In this paper we study the problem of predictability in partially observable discrete event systems, i.e., the question whether an observer can predict the occurrence of a fault. We extend the definition of predictability to consider the time interval where the fault will occur: the @math -predictability does not only specify that the fault will be predicted before it occurs, but also that the predictor will be able to predict that its occurrence will occur in @math to @math observations from now. We also provide a quadratic algorithm that decides predictability of the system.
Brand 'an Briones and Madalinski presented the notions of @math -predictability and @math -predictability @cite_15 . @math -predictability is similar to our definition of @math -predictability meaning that the fault is predicted at least @math observations before the fault occurs. @math -predictability is the equivalent of our property of @math -predictability, meaning that it is possible to predict the fault occurrence before it occurs but when at most @math observations are still possible before the fault (in other words, the fault prediction is not too early).
@cite_15
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A discrete event system that is predictable can anticipate faults and act accordingly. However, bare predictability (as found in the literature) has some drawbacks. One does not know exactly when a fault occurs (it could be immediately or long after it is predicted). We propose lower and upper bound refinements of predictability, called (lb; ub)-predictability. A lower bound guarantees a fault to occur after certain execution steps, whereas an upper bound guarantees a fault to occur, in the future, but before some steps. This information can be exploited by the system to adopt the best contingency plan. We formally define the notions of lb-predictability and ub-predictability, present a decision algorithm to verify it on arbitrary systems, and illustrate them with examples. Background: The accurate prediction of where faults are likely to occur in code can help direct test effort, reduce costs, and improve the quality of software. Objective: We investigate how the context of models, the independent variables used, and the modeling techniques applied influence the performance of fault prediction models. Method: We used a systematic literature review to identify 208 fault prediction studies published from January 2000 to December 2010. We synthesize the quantitative and qualitative results of 36 studies which report sufficient contextual and methodological information according to the criteria we develop and apply. Results: The models that perform well tend to be based on simple modeling techniques such as Naive Bayes or Logistic Regression. Combinations of independent variables have been used by models that perform well. Feature selection has been applied to these combinations when models are performing particularly well. Conclusion: The methodology used to build models seems to be influential to predictive performance. Although there are a set of fault prediction studies in which confidence is possible, more studies are needed that use a reliable methodology and which report their context, methodology, and performance comprehensively. We consider the problem of identifying the source of failure in a network after receiving alarms or having observed symptoms. To locate the root cause accurately and timely in a large communication system is challenging because a single fault can often result in a large number of alarms, and multiple faults can occur concurrently. In this paper, we present a new fault localization method using a machine-learning approach. We propose to use logistic regression to study the correlation among network events based on end-to-end measurements. Then based on the regression model, we develop fault hypothesis that best explains the observed symptoms. Unlike previous work, the machine-learning algorithm requires neither the knowledge of dependencies among network events, nor the probabilities of faults, nor the conditional probabilities of fault propagation as input. The “low requirement” feature makes it suitable for large complex networks where accurate dependencies and prior probabilities are difficult to obtain. We then evaluate the performance of the learning algorithm with respect to the accuracy of fault hypothesis and the concentration property. Experimental results and theoretical analysis both show satisfactory performance. The exponential growth of computational power of the extreme scale machines over the past few decades has led to a corresponding decrease in reliability and a sharp increase of the frequency of hardware faults. Our research focuses on the mathematical challenges presented by the silent hardware faults; i.e., faults that can perturb the result of computations in an inconspicuous way. Using the approach of selective reliability, we present an analytic fault mode that can be used to study the resilience properties of a numerical algorithm. We apply our approach to the classical fixed point iteration and demonstrate that in the presence of hardware faults, the classical method fails to converge in expectation. We preset a modified resilient algorithm that detects and rejects faults resulting in error with large magnitude, while small faults are negated by the natural self-correcting properties of the algorithm. We show that our method is convergent (in first and second statistical moments) even in the presenc... Learnability in Valiant's PAC learning model has been shown to be strongly related to the existence of uniform laws of large numbers. These laws define a distribution-free convergence property of means to expectations uniformly over classes of random variables. Classes of real-valued functions enjoying such a property are also known as uniform Glivenko-Cantelli classes. In this paper, we prove, through a generalization of Sauer's lemma that may be interesting in its own right, a new characterization of uniform Glivenko-Cantelli classes. Our characterization yields Dudley, Gine´, and Zinn's previous characterization as a corollary. Furthermore, it is the first based on a Gine´, and Zinn's previous characterization as a corollary. Furthermore, it is the first based on a simple combinatorial quantity generalizing the Vapnik-Chervonenkis dimension. We apply this result to obtain the weakest combinatorial condition known to imply PAC learnability