Photo by Rafael Hoyos Weht on UnsplashFurutsu-Novikov — like cross-correlation — response relations for methods pushed by shot noiseAuthors: Jakob Stubenrauch, Benjamin LindnerAbstract: We take into account a dynamic system that’s pushed by an intensity-modulated Poisson course of with depth Λ(t)=λ(t)+εν(t). We derive an actual relation between the input-output cross-correlation in the spontaneous state (ε=0) and the linear response to the modulation (ε>0). This may be thought to be a variant of the Furutsu-Novikov theorem for the case of shot noise. As we present, the relation remains to be legitimate in the presence of further unbiased noise. Furthermore, we derive an extension to Cox-process enter, i.e. to coloured shot noise. We talk about purposes to particle detection and to neuroscience. Using the brand new relation, we get hold of a fluctuation-response-relation for a leaky integrate-and-fire neuron. We additionally present how the brand new relation can be utilized in a distant management drawback in a recurrent neural community. The relations are numerically examined for each stationary and non-stationary dynamics. Lastly, extensions to marked Poisson processes and to higher-order statistics are introduced.2. Machine Learning for Exoplanet Detection in High-Contrast Spectroscopy: Revealing Exoplanets by Leveraging Hidden Molecular Signatures in Cross-Correlated Spectra with Convolutional Neural NetworksAuthors: Emily O. Garvin, Markus J. Bonse, Jean Hayoz, Gabriele Cugno, Jonas Spiller, Polychronis A. Patapis, Dominique Petit Dit de la Roche, Rakesh Nath-Ranga, Olivier Absil, Nicolai F. Meinshausen, Sascha P. QuanzAbstract: The new technology of observatories and devices (VLT/ERIS, JWST, ELT) inspire the event of strong strategies to detect and characterise faint and close-in exoplanets. Molecular mapping and cross-correlation for spectroscopy use molecular templates to isolate a planet’s spectrum from its host star. However, reliance on signal-to-noise ratio (S/N) metrics can result in missed discoveries, on account of robust assumptions of Gaussian unbiased and identically distributed noise. We introduce machine studying for cross-correlation spectroscopy (MLCCS); the strategy goals to leverage weak assumptions on exoplanet characterisation, such because the presence of particular molecules in atmospheres, to enhance detection sensitivity for exoplanets. MLCCS strategies, together with a perceptron and unidimensional convolutional neural networks, function in the cross-correlated spectral dimension, in which patterns from molecules may be recognized. We check on mock datasets of artificial planets inserted into actual noise from SINFONI at Ok-band. The outcomes from MLCCS present excellent enhancements. The end result on a grid of faint artificial gasoline giants exhibits that for a false discovery charge as much as 5%, a perceptron can detect about 26 instances the quantity of planets in comparison with an S/N metric. This issue will increase as much as 77 instances with convolutional neural networks, with a statistical sensitivity shift from 0.7% to 55.5%. In addition, MLCCS strategies present a drastic enchancment in detection confidence and conspicuity on imaging spectroscopy. Once skilled, MLCCS strategies supply delicate and fast detection of exoplanets and their molecular species in the spectral dimension. They deal with systematic noise and difficult seeing circumstances, can adapt to many spectroscopic devices and modes, and are versatile concerning atmospheric traits, which might allow identification of numerous planets in archival and future knowledge.
https://medium.com/@monocosmo77/increasing-importance-of-cross-correlation-in-machine-learning-research-part1-a82ba2424224?responsesOpen=true&sortBy=REVERSE_CHRON
Increasing importance of Cross-Correlation in Machine Learning research part1 | by Monodeep Mukherjee | May, 2024
