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Register a new userAn Information Theoretic Algorithm for Finding Periodicities in Stellar Light Curves
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We propose a new information theoretic metric for finding periodicities in stellar light curves. Light curves are astronomical time series of brightness over time, and are characterized as being noisy and unevenly sampled. The proposed metric combines correntropy (generalized correlation) with a periodic kernel to measure similarity among samples separated by a given period. The new metric provides a periodogram, called Correntropy Kernelized Periodogram (CKP), whose peaks are associated with the fundamental frequencies present in the data. The CKP does not require any resampling, slotting or folding scheme as it is computed directly from the available samples. CKP is the main part of a fully-automated pipeline for periodic light curve discrimination to be used in astronomical survey databases. We show that the CKP method outperformed the slotted correntropy, and conventional methods used in astronomy for periodicity discrimination and period estimation tasks, using a set of light curves drawn from the MACHO survey. The proposed metric achieved 97.2% of true positives with 0% of false positives at the confidence level of 99% for the periodicity discrimination task; and 88% of hits with 11.6% of multiples and 0.4% of misses in the period estimation task.
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The Large Synoptic Survey Telescope (LSST) will produce an unprecedented amount of light curves using six optical bands. Robust and efficient methods that can aggregate data from multidimensional sparsely-sampled time series are needed. In this paper we present a new method for light curve period estimation based on the quadratic mutual information (QMI). The proposed method does not assume a particular model for the light curve nor its underlying probability density and it is robust to non-Gaussian noise and outliers. By combining the QMI from several bands the true period can be estimated even when no single-band QMI yields the period. Period recovery performance as a function of average magnitude and sample size is measured using 30,000 synthetic multi-band light curves of RR Lyrae and Cepheid variables generated by the LSST Operations and Catalog simulators. The results show that aggregating information from several bands is highly beneficial in LSST sparsely-sampled time series, obtaining an absolute increase in period recovery rate up to 50%. We also show that the QMI is more robust to noise and light curve length (sample size) than the multiband generalizations of the Lomb Scargle and Analysis of Variance periodograms, recovering the true period in 10-30% more cases than its competitors. A python package containing efficient Cython implementations of the QMI and other methods is provided.
Safely deploying machine learning models to the real world is often a challenging process. Models trained with data obtained from a specific geographic location tend to fail when queried with data obtained elsewhere, agents trained in a simulation can struggle to adapt when deployed in the real world or novel environments, and neural networks that are fit to a subset of the population might carry some selection bias into their decision process. In this work, we describe the problem of data shift from a novel information-theoretic perspective by (i) identifying and describing the different sources of error, (ii) comparing some of the most promising objectives explored in the recent domain generalization, and fair classification literature. From our theoretical analysis and empirical evaluation, we conclude that the model selection procedure needs to be guided by careful considerations regarding the observed data, the factors used for correction, and the structure of the data-generating process.
As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is network comparison, developing a similarity or distance measure between networks so that meaningful comparisons can be drawn. The best means to accomplish this task remains an open area of research. Here we introduce a new measure to compare networks, the Network Portrait Divergence, that is mathematically principled, incorporates the topological characteristics of networks at all structural scales, and is general-purpose and applicable to all types of networks. An important feature of our measure that enables many of its useful properties is that it is based on a graph invariant, the network portrait. We test our measure on both synthetic graphs and real world networks taken from protein interaction data, neuroscience, and computational social science applications. The Network Portrait Divergence reveals important characteristics of multilayer and temporal networks extracted from data.
Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations encode exactly the same information about a target task as the original sentences. The mutual information, however, assumes the true probability distribution of a pair of random variables is known, leading to unintuitive results in settings where it is not. This paper proposes a new framework to measure what we term Bayesian mutual information, which analyses information from the perspective of Bayesian agents -- allowing for more intuitive findings in scenarios with finite data. For instance, under Bayesian MI we have that data can add information, processing can help, and information can hurt, which makes it more intuitive for machine learning applications. Finally, we apply our framework to probing where we believe Bayesian mutual information naturally operationalises ease of extraction by explicitly limiting the available background knowledge to solve a task.
Within the last years, the classification of variable stars with Machine Learning has become a mainstream area of research. Recently, visualization of time series is attracting more attention in data science as a tool to visually help scientists to recognize significant patterns in complex dynamics. Within the Machine Learning literature, dictionary-based methods have been widely used to encode relevant parts of image data. These methods intrinsically assign a degree of importance to patches in pictures, according to their contribution in the image reconstruction. Inspired by dictionary-based techniques, we present an approach that naturally provides the visualization of salient parts in astronomical light curves, making the analogy between image patches and relevant pieces in time series. Our approach encodes the most meaningful patterns such that we can approximately reconstruct light curves by just using the encoded information. We test our method in light curves from the OGLE-III and StarLight databases. Our results show that the proposed model delivers an automatic and intuitive visualization of relevant light curve parts, such as local peaks and drops in magnitude.
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