in the statistical regression (or “agnostic”) framework. Furthermore, we find a characterization of learnability in the probabilistic concept model, solving an open problem posed by Kearns and Schapire. These results show that the accuracy parameter plays a crucial role in determining the effective complexity of the learner's hypothesis class. In the literature the fault-proneness of classes or methods has been used to devise strategies for reducing testing costs and efforts. In general, fault-proneness is predicted through a set of design metrics and, most recently, by using Machine Learning (ML) techniques. However, some ML techniques cannot deal with unbalanced data, characteristic very common of the fault datasets and, their produced results are not easily interpreted by most programmers and testers. Considering these facts, this paper introduces a novel fault-prediction approach based on Multiobjective Particle Swarm Optimization (MOPSO). Exploring Pareto dominance concepts, the approach generates a model composed by rules with specific properties. These rules can be used as an unordered classifier, and because of this, they are more intuitive and comprehensible. Two experiments were accomplished, considering, respectively, fault-proneness of classes and methods. The results show interesting relationships between the studied metrics and fault prediction. In addition to this, the performance of the introduced MOPSO approach is compared with other ML algorithms by using several measures including the area under the ROC curve, which is a relevant criterion to deal with unbalanced data. This paper studies the problem of predicting occurrences of a significant event in a partially-observed discrete-event system. The predictability of occurrences of an event in a system is defined in the context of formal languages. The predictability of a language is a stronger condition than the diagnosability of the language. Two necessary and sufficient conditions for predictability of occurrences of an event in systems modeled by regular languages are presented. Both conditions can be algorithmically tested. The first condition employs diagnosers. The second condition employs verifiers and results in a polynomial-time (in the number of states) complexity test for verification of predictability. When predictability holds, diagnosers can be used online to predict the significant event. This paper describes a study performed in an industrial setting that attempts to build predictive models to identify parts of a Java system with a high fault probability. The system under consideration is constantly evolving as several releases a year are shipped to customers. Developers usually have limited resources for their testing and would like to devote extra resources to faulty system parts. The main research focus of this paper is to systematically assess three aspects on how to build and evaluate fault-proneness models in the context of this large Java legacy system development project: (1) compare many data mining and machine learning techniques to build fault-proneness models, (2) assess the impact of using different metric sets such as source code structural measures and change fault history (process measures), and (3) compare several alternative ways of assessing the performance of the models, in terms of (i) confusion matrix criteria such as accuracy and precision recall, (ii) ranking ability, using the receiver operating characteristic area (ROC), and (iii) our proposed cost-effectiveness measure (CE). The results of the study indicate that the choice of fault-proneness modeling technique has limited impact on the resulting classification accuracy or cost-effectiveness. There is however large differences between the individual metric sets in terms of cost-effectiveness, and although the process measures are among the most expensive ones to collect, including them as candidate measures significantly improves the prediction models compared with models that only include structural measures and or their deltas between releases - both in terms of ROC area and in terms of CE. Further, we observe that what is considered the best model is highly dependent on the criteria that are used to evaluate and compare the models. And the regular confusion matrix criteria, although popular, are not clearly related to the problem at hand, namely the cost-effectiveness of using fault-proneness prediction models to focus verification efforts to deliver software with less faults at less cost. Suppose we are given a time series or a signal @math for @math . We consider the problem of predicting the signal in the interval @math based on a knowledge of its history and nothing more. We ask the following question: what is the largest value of @math for which a prediction can be made? We show that the answer to this question is contained in a fundamental result of information theory due to Wyner, Ziv, Ornstein, and Weiss. In particular, for the class of chaotic signals, the upper bound is @math in the limit @math , with @math being entropy in a sense that is explained in the text. If @math is small for @math , where @math is of the order of a characteristic time scale, the pattern of events leading up to @math is similar to the pattern of events leading up to @math . It is reasonable to expect @math to be a good predictor of @math . All existing methods for prediction use this idea... In the (d,n) group testing problem n items have to be identified as either good or defective and the number of defective items is known to be d. A test on an arbitrary group (subset) of items reveals either that all items in the group are good or that at least one of the items is defective, but not how many or which items are defective. We present a new algorithm which in the worst case needs less than @math tests more than the information lower bound @math for n d≥2. For n d≥38, the difference decreases to less than @math tests. For d≥10, this is a considerable improvement over the d−1 additional tests given for the best previously known algorithm by Hwang. We conjecture that the behaviour for large n and d of the difference is optimal for @math . This implies that the @math tests per defective given in the bound above are the best possible. We study fault-tolerant distributed optimization of a sum of convex (cost) functions with real-valued scalar input output in the presence of crash faults or Byzantine faults. In particular, the goal is to