On Estimation of a Probability Density Function and Mode
01 Sep 1962-Annals of Mathematical Statistics (Institute of Mathematical Statistics)-Vol. 33, Iss: 3, pp 1065-1076
TL;DR: In this paper, the problem of the estimation of a probability density function and of determining the mode of the probability function is discussed. Only estimates which are consistent and asymptotically normal are constructed.
Abstract: : Given a sequence of independent identically distributed random variables with a common probability density function, the problem of the estimation of a probability density function and of determining the mode of a probability function are discussed. Only estimates which are consistent and asymptotically normal are constructed. (Author)
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01 Jan 1995TL;DR: This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition, and is designed as a text, with over 100 exercises, to benefit anyone involved in the fields of neural computation and pattern recognition.
Abstract: From the Publisher:
This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts, the book examines techniques for modelling probability density functions and the properties and merits of the multi-layer perceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100 exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.
19,056 citations
Cites background from "On Estimation of a Probability Dens..."
...We can find an expression for K, the number of points which fall within this region, by defining a kernel junction H(u), also known as a Parzen window (Rosenblatt, 1956; Parzen, 1962) given by...
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TL;DR: This survey tries to provide a structured and comprehensive overview of the research on anomaly detection by grouping existing techniques into different categories based on the underlying approach adopted by each technique.
Abstract: Anomaly detection is an important problem that has been researched within diverse research areas and application domains. Many anomaly detection techniques have been specifically developed for certain application domains, while others are more generic. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection. We have grouped existing techniques into different categories based on the underlying approach adopted by each technique. For each category we have identified key assumptions, which are used by the techniques to differentiate between normal and anomalous behavior. When applying a given technique to a particular domain, these assumptions can be used as guidelines to assess the effectiveness of the technique in that domain. For each category, we provide a basic anomaly detection technique, and then show how the different existing techniques in that category are variants of the basic technique. This template provides an easier and more succinct understanding of the techniques belonging to each category. Further, for each category, we identify the advantages and disadvantages of the techniques in that category. We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains. We hope that this survey will provide a better understanding of the different directions in which research has been done on this topic, and how techniques developed in one area can be applied in domains for which they were not intended to begin with.
9,627 citations
Cites methods from "On Estimation of a Probability Dens..."
...A non-parametric technique for probability density estimation is parzen windows estimation [Parzen 1962]....
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...A non-parametric technique for probability density estimation is parzen windows estimation [Parzen 1962]....
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TL;DR: In this article, the maximal statistical dependency criterion based on mutual information (mRMR) was proposed to select good features according to the maximal dependency condition. But the problem of feature selection is not solved by directly implementing mRMR.
Abstract: Feature selection is an important problem for pattern classification systems. We study how to select good features according to the maximal statistical dependency criterion based on mutual information. Because of the difficulty in directly implementing the maximal dependency condition, we first derive an equivalent form, called minimal-redundancy-maximal-relevance criterion (mRMR), for first-order incremental feature selection. Then, we present a two-stage feature selection algorithm by combining mRMR and other more sophisticated feature selectors (e.g., wrappers). This allows us to select a compact set of superior features at very low cost. We perform extensive experimental comparison of our algorithm and other methods using three different classifiers (naive Bayes, support vector machine, and linear discriminate analysis) and four different data sets (handwritten digits, arrhythmia, NCI cancer cell lines, and lymphoma tissues). The results confirm that mRMR leads to promising improvement on feature selection and classification accuracy.
8,078 citations
05 Aug 2003
TL;DR: This work derives an equivalent form, called minimal-redundancy-maximal-relevance criterion (mRMR), for first-order incremental feature selection, and presents a two-stage feature selection algorithm by combining mRMR and other more sophisticated feature selectors (e.g., wrappers).
7,075 citations
Cites background from "On Estimation of a Probability Dens..."
...As one of the earliest classifiers, LDA [30] learns a linear classification boundary in the input feature space....
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TL;DR: In this article, a new method is presented for flexible regression modeling of high dimensional data, which takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data.
Abstract: A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data. This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however, this method produces continuous models with continuous derivatives. It has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions.
6,651 citations
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01 Jan 1953
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