We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available.
Half-sibling regression @cite_42 is a method to reconstruct a source from noisy observations by exploiting other sources that are affected by the same noise process but otherwise independent from it.
@cite_42
2470207857 2018417093 2018808115 2165773639
Abstract We describe a method for removing the effect of confounders to reconstruct a latent quantity of interest. The method, referred to as “half-sibling regression,” is inspired by recent work in causal inference using additive noise models. We provide a theoretical justification, discussing both independent and identically distributed as well as time series data, respectively, and illustrate the potential of the method in a challenging astronomy application. A novel framework for image filtering based on regression is presented. Regression is a supervised technique from pattern recognition theory in which a mapping from a number of input variables (features) to a continuous output variable is learned from a set of examples from which both input and output are known. We apply regression on a pixel level. A new, substantially different, image is estimated from an input image by computing a number of filtered input images (feature images) and mapping these to the desired output for every pixel in the image. The essential difference between conventional image filters and the proposed regression filter is that the latter filter is learned from training data. The total scheme consists of preprocessing, feature computation, feature extraction by a novel dimensionality reduction scheme designed specifically for regression, regression by k-nearest neighbor averaging, and (optionally) iterative application of the algorithm. The framework is applied to estimate the bone and soft-tissue components from standard frontal chest radiographs. As training material, radiographs with known soft-tissue and bone components, obtained by dual energy imaging, are used. The results show that good correlation with the true soft-tissue images can be obtained and that the scheme can be applied to images from a different source with good results. We show that bone structures are effectively enhanced and suppressed and that in most soft-tissue images local contrast of ribs decreases more than contrast between pulmonary nodules and their surrounding, making them relatively more pronounced. We propose two test statistics for use in inverse regression problems "Y"e"K""t"p"e", where "K" is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations "Y" for the function "t" are available. Both test statistics have a counterpart in classical hypothesis testing, where they are called the order selection test and the data-driven Neyman smooth test. We also introduce two model selection criteria which extend the classical Akaike information criterion and Bayes information criterion to inverse regression problems. In a simulation study we show that the inverse order selection and Neyman smooth tests outperform their direct counterparts in many cases. The theory is motivated by data arising in confocal fluorescence microscopy. Here, images are observed with blurring, modelled as convolution, and stochastic error at subsequent times. The aim is then to reduce the signal-to-noise ratio by averaging over the distinct images. In this context it is relevant to decide whether the images are still equal, or have changed by outside influences such as moving of the object table. Copyright (c) 2009 Royal Statistical Society. Various methods for estimating the self-similarity parameter and or the intensity of long-range dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and fractional ARIMA (0, d, 0). We also provide here a theoretical justification for the method of residuals of regression.