optimize a global cost function @math , where @math is the collection of agents, and @math is agent @math 's local cost function, which is initially known only to agent @math . Since the above global cost function cannot be optimized exactly in presence of crash faults or Byzantine faults, we define two weaker versions of the problem for crash faults and Byzantine faults, respectively. When some agents may crash, the goal for the weaker problem is to generate an output that is an optimum of a function formed as @math where @math is the set of non-faulty agents, @math is the set of faulty agents (crashed agents), @math for each @math and @math is a normalization constant such that @math . We present an iterative algorithm in which each agent only needs to perform local computation, and send one message per iteration. When some agents may be Byzantine, the system cannot take full advantage of the data kept by non-faulty agents. The goal for the associated weaker problem is to generate an output that is an optimum of a function formed as @math such that @math for each @math and @math . We present an iterative algorithm, where only local computation is needed and only one message per agent is sent in each iteration, that ensures that at least @math agents have weights ( @math 's) that are lower bounded by @math . The increasing complexity in nowadays engineered systems requires great attention to safety hazards and occurrence of faults, which must be readily detected to possibly restore nominal behavior of the system. The notion of diagnosability plays a key role in this regard, since it corresponds to the possibility of detecting within a finite delay if a fault, or in general a hazardous situation, did occur. In this letter, we introduce and characterize the notion of approximate diagnosability for the general class of metric systems, which are typically used in the research community working on hybrid systems to deal with complex heterogeneous processes in, e.g., cyber-physical systems. This notion captures the possibility of detecting faults on the basis of measurements corrupted by errors, always introduced by non-ideal sensors in a real environment. Relations are established between approximate diagnosability of a given metric system and approximate diagnosability of a system that approximately simulates the given one. Application of the proposed results to the analysis of approximate diagnosability of nonlinear systems is finally discussed. Abstract In this paper we introduce and characterize the notion of approximate predictability for the general class of metric systems, which are a powerful modeling framework to deal with complex heterogeneous systems such as hybrid systems. Approximate predictability corresponds to the possibility of predicting the occurrence of specific states belonging to a particular subset of interest, in advance with respect to their occurrence, on the basis of observations corrupted by measurement errors. We establish a relation between approximate predictability of a given metric system and approximate predictability of a metric system that approximately simulates the given one. This relation allows checking approximate predictability of a system with an infinite number of states, provided that one is able to construct a metric system with a finite number of states and inputs, approximating the original one in the sense of approximate simulation. The analysis of approximate predictability of Piecewise Affine (PWA) systems is carried out as an application of the proposed approach. We study Byzantine fault-tolerant distributed optimization of a sum of convex (cost) functions with real-valued scalar input ouput. In particular, the goal is to optimize a global cost function @math , where @math is the set of non-faulty agents, and @math is agent @math 's local cost function, which is initially known only to agent @math . In general, when some of the agents may be Byzantine faulty, the above goal is unachievable, because the identity of the faulty agents is not necessarily known to the non-faulty agents, and the faulty agents may behave arbitrarily. Since the above global cost function cannot be optimized exactly in presence of Byzantine agents, we define a weaker version of the problem. The goal for the weaker problem is to generate an output that is an optimum of a function formed as a convex combination of local cost functions of the non-faulty agents. More precisely, for some choice of weights @math for @math such that @math and @math , the output must be an optimum of the cost function @math . Ideally, we would like @math for all @math -- however, this cannot be guaranteed due to the presence of faulty agents. In fact, we show that the maximum achievable number of nonzero weights ( @math 's) is @math , where @math is the upper bound on the number of Byzantine agents. In addition, we present algorithms that ensure that at least @math agents have weights that are bounded away from 0. We also propose a low-complexity suboptimal algorithm, which ensures that at least @math agents have weights that are bounded away from 0, where @math is the total number of agents, and @math ( @math ) is the actual number of Byzantine agents. Motivated by online recommendation and advertising systems, we consider a causal model for stochastic contextual bandits with a latent low-dimensional confounder. In our model, there are @math observed contexts and @math arms of the bandit. The observed context influences the reward obtained through a latent confounder variable with cardinality @math ( @math ). The arm choice and the latent confounder causally determines the reward while the observed context is correlated with the confounder. Under this model, the @math mean reward matrix @math (for each context in @math and each arm in @math ) factorizes into non-negative factors @math ( @math ) and @math ( @math ). This insight enables us to propose an @math -greedy NMF-Bandit algorithm that designs a sequence of interventions (selecting specific arms), that achieves a balance between learning this low-dimensional structure and selecting the best arm to minimize regret. Our algorithm achieves a regret of @math at time @math , as compared to @math for conventional contextual bandits, assuming a constant gap between the best arm and the rest for each context. These guarantees are obtained under mild sufficiency conditions on the factors that are weaker versions of the well-known Statistical