Large and moderate deviation principles for recursive kernel density estimators defined by stochastic approximation method

In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. [2009. The stochastic approximation method for the estimation of a probability density. J. Statist. Plann. Inference 139, 2459-2478]. We show that the estimator constructed using the stepsize which minimize the variance of the class of the recursive estimators defined in Mokkadem et al. (2009) gives the same pointwise LDP and MDP as the Rosenblatt kernel estimator. We provide results both for the pointwise and the uniform deviations.Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:math/0601429 by other author

Learning multiple fault diagnosis

This paper describes two methods for integrating model-based diagnosis (MBD) and explanation-based learning. The first method (EBL) uses a generate-test-debug paradigm, generating diagnostic hypotheses using learned associational rules that summarize model-based diagnostic experiences. This strategy is a form of "learning while doing" model-based troubleshooting and could be called "online learning." The second diagnosis and learning method described here (EEL-STATIC) involves ''learning in advance." Learning begins in a training phase prior to performance or testing. Empirical results of computational experiments comparing the learning methods with MBD on two devices (the polybox and the binary full adder) are reported. For the same diagnostic performance, EBL-STATIC is several orders of magnitude faster than MBD while EBL can cause performance slow-down

Explanation-based learning for diagnosis

Diagnostic expert systems constructed using traditional knowledge-engineering techniques identify malfunctioning components using rules that associate symptoms with diagnoses. Model-based diagnosis (MBD) systems use models of devices to find faults given observations of abnormal behavior. These approaches to diagnosis are complementary. We consider hybrid diagnosis systems that include both associational and model-based diagnostic components. We present results on explanation-based learning (EBL) methods aimed at improving the performance of hybrid diagnostic problem solvers. We describe two architectures called EBL_IA and EBL(p). EBL_IA is a form fo "learning in advance" that pre-compiles models into associations. At run-time the diagnostic system is purely associational. In EBL(p), the run-time diagnosis system contains associational, MBD, and EBL components. Learned associational rules are preferred but when they are incomplete they may produce too many incorrect diagnoses. When errors cause performance to dip below a give threshold p, EBL(p) activates MBD and explanation-based "learning while doing". We present results of empirical studies comparing MBD without learning versus EBL_IA and EBL(p). The main conclusions are as follows. EBL_IA is superior when it is feasible but it is not feasible for large devices. EBL(p) can speed-up MBD and scale-up to larger devices in situations where perfect accuracy is not required

Learning approximate diagnosis

Model-based diagnosis (MBD) provides several advantages over experiential rule-based systems. A principal shortcoming of MBD is that MBD learns nothing from any given example. An MBD system facing the same task a second time will incur the same computational effort as that incurred the first time. Our earlier work on incorporating explanation-based learning (EBL) in MBD [4] suggested a diagnostic architecture integrating EBL and MBD components. In this architecture, EBL was used to learn diagnostic rules. But the diagnoses proposed by the rules could be erroneous. So constraint suspension testing was used to check all proposed diagnoses. Insisting on perfect accuracy causes the performance of this scheme for "learning while doing" to deteriorate rapidly with the size of the device to be diagnosed. In this paper, we describe a method for trading off accuracy for efficiency. In this approach, most diagnosis problems are handled by the associational rules learned from previous problems. Model-based reasoning and learning are activated only when performance drops below a given threshold. We present empirical results on circuits of increasing number of components illustrating how this approach scales up