Spectral Mixture Kernels with Time and Phase Delay Dependencies

Spectral Mixture (SM) kernels form a powerful class of kernels for Gaussian processes, capable to discover patterns, extrapolate, and model negative covariances. Being a linear superposition of quasi-periodical Gaussian components, an SM kernel does not explicitly model dependencies between components. In this paper we investigate the benefits of modeling explicitly time and phase delay dependencies between components in an AM kernel. We analyze the presence of statistical dependencies between components using Gaussian conditionals and posterior covariance and use this framework to motivate the proposed SM kernel extension, called Spectral Mixture kernel with time and phase delay Dependencies (SMD). SMD is constructed in two steps: first, time delay and phase delay are incorporated into each base component; next, cross-convolution between a base component and the reversed complex conjugate of another base component is performed which yields a complex-valued and positive definite kernel representing correlations between base components. The number of hyper-parameters of SMD, except the time and phase delay ones, remains equal to that of the SM kernel. We perform a thorough comparative experimental analysis of SMD on synthetic and real-life data sets. Results indicate the beneficial effect of modeling time and phase delay dependencies between base components, notably for natural phenomena involving little or no influence from human activity.Comment: 28 page

Data Mining and Machine Learning in Astronomy

We review the current state of data mining and machine learning in astronomy. 'Data Mining' can have a somewhat mixed connotation from the point of view of a researcher in this field. If used correctly, it can be a powerful approach, holding the potential to fully exploit the exponentially increasing amount of available data, promising great scientific advance. However, if misused, it can be little more than the black-box application of complex computing algorithms that may give little physical insight, and provide questionable results. Here, we give an overview of the entire data mining process, from data collection through to the interpretation of results. We cover common machine learning algorithms, such as artificial neural networks and support vector machines, applications from a broad range of astronomy, emphasizing those where data mining techniques directly resulted in improved science, and important current and future directions, including probability density functions, parallel algorithms, petascale computing, and the time domain. We conclude that, so long as one carefully selects an appropriate algorithm, and is guided by the astronomical problem at hand, data mining can be very much the powerful tool, and not the questionable black box.Comment: Published in IJMPD. 61 pages, uses ws-ijmpd.cls. Several extra figures, some minor additions to the tex