RIP condition. We further propose a class of generative models that satisfy our sufficient conditions, and derive a lower bound of @math . These are the first regret guarantees for online matrix completion with bandit feedback, when the rank is greater than one. We further compare the performance of our algorithm with the state of the art, on synthetic and real world data-sets. We consider the scenario where the executions of different business processes are traced into a log, where each trace describes a process instance as a sequence of low-level events representing basic kinds of operations. In this context, we address a novel problem: given a description of the processes' behaviors in terms of high-level activities instead of low-level events, and in the presence of uncertainty in the mapping between events and activities, find all the interpretations of each trace @math . Specifically, an interpretation is a pair @math that provides a two-level "explanation" for @math : @math is a sequence of activities that may have triggered the events in @math , and W is a process whose model admits @math . To solve this problem, we propose a probabilistic framework representing "consistent" @math 's interpretations, where each interpretation is associated with a probability score. We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning the theory underlying this trade-off. In this work, we decompose the prediction error for adversarial examples (robust error) as the sum of the natural (classification) error and boundary error, and provide a differentiable upper bound using the theory of classification-calibrated loss, which is shown to be the tightest possible upper bound uniform over all probability distributions and measurable predictors. Inspired by our theoretical analysis, we also design a new defense method, TRADES, to trade adversarial robustness off against accuracy. Our proposed algorithm performs well experimentally in real-world datasets. The methodology is the foundation of our entry to the NeurIPS 2018 Adversarial Vision Challenge in which we won the 1st place out of 2,000 submissions, surpassing the runner-up approach by @math in terms of mean @math perturbation distance. The importance of software testing to quality assurance cannot be overemphasized. The estimation of a module's fault-proneness is important for minimizing cost and improving the effectiveness of the software testing process. Unfortunately, no general technique for estimating software fault-proneness is available. The observed correlation between some software metrics and fault-proneness has resulted in a variety of predictive models based on multiple metrics. Much work has concentrated on how to select the software metrics that are most likely to indicate fault-proneness. In this paper, we propose the use of machine learning for this purpose. Specifically, given historical data on software metric values and number of reported errors, an Artificial Neural Network (ANN) is trained. Then, in order to determine the importance of each software metric in predicting fault-proneness, a sensitivity analysis is performed on the trained ANN. The software metrics that are deemed to be the most critical are then used as the basis of an ANN-based predictive model of a continuous measure of fault-proneness. We also view fault-proneness prediction as a binary classification task (i.e., a module can either contain errors or be error-free) and use Support Vector Machines (SVM) as a state-of-the-art classification method. We perform a comparative experimental study of the effectiveness of ANNs and SVMs on a data set obtained from NASA's Metrics Data Program data repository. The aim of this paper is to study communication in networks where nodes fail in a random dependent way. In order to capture fault dependencies, we introduce the neighborhood fault model, where damaging events, called spots, occur randomly and independently with probability p at nodes of a network, and cause faults in the given node and all of its neighbors. Faults at distance at most 2 become dependent in this model and are positively correlated. We investigate the impact of spot probability on feasibility and time of communication in the fault-free part of the network. We show a network which supports fast communication with high probability, if p = 1 c log n. We also show that communication is not feasible with high probability in most classes of networks, for constant spot probabilities. For smaller spot probabilities, high probability communication is supported even by bounded degree networks. It is shown that the torus supports communication with high probability when p decreases faster than 1 n1 2, and does not when p ? 1 O(n1 2). Furthermore, a network built of tori is designed, with the same faulttolerance properties and additionally supporting fast communication. We show, however, that networks of degree bounded by a constant d do not support communication with high probability, if p ? 1 O(n1 d). While communication in networks with independent faults was widely studied, this is the first analytic paper which investigates network communication for random dependent faults. This paper studies fault-tolerant algorithms for the problem of gathering @math autonomous mobile robots. A gathering algorithm, executed independently by each robot, must ensure that all robots are gathered at one point within finite time. In a failure-prone system, a gathering algorithm is required to successfully gather the nonfaulty robots, independently of the behavior of the faulty ones. Both crash and Byzantine faults are considered. It is first observed that most existing algorithms fail to operate correctly in a setting allowing crash failures. Subsequently, an algorithm tolerant against one crash-faulty robot in a system of three or more robots is presented. It is then observed that all known algorithms fail to operate correctly in a system prone to Byzantine faults, even in the presence of a single fault. Moreover, it is shown that in an asynchronous environment it is impossible to perform a successful gathering in a @math -robot system, even if at most one of them might fail in a Byzantine manner. Thus, the problem is studied in a fully synchronous system. An algorithm is provided in this model for gathering @math robots with at most a single faulty robot, and a more general gathering algorithm is given in an @math -robot system with up to @math faults, where @math .