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Ann B. Lee

Publications and source records attributed to Ann B. Lee.

42 records · Page 3Linked to original sources
arXiv2009

High-Dimensional Density Estimation via SCA: An Example in the Modelling of Hurricane Tracks

We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional representation of the data is critical in such situations because of the curse of dimensionality. Our proposed methodology consists of three main parts: (1) data reparameterization via dimensionality reduction, wherein the data are mapped into a space where standard techniques can be used for density estimation and simulation; (2) inverse mapping, in which simulated points are mapped back to the high-dimensional input space; and (3) verification, in which the quality of the estimate is assessed by comparing simulated samples with the observed data. These approaches are illustrated via an exploration of the spatial variability of tropical cyclones in the North Atlantic; each datum in this case is an entire hurricane trajectory. We conclude the paper with a discussion of extending the methods to model the relationship between TC variability and climatic variables.

stat.AP↗
arXiv2009

Accurate parameter estimation for star formation history in galaxies using SDSS spectra

To further our knowledge of the complex physical process of galaxy formation, it is essential that we characterize the formation and evolution of large databases of galaxies. The spectral synthesis STARLIGHT code of Cid Fernandes et al. (2004) was designed for this purpose. Results of STARLIGHT are highly dependent on the choice of input basis of simple stellar population (SSP) spectra. Speed of the code, which uses random walks through the parameter space, scales as the square of the number of basis spectra, making it computationally necessary to choose a small number of SSPs that are coarsely sampled in age and metallicity. In this paper, we develop methods based on diffusion map (Lafon & Lee, 2006) that, for the first time, choose appropriate bases of prototype SSP spectra from a large set of SSP spectra designed to approximate the continuous grid of age and metallicity of SSPs of which galaxies are truly composed. We show that our techniques achieve better accuracy of physical parameter estimation for simulated galaxies. Specifically, we show that our methods significantly decrease the age-metallicity degeneracy that is common in galaxy population synthesis methods. We analyze a sample of 3046 galaxies in SDSS DR6 and compare the parameter estimates obtained from different basis choices.

astro-ph.CO↗
arXiv2008

Spectral Connectivity Analysis

Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We analyze the dependence of the method on these tuning parameters. We focus on one particular technique - diffusion maps - but our analysis can be used for other methods as well. We identify the population quantities implicitly being estimated, we explain how these methods relate to classical kernel smoothing and we define an appropriate risk function for analyzing the estimators. We also show that, in some cases, fast rates of convergence are possible even in high dimensions.

stat.ME↗
arXiv2008

Treelets--An adaptive multi-scale basis for sparse unordered data

In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often possible due to sparsity: the fact that the data are typically redundant with underlying structures that can be represented by only a few features. In this paper we present treelets--a novel construction of multi-scale bases that extends wavelets to nonsmooth signals. The method is fully adaptive, as it returns a hierarchical tree and an orthonormal basis which both reflect the internal structure of the data. Treelets are especially well-suited as a dimensionality reduction and feature selection tool prior to regression and classification, in situations where sample sizes are small and the data are sparse with unknown groupings of correlated or collinear variables. The method is also simple to implement and analyze theoretically. Here we describe a variety of situations where treelets perform better than principal component analysis, as well as some common variable selection and cluster averaging schemes. We illustrate treelets on a blocked covariance model and on several data sets (hyperspectral image data, DNA microarray data, and internet advertisements) with highly complex dependencies between variables.

stat.ME↗
arXiv2008

Exploiting Low-Dimensional Structure in Astronomical Spectra

Dimension-reduction techniques can greatly improve statistical inference in astronomy. A standard approach is to use Principal Components Analysis (PCA). In this work we apply a recently-developed technique, diffusion maps, to astronomical spectra for data parameterization and dimensionality reduction, and develop a robust, eigenmode-based framework for regression. We show how our framework provides a computationally efficient means by which to predict redshifts of galaxies, and thus could inform more expensive redshift estimators such as template cross-correlation. It also provides a natural means by which to identify outliers (e.g., misclassified spectra, spectra with anomalous features). We analyze 3835 SDSS spectra and show how our framework yields a more than 95% reduction in dimensionality. Finally, we show that the prediction error of the diffusion map-based regression approach is markedly smaller than that of a similar approach based on PCA, clearly demonstrating the superiority of diffusion maps over PCA for this regression task.

astro-ph↗