Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and implementable.

Decision trees are surprisingly adaptive in three important respects: They automatically (1) adapt to favorable conditions near the Bayes decision boundary; (2) focus on data distributed on lower dimensional manifolds; (3) reject irrelevant features. In this paper we examine a decision tree based on dyadic splits that adapts to each of these conditions to achieve minimax optimal rates of convergence. The proposed classifier is the first known to achieve these optimal rates while being practical and implementable.

The automotive industry was the first to promote the development of applications of model-based systems technology on a broad scale and, as a result, has produced some of the most advanced prototypes and products. In this article, we illustrate the features and benefits of model-based systems and qualitative modeling by prototypes and application systems that were developed in the automotive industry to support on-board diagnosis, design for diagnosability, and failure modes and effects analysis.

The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded applications. In this paper we extend the approach to deal with temporal information. We introduce a notion of temporal decision tree, which is designed to make use of relevant information as long as it is acquired, and we present an algorithm for compiling such trees from a model-based reasoning system.

I report on my experience over the past few years in introducing automated, model-based diagnostic technologies into industrial settings. In partic-ular, I discuss the competition that this technology has been receiving from handcrafted, rule-based diagnostic systems that has set some high standards that must be met by model-based systems before they can be viewed as viable alternatives. My goal in this article is to provide a perspective on this competition and discuss a diagnostic tool, called DTOOL/CNETS, that I have been developing over the years as I tried to address the major challenges posed by rule-based systems. In particular, I discuss three major features of the developed tool that were either adopted, designed, or innovated to address these challenges: (1) its compositional modeling approach, (2) its structure-based computational approach, and (3) its ability to synthesize embeddable diagnostic systems for a variety of software and hardware platforms.

I report on my experience over the past few years in introducing automated, model-based diagnostic technologies into industrial settings. In partic-ular, I discuss the competition that this technology has been receiving from handcrafted, rule-based diagnostic systems that has set some high standards that must be met by model-based systems before they can be viewed as viable alternatives. The battle between model-based and rule-based approaches to diagnosis has been over in the academic literature for many years, but the situation is different in industry where rule-based systems are dominant and appear to be attractive given the considerations of efficiency, embeddability, and cost effectiveness. My goal in this article is to provide a perspective on this competition and discuss a diagnostic tool, called DTOOL/CNETS, that I have been developing over the years as I tried to address the major challenges posed by rule-based systems. In particular, I discuss three major features of the developed tool that were either adopted, designed, or innovated to address these challenges: (1) its compositional modeling approach, (2) its structure-based computational approach, and (3) its ability to synthesize embeddable diagnostic systems for a variety of software and hardware platforms.

AI has embraced medical applications from its inception, and some of the earliest work in successful application of AI technology occurred in medical contexts. Medicine in the twenty-first century will be very different than medicine in the late twentieth century. Fortunately, the technical challenges to AI that emerge are similar, and the prospects for success are high.

An adaptive online algorithm is proposed to estimate hierarchical data structures for non-stationary data sources. The approach is based on the principle of minimum cross entropy to derive a decision tree for data clustering and it employs a metalearning idea (learning to learn) to adapt to changes in data characteristics. Its efficiency is demonstrated by grouping non-stationary artifical data and by hierarchical segmentation of LANDSAT images. 1 Introduction Unsupervised learning addresses the problem to detect structure inherent in unlabeled and unclassified data. N. The encoding usually is represented by an assignment matrix M (Mia), where Mia 1 if and only if Xi belongs to cluster L: 1 MiaV (Xi, Ya) measures the quality of a data partition, Le., optimal assignments and prototypes (M,y)OPt argminM,y1i (M,Y) minimize the inhomogeneity of clusters w.r.t. a given distance measure V. For reasons of simplicity we restrict the presentation to the ' sum-of-squared-error criterion V(x, y) To facilitate this minimization a deterministic annealing approach was proposed in [5] signments, which maps the discrete optimization problem, i.e. how to determine the data as via the Maximum Entropy Principle [2] to a continuous parameter es- Unsupervised Online Learning of Decision Trees for Data Analysis 515 timation problem.

An adaptive online algorithm is proposed to estimate hierarchical data structures for non-stationary data sources. The approach is based on the principle of minimum cross entropy to derive a decision tree for data clustering and it employs a metalearning idea (learning to learn) to adapt to changes in data characteristics. Its efficiency is demonstrated by grouping non-stationary artifical data and by hierarchical segmentation of LANDSAT images. 1 Introduction Unsupervised learning addresses the problem to detect structure inherent in unlabeled and unclassified data. N. The encoding usually is represented by an assignment matrix M (Mia), where Mia 1 if and only if Xi belongs to cluster L: 1 MiaV (Xi, Ya) measures the quality of a data partition, Le., optimal assignments and prototypes (M,y)OPt argminM,y1i (M,Y) minimize the inhomogeneity of clusters w.r.t. a given distance measure V. For reasons of simplicity we restrict the presentation to the ' sum-of-squared-error criterion V(x, y) To facilitate this minimization a deterministic annealing approach was proposed in [5] signments, which maps the discrete optimization problem, i.e. how to determine the data as via the Maximum Entropy Principle [2] to a continuous parameter es- Unsupervised Online Learning of Decision Trees for Data Analysis 515 timation problem.

This paper presents a comprehensive approach for model-based diagnosis which includes proposals for characterizing and computing preferred diagnoses, assuming that the system description is augmented with a system structure (a directed graph explicating the interconnections between system components). Specifically, we first introduce the notion of a consequence, which is a syntactically unconstrained propositional sentence that characterizes all consistency-based diagnoses and show that standard characterizations of diagnoses, such as minimal conflicts, correspond to syntactic variations on a consequence. Second, we propose a new syntactic variation on the consequence known as negation normal form (NNF) and discuss its merits compared to standard variations. Third, we introduce a basic algorithm for computing consequences in NNF given a structured system description. We show that if the system structure does not contain cycles, then there is always a linear-size consequence in NNF which can be computed in linear time. For arbitrary system structures, we show a precise connection between the complexity of computing consequences and the topology of the underlying system structure. Finally, we present an algorithm that enumerates the preferred diagnoses characterized by a consequence. The algorithm is shown to take linear time in the size of the consequence if the preference criterion satisfies some general conditions.