Global and Local Two-Sample Tests via Regression

Kim, Ilmun; Lee, Ann B.; Lei, Jing

doi:10.48550/arxiv.1812.08927

Cited by 2 publications

(4 citation statements)

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“…The optimization process may be approached in different ways. One of them consists of optimizing all variables at once by maximizing a metric which is output from the application of a local two-sample test (Kim et al, 2019). In this work, we focus on a variable-by-variable optimization which not only enables to select the best configuration and input metrics to TML methods but also leaves to the same accuracy in morphology as that obtained in GZ1 (see Section 6).…”

Section: Optimizing Morphological Metrics Configurationmentioning

confidence: 99%

Machine and Deep Learning applied to galaxy morphology - A comparative study

Barchi

Carvalho

Rosa

et al. 2020

Astronomy and Computing

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Morphological classification is a key piece of information to define samples of galaxies aiming to study the large-scale structure of the universe. In essence, the challenge is to build up a robust methodology to perform a reliable morphological estimate from galaxy images. Here, we investigate how to substantially improve the galaxy classification within large datasets by mimicking human classification. We combine accurate visual classifications from the Galaxy Zoo project with machine and deep learning methodologies. We propose two distinct approaches for galaxy morphology: one based on non-parametric morphology and traditional machine learning algorithms; and another based on Deep Learning. To measure the input features for the traditional machine learning methodology, we have developed a system called CyMorph, with a novel non-parametric approach to study galaxy morphology. The main datasets employed comes from the Sloan Digital Sky Survey Data Release 7 (SDSS-DR7). We also discuss the class imbalance problem considering three classes. Performance of each model is mainly measured by Overall Accuracy (OA). A spectroscopic validation with astrophysical parameters is also provided for Decision Tree models to assess the quality of our morphological classification. In all of our samples, both Deep and Traditional Machine Learning approaches have over 94.5% OA to classify galaxies in two classes (elliptical and spiral). We compare our classification with state-of-the-art morphological classification from literature. Considering only two classes separation, we achieve 99% of overall accuracy in average when using our deep learning models, and 82% when using three classes. We provide a catalog with 670,560 galaxies containing our best results, including morphological metrics and classification.ETGs have T-Type ≤ 0 and LTGs have T-Type > 0 (de Vaucouleurs, 1963). T-Type considers ellipticity and spiral arms strength but does not reflect the presence or absence of the bar feature in spirals.Morphology reveals structural, intrinsic and environmental properties of galaxies. In the local universe, ETGs are mostly situated in the center of galaxy clusters, have a larger mass, less gas, higher velocity dispersion, and older stellar populations than LTGs, which are rich star-forming systems (Roberts and Haynes, 1994;Blanton and Moustakas, 2009;Pozzetti et al., 2010). By mapping where the ETGs are, it is possible to map the large-scale structure of the universe. Therefore, galaxy morphology is of paramount importance for extragalactic research as it relates to stellar properties and key aspects of the evolution and structure of the universe.Astronomy has become an extremely data-rich field of knowledge with the advance of new technologies in recent decades. Nowadays it is impossible to rely on human classification given the huge flow of data attained by current research

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Section: Optimizing Morphological Metrics Configurationmentioning

confidence: 99%

Machine and Deep Learning applied to galaxy morphology - A comparative study

Barchi

Carvalho

Rosa

et al. 2020

Astronomy and Computing

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“…These methods, however, only provide a binary answer of the form "reject" or "fail to reject" the null hypothesis. Here we use a new regression-based approach to two-sample testing [39] 1 that can adapt to any structure in X where there is a suitable regression method; Theorem 1 relates the power of the test to the Mean Integrated Squared Error (MISE) of the regression. Moreover, the regression test can detect and describe local differences (beyond the usual location and scale alternatives) in L(x; θ 0 ) and L(x; θ 0 ) in feature space X .…”

Section: Two-sample Test Via Regressionmentioning

confidence: 99%

“…Moreover, the regression test can detect and describe local differences (beyond the usual location and scale alternatives) in L(x; θ 0 ) and L(x; θ 0 ) in feature space X . We briefly describe the method below; see Supplementary Material E and [39] for theoretical details, and see Sections 2.2 and 3.2 for examples based on random forests regression. Let P 0 be the distribution over X induced by L(x; θ 0 ) and let P 1 be the distribution over X induced by L(x; θ 0 ).…”

Section: Two-sample Test Via Regressionmentioning

confidence: 99%

“…These procedures are inspired by classical hypothesis testing, but generalize to complex high-dimensional data with an LFI setting, and can identify any statistically significant deviation from the simulated distribution. We use a new regression-based two-sample test [39] to first compare the simulator and emulator models locally, i.e., at fixed parameters; these local tests are then turned into a "global" goodness-of-fit test that is statistically consistent (see Theorem 2). Our framework can adopt any machine-learning regression method to handle different structures in high-dimensional data.…”

Section: Introductionmentioning

confidence: 99%

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Validation of Approximate Likelihood and Emulator Models for Computationally Intensive Simulations

Dalmasso,

Lee,

Izbicki

et al. 2019

Preprint

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Complex phenomena are often modeled with computationally intensive feedforward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to use an approximate likelihood or faster emulator model for efficient statistical inference. We describe a new two-sample testing framework for quantifying the quality of the fit to simulations at fixed parameter values. This framework can leverage any regression method to handle complex high-dimensional data and attain higher power in settings where wellknown distance-based tests would not. We also introduce a statistically rigorous test for assessing global goodness-of-fit across simulation parameters. In cases where the fit is inadequate, our method provides valuable diagnostics by allowing one to identify regions in both feature and parameter space which the model fails to reproduce well. We provide both theoretical results and examples which illustrate the effectiveness of our approach.Preprint. Under review.

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Global and Local Two-Sample Tests via Regression

Cited by 2 publications

References 46 publications

Machine and Deep Learning applied to galaxy morphology - A comparative study

Machine and Deep Learning applied to galaxy morphology - A comparative study

Validation of Approximate Likelihood and Emulator Models for Computationally Intensive Simulations

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