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Maximin effects in inhomogeneous largescale data
, 2014
"... Largescale data are often characterised by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dime ..."
Abstract

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Largescale data are often characterised by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dimension or even without any such structure. Fitting varyingcoefficient models or mixture models can be appropriate solutions but are computationally very demanding and often try to return more information than necessary. If we just ask for a model estimator that shows good predictive properties for all regimes of the data, then we are aiming for a simple linear model that is reliable for all possible subsets of the data. We propose a maximin effects estimator and look at its prediction accuracy from a theoretical point of view in a mixture model with known or unknown group structure. Under certain circumstances the estimator can be computed orders of magnitudes faster than standard penalised regression estimators, making computations on largescale data feasible. Empirical examples complement the novel methodology and theory. 1
JMLR: Workshop and Conference Proceedings vol 35:1–15, 2014 Learning without Concentration
"... We obtain sharp bounds on the convergence rate of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without any boundedness assumptions on class members or on the target. Rather than resorting to a concentrationbased argument, the method relies on a ‘smal ..."
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We obtain sharp bounds on the convergence rate of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without any boundedness assumptions on class members or on the target. Rather than resorting to a concentrationbased argument, the method relies on a ‘smallball’ assumption and thus holds for heavytailed sampling and heavytailed targets. Moreover, the resulting estimates scale correctly with the ‘noise level ’ of the problem. When applied to the classical, bounded scenario, the method always improves the known estimates. 1.