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作者：Jin, Jiashun; Ke, Zheng Tracy; Wang, Wanjie
作者单位：Carnegie Mellon University; University of Chicago; University of Pennsylvania
摘要：Consider a two-class clustering problem where we observe X-i = l(i)mu + Zi, Zi((i,i,d) under tilde) N(0, I-p), 1 <= i <= n. The feature vector mu is an element of R-p is unknown but is presumably sparse. The class labels l(i) is an element of {-1, 1} are also unknown and the main interest is to estimate them. We are interested in the statistical limits. In the two-dimensional phase space calibrating the rarity and strengths of useful features, we find the precise demarcation for the Region of ...
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作者：Mendelson, Shahar
作者单位：Technion Israel Institute of Technology
摘要：We show that if F is a convex class of functions that is L-sub-Gaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by local covering estimates of the class (i.e., the covering number at a specific level), rather than by the Gaussian average, which takes into account the structure of F at an arbitrarily small scale. To that end, we establish new sharp upper and lower estimates on the error rate in such learning problems.
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作者：Feller, Chrystel; Schorning, Kirsten; Dette, Holger; Bermann, Georgina; Bornkamp, Bjoern
作者单位：Novartis; Ruhr University Bochum
摘要：A common problem in Phase II clinical trials is the comparison of dose response curves corresponding to different treatment groups. If the effect of the dose level is described by parametric regression models and the treatments differ in the administration frequency (but not in the sort of drug), a reasonable assumption is that the regression models for the different treatments share common parameters. This paper develops optimal design theory for the comparison of different regression models ...
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作者：Kong, Weihao; Valiant, Gregory
作者单位：Stanford University
摘要：We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the population spectrum), given access to samples drawn from the distribution. We consider this recovery problem in the regime where the sample size is comparable to, or even sublinear in the dimensionality of the distribution. First, we propose a theoretically optimal and computationally efficient algorithm for recovering the momen...
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作者：Metelkina, Asya; Pronzato, Luc
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS)
摘要：Covariate-adaptive treatment allocation is considered in the situation when a compromise must be made between information (about the dependency of the probability of success of each treatment upon influential covariates) and cost (in terms of number of subjects receiving the poorest treatment). Information is measured through a design criterion for parameter estimation, the cost is additive and is related to the success probabilities. Within the framework of approximate design theory, the dete...
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作者：Su, Weijie; Bogdan, Malgorzata; Candes, Emmanuel
作者单位：University of Pennsylvania; University of Wroclaw; Stanford University; Stanford University
摘要：In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that in a regime of linear sparsity-meaning that the fraction of variables with a nonvanishing effect tends to a constant, however small-this cannot really be the case, even when the design variables are stochastically independent. We demonstrate that true featur...
