Soft Maximin Aggregation of Heterogeneous Array Data
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The extraction of a common signal across many recordings is difficult when each recording -- in addition to the signal -- contains large, unique variation components. This is observed for voltage sensitive dye imaging (VDSI), an imaging technique used to measure neuronal activity, for which the resulting 3D array data have a highly heterogeneous noise structure. Maximin aggregation (magging) has previously been proposed as a robust estimation method in the presence of heterogeneous noise. We propose soft maximin aggregation as a general methodology for estimating a common signal from heterogeneous data. The soft maximin loss is introduced as an aggregation of explained variances, and the estimator is obtained by minimizing the penalized soft maximin loss. For a convex penalty we show convergence of a proximal gradient based algorithm, and we demonstrate how tensor structures for array data can be exploited by this algorithm to achieve time and memory efficiency. An implementation is provided in the R package SMMA available from CRAN. We demonstrate that soft maximin aggregation performs well on a VSDI data set with 275 recordings, for which magging does not work.
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