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Results for “non-parametric density estimation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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A new approach to evaluate gamma-ray measurements

Misunderstandings about the term random samples its implications may easily arise. Conditions under which the phases, obtained from arrival times, do not form a random sample and the dangers involved are discussed. Watson's U sup 2 test for uniformity is recommended for light curves with duty cycles larger than 10%. Under certain conditions, non-parametric density estimation may be used to determine estimates of the true light curve and its parameters.

Dejager, O. C.↗

Particle Filtering for Model-Based Anomaly Detection in Sensor Networks

A novel technique has been developed for anomaly detection of rocket engine test stand (RETS) data. The objective was to develop a system that postprocesses a csv file containing the sensor readings and activities (time-series) from a rocket engine test, and detects any anomalies that might have occurred during the test. The output consists of the names of the sensors that show anomalous behavior, and the start and end time of each anomaly. In order to reduce the involvement of domain experts significantly, several data-driven approaches have been proposed where models are automatically acquired from the data, thus bypassing the cost and effort of building system models. Many supervised learning methods can efficiently learn operational and fault models, given large amounts of both nominal and fault data. However, for domains such as RETS data, the amount of anomalous data that is actually available is relatively small, making most supervised learning methods rather ineffective, and in general met with limited success in anomaly detection. The fundamental problem with existing approaches is that they assume that the data are iid, i.e., independent and identically distributed, which is violated in typical RETS data. None of these techniques naturally exploit the temporal information inherent in time series data from the sensor networks. There are correlations among the sensor readings, not only at the same time, but also across time. However, these approaches have not explicitly identified and exploited such correlations. Given these limitations of model-free methods, there has been renewed interest in model-based methods, specifically graphical methods that explicitly reason temporally. The Gaussian Mixture Model (GMM) in a Linear Dynamic System approach assumes that the multi-dimensional test data is a mixture of multi-variate Gaussians, and fits a given number of Gaussian clusters with the help of the wellknown Expectation Maximization (EM) algorithm. The parameters thus learned are used for calculating the joint distribution of the observations. However, this GMM assumption is essentially an approximation and signals the potential viability of non-parametric density estimators. This is the key idea underlying the new approach.

Solano, Wanda↗

A Deterministic Annealing Approach to Clustering AIRS Data

We will examine the validity of means and standard deviations as a basis for climate data products. We will explore the conditions under which these two simple statistics are inadequate summaries of the underlying empirical probability distributions by contrasting them with a nonparametric, method called Deterministic Annealing technique

clustering↗

Quantiles, parametric-select density estimation, and bi-information parameter estimators

A quantile-based approach to statistical analysis and probability modeling of data is presented which formulates statistical inference problems as functional inference problems in which the parameters to be estimated are density functions. Density estimators can be non-parametric (computed independently of model identified) or parametric-select (approximated by finite parametric models that can provide standard models whose fit can be tested). Exponential models and autoregressive models are approximating densities which can be justified as maximum entropy for respectively the entropy of a probability density and the entropy of a quantile density. Applications of these ideas are outlined to the problems of modeling: (1) univariate data; (2) bivariate data and tests for independence; and (3) two samples and likelihood ratios. It is proposed that bi-information estimation of a density function can be developed by analogy to the problem of identification of regression models.

Parzen, E.↗

Decision Boundary Feature Extraction for Nonparametric Classification

Feature extraction has long been an important topic in pattern recognition. Although many authors have studied feature extraction for parametric classifiers, relatively few feature extraction algorithms are available for nonparametric classifiers. A new feature extraction algorithm based on decision boundaries for nonparametric classifiers is proposed. It is noted that feature extraction for pattern recognition is equivalent to retaining 'discriminantly informative features' and a discriminantly informative feature is related to the decision boundary. Since nonparametric classifiers do not define decision boundaries in analytic form, the decision boundary and normal vectors must be estimated numerically. A procedure to extract discriminantly informative features based on a decision boundary for non-parametric classification is proposed. Experiments show that the proposed algorithm finds effective features for the nonparametric classifier with Parzen density estimation.

Lee, Chulhee↗

Decision boundary feature selection for non-parametric classifier

Feature selection has been one of the most important topics in pattern recognition. Although many authors have studied feature selection for parametric classifiers, few algorithms are available for feature selection for nonparametric classifiers. In this paper we propose a new feature selection algorithm based on decision boundaries for nonparametric classifiers. We first note that feature selection for pattern recognition is equivalent to retaining 'discriminantly informative features', and a discriminantly informative feature is related to the decision boundary. A procedure to extract discriminantly informative features based on a decision boundary for nonparametric classification is proposed. Experiments show that the proposed algorithm finds effective features for the nonparametric classifier with Parzen density estimation.

Lee, Chulhee↗

Modeling and Visualizing Uncertainty in Continuous Variables Predicted using Remotely Sensed Data

The use of remotely sensed images to map continuous biophysical variables, such as those related to terrestrial vegetation amount, sea surface temperature, and many other targets of NASA s Earth Observing System (EOS), includes variable, parametric, positional, spatial support and structural sources of uncertainty. A complete description of uncertainty will lead to a probability distribution at each location, allowing the exploration of the spatial dimension of uncertainty, that is, where the field is not well quantified. To achieve this purpose, convenient visualization tools are required. We have produced such a tool, called PDFVis, that facilitates the display of probability density functions (pdfs) on a per-grid-cell basis. The density estimate from Monte-Carlo generated realizations is interactively displayed as well as parametric and non-parametric summaries of the pdf field (such as mean, median, quartiles, standard deviation, number of modes, and locations of modes). Shaded surface renderings of pdfs along a transect can also be projected onto a plane. This tool will become more useful as richer descriptions of spatial uncertainty become available.

Dungan, Jennifer L.↗