL context. For example, combining structural criteria with statistical testing has been discussed in @cite_5 @cite_21 . We do not make any assumption on the way the DTMC is obtained: via an operational profile @cite_3 or by analyzing the source code or the specification @cite_21 . However, an uniform distribution of probabilities over the DTMC would probably be less interesting. As noted by Witthaker @cite_22 , in such case only the structure of traces would be considered and therefore basing their selection on their probabilities would just be a means to limit their number in a mainly random-testing approach. In such cases, structural test generation has to be employed @cite_29 .
@cite_22 @cite_29 @cite_21 @cite_3 @cite_5
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We study the problem of optimal sub-Nyquist sampling for perfect reconstruction of multiband signals. The signals are assumed to have a known spectral support spl Fscr that does not tile under translation. Such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching Landau's (1967) lower bound equal to the measure of spl Fscr . For signals with sparse spl Fscr , this rate can be much smaller than the Nyquist rate. Unfortunately the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In a previous study, we derived bounds on the error due to mismodeling and sample additive noise. Adopting these bounds as performance measures, we consider the problems of optimizing the reconstruction sections of the system, choosing the optimal base sampling rate, and designing the nonuniform sampling pattern. We find that optimizing these parameters can improve system performance significantly. Furthermore, uniform sampling is optimal for signals with spl Fscr that tiles under translation. For signals with nontiling spl Fscr , which are not amenable to efficient uniform sampling, the results reveal increased error sensitivities with sub-Nyquist sampling. However, these can be controlled by optimal design, demonstrating the potential for practical multifold reductions in sampling rate. Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and accurate inference on such problems using Markov chain Monte Carlo (MCMC) techniques with customized proposal distributions. Currently, implementing such a system requires coding MCMC state representations and acceptance probability calculations that are specific to a particular application. An alternative approach, which we pursue in this paper, is to use a general-purpose probabilistic modeling language (such as BLOG) and a generic Metropolis-Hastings MCMC algorithm that supports user-supplied proposal distributions. Our algorithm gains flexibility by using MCMC states that are only partial descriptions of possible worlds; we provide conditions under which MCMC over partial worlds yields correct answers to queries. We also show how to use a context-specific Bayes net to identify the factors in the acceptance probability that need to be computed for a given proposed move. Experimental results on a citation matching task show that our general-purpose MCMC engine compares favorably with an application-specific system. We present a novel probabilistic approach for fitting a statistical model to an image. A 3D Morphable Model (3DMM) of faces is interpreted as a generative (Top-Down) Bayesian model. Random Forests are used as noisy detectors (Bottom-Up) for the face and facial landmark positions. The Top-Down and Bottom-Up parts are then combined using a Data-Driven Markov Chain Monte Carlo Method (DDMCMC). As core of the integration, we use the Metropolis-Hastings algorithm which has two main advantages. First, the algorithm can handle unreliable detections and therefore does not need the detectors to take an early and possible wrong hard decision before fitting. Second, it is open for integration of various cues to guide the fitting process. Based on the proposed approach, we implemented a completely automatic, pose and illumination invariant face recognition application. We are able to train and test the building blocks of our application on different databases. The system is evaluated on the Multi-PIE database and reaches state of the art performance. We observe a training set Q composed of l labeled samples (X sub 1 , spl theta sub 1 ),...,(X sub l , spl theta sub l ) and u unlabeled samples X sub 1 ',...,X sub u ' . The labels spl theta sub i are independent random variables satisfying Pr spl theta sub i =1 = spl eta , Pr spl theta sub i =2 =1- spl eta . The labeled observations X sub i are independently distributed with conditional density f sub spl theta i ( spl middot ) given spl theta sub i . Let (X sub 0 , spl theta sub 0 ) be a new sample, independently distributed as the samples in the training set. We observe X sub 0 and we wish to infer the classification spl theta sub 0 . In this paper we first assume that the distributions f sub 1 ( spl middot ) and f sub 2 ( spl middot ) are given and that the mixing parameter is unknown. We show that the relative value of labeled and unlabeled samples in reducing the risk of optimal classifiers is the ratio of the Fisher informations they carry about the parameter spl eta . We then assume that two densities g sub 1 ( spl middot ) and g sub 2 ( spl middot ) are given, but we do not know whether g sub 1 ( spl middot )=f sub 1 ( spl middot ) and g sub 2 ( spl middot )=f sub 2 ( spl middot ) or if the opposite holds, nor do we know spl eta . Thus the learning problem consists of both estimating the optimum partition of the observation space and assigning the classifications to the decision regions. Here, we show that labeled samples are necessary to construct a classification rule and that they are exponentially more valuable than unlabeled samples.