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作者：Toulis, Panos; Airoldi, Edoardo M.
作者单位：University of Chicago; Harvard University
摘要：Stochastic gradient descent procedures have gained popularity for parameter estimation from large data sets. However, their statistical properties are not well understood, in theory. And in practice, avoiding numerical instability requires careful tuning of key parameters. Here, we introduce implicit stochastic gradient descent procedures, which involve parameter updates that are implicitly defined. Intuitively, implicit updates shrink standard stochastic gradient descent updates. The amount o...
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作者：Nickl, Richard; Soehl, Jakob
作者单位：University of Cambridge
摘要：We consider nonparametric Bayesian inference in a reflected diffusion model dX(t) = b(X-t) dt + sigma(Xt) dW(t), with discretely sampled observations X-0, X-Delta , . . . , X-n Delta. We analyse the nonlinear inverse problem corresponding to the low frequency sampling regime where Delta > 0 is fixed and n -> infinity. A general theorem is proved that gives conditions for prior distributions Pi on the diffusion coefficient sigma and the drift function b that ensure minimax optimal contraction r...
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作者：Choi, David
作者单位：Carnegie Mellon University
摘要：Performance bounds are given for exploratory co-clustering/blockmodeling of bipartite graph data, where we assume the rows and columns of the data matrix are samples from an arbitrary population. This is equivalent to assuming that the data is generated from a nonsmooth graphon. It is shown that co-clusters found by any method can be extended to the row and column populations, or equivalently that the estimated blockmodel approximates a blocked version of the generative graphon, with estimatio...
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作者：Dobriban, Edgar
作者单位：Stanford University
摘要：Principal component analysis (PCA) is a widely used method for dimension reduction. In high-dimensional data, the signal eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the noise eigenvalues. Therefore, popular tests based on the largest eigenvalue have little power to detect weak PCs. In the special case of the spiked model, certain tests asymptotically equivalent to linear spectral statistics (LSS)-averaging effects over all eigenvalu...
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作者：Hu, Rui; Wiens, Douglas P.
作者单位：MacEwan University; University of Alberta
摘要：To aid in the discrimination between two, possibly nonlinear, regression models, we study the construction of experimental designs. Considering that each of these two models might be only approximately specified, robust maximin designs are proposed. The rough idea is as follows. We impose neighbourhood structures on each regression response, to describe the uncertainty in the specifications of the true underlying models. We determine the least favourable-in terms of Kullback-Leibler divergence...
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作者：Han, Dong; Tsung, Fugee; Xian, Jinguo
作者单位：Shanghai Jiao Tong University; Hong Kong University of Science & Technology
摘要：By introducing suitable loss random variables of detection, we obtain optimal tests in terms of the stopping time or alarm time for Bayesian changepoint detection not only for a general prior distribution of change-points but also for observations being a Markov process. Moreover, the optimal (minimal) average detection delay is proved to be equal to 1 for any (possibly large) average run length to false alarm if the number of possible change-points is finite.
