Principal Component Analysis of the Time- and Position-Dependent Point Spread Function of the Advanced Camera for Surveys

We describe the time- and position-dependent point spread function (PSF) variation of the Wide Field Channel (WFC) of the Advanced Camera for Surveys (ACS) with the principal component analysis (PCA) technique. The time-dependent change is caused by the temporal variation of the $HST$ focus whereas the position-dependent PSF variation in ACS/WFC at a given focus is mainly the result of changes in aberrations and charge diffusion across the detector, which appear as position-dependent changes in elongation of the astigmatic core and blurring of the PSF, respectively. Using >400 archival images of star cluster fields, we construct a ACS PSF library covering diverse environments of the $HST$ observations (e.g., focus values). We find that interpolation of a small number ($\sim20$) of principal components or ``eigen-PSFs'' per exposure can robustly reproduce the observed variation of the ellipticity and size of the PSF. Our primary interest in this investigation is the application of this PSF library to precision weak-lensing analyses, where accurate knowledge of the instrument's PSF is crucial. However, the high-fidelity of the model judged from the nice agreement with observed PSFs suggests that the model is potentially also useful in other applications such as crowded field stellar photometry, galaxy profile fitting, AGN studies, etc., which similarly demand a fair knowledge of the PSFs at objects' locations. Our PSF models, applicable to any WFC image rectified with the Lanczos3 kernel, are publicly available.Comment: Accepted to PASP. To appear in December issue. Figures are degraded to meet the size limit. High-resolution version can be downloaded at http://acs.pha.jhu.edu/~mkjee/acs_psf/acspsf.pd

Feature-based time-series analysis

This work presents an introduction to feature-based time-series analysis. The time series as a data type is first described, along with an overview of the interdisciplinary time-series analysis literature. I then summarize the range of feature-based representations for time series that have been developed to aid interpretable insights into time-series structure. Particular emphasis is given to emerging research that facilitates wide comparison of feature-based representations that allow us to understand the properties of a time-series dataset that make it suited to a particular feature-based representation or analysis algorithm. The future of time-series analysis is likely to embrace approaches that exploit machine learning methods to partially automate human learning to aid understanding of the complex dynamical patterns in the time series we measure from the world.Comment: 28 pages, 9 figure

Fast Point Spread Function Modeling with Deep Learning

Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to be taken into account when inferring properties of galaxies from astronomical images. In the case of cosmic shear, the PSF is one of the dominant sources of systematic errors and must be treated carefully to avoid biases in cosmological parameters. Recently, forward modeling approaches to calibrate shear measurements within the Monte-Carlo Control Loops ($MCCL$) framework have been developed. These methods typically require simulating a large amount of wide-field images, thus, the simulations need to be very fast yet have realistic properties in key features such as the PSF pattern. Hence, such forward modeling approaches require a very flexible PSF model, which is quick to evaluate and whose parameters can be estimated reliably from survey data. We present a PSF model that meets these requirements based on a fast deep-learning method to estimate its free parameters. We demonstrate our approach on publicly available SDSS data. We extract the most important features of the SDSS sample via principal component analysis. Next, we construct our model based on perturbations of a fixed base profile, ensuring that it captures these features. We then train a Convolutional Neural Network to estimate the free parameters of the model from noisy images of the PSF. This allows us to render a model image of each star, which we compare to the SDSS stars to evaluate the performance of our method. We find that our approach is able to accurately reproduce the SDSS PSF at the pixel level, which, due to the speed of both the model evaluation and the parameter estimation, offers good prospects for incorporating our method into the $MCCL$ framework.Comment: 25 pages, 8 figures, 1 tabl

GENDIS : genetic discovery of shapelets

In the time series classification domain, shapelets are subsequences that are discriminative of a certain class. It has been shown that classifiers are able to achieve state-of-the-art results by taking the distances from the input time series to different discriminative shapelets as the input. Additionally, these shapelets can be visualized and thus possess an interpretable characteristic, making them appealing in critical domains, where longitudinal data are ubiquitous. In this study, a new paradigm for shapelet discovery is proposed, which is based on evolutionary computation. The advantages of the proposed approach are that: (i) it is gradient-free, which could allow escaping from local optima more easily and supports non-differentiable objectives; (ii) no brute-force search is required, making the algorithm scalable; (iii) the total amount of shapelets and the length of each of these shapelets are evolved jointly with the shapelets themselves, alleviating the need to specify this beforehand; (iv) entire sets are evaluated at once as opposed to single shapelets, which results in smaller final sets with fewer similar shapelets that result in similar predictive performances; and (v) the discovered shapelets do not need to be a subsequence of the input time series. We present the results of the experiments, which validate the enumerated advantages

Random Dilated Shapelet Transform: A New Approach for Time Series Shapelets

Shapelet-based algorithms are widely used for time series classification because of their ease of interpretation, but they are currently outperformed by recent state-of-the-art approaches. We present a new formulation of time series shapelets including the notion of dilation, and we introduce a new shapelet feature to enhance their discriminative power for classification. Experiments performed on 112 datasets show that our method improves on the state-of-the-art shapelet algorithm, and achieves comparable accuracy to recent state-of-the-art approaches, without sacrificing neither scalability, nor interpretability