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作者：Belloni, Alexandre; Oliveira, Roberto I.
作者单位：Duke University; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and estimation method which is computationally efficient. We develop oracle and adaptivity inequalities, as well as model selection properties, that hold under continuity of the transition probabilities and polynomial (ss)-mixing. In particular, model misspecification...
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作者：Overgaard, Morten; Parner, Erik Thorlund; Pedersen, Jan
作者单位：Aarhus University; Aarhus University
摘要：A general asymptotic theory of estimates from estimating functions based on jack-knife pseudo-observations is established by requiring that the underlying estimator can be expressed as a smooth functional of the empirical distribution. Using results in p-variation norms, the theory is applied to important estimators from time-to-event analysis, namely the Kaplan-Meier estimator and the Aalen-Johansen estimator in a competing risks model, and the corresponding estimators of restricted mean surv...
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作者：Atchade, Yves A.
作者单位：University of Michigan System; University of Michigan
摘要：We study the contraction properties of a quasi-posterior distribution (sic)(n, d) obtained by combining a quasi-likelihood function and a sparsity inducing prior distribution on R-d, as both n (the sample size), and d (the dimension of the parameter) increase. We derive some general results that highlight a set of sufficient conditions under which (sic)(n, d) puts increasingly high probability on sparse subsets of R-d, and contracts toward the true value of the parameter. We apply these result...
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作者：Loh, Po-Ling
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison
摘要：We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and covariates. We first establish a form of local statistical consistency for the penalized regression estimators under fairly mild conditions on the error distribution: When the derivative of the loss function is bounded and satisfies a local restricted curvature con...
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作者：Nandy, Preetam; Maathuis, Marloes H.; Richardson, Thomas S.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Washington; University of Washington Seattle
摘要：We consider the estimation of joint causal effects from observational data. In particular, we propose new methods to estimate the effect of multiple simultaneous interventions (e.g., multiple gene knockouts), under the assumption that the observational data come from an unknown linear structural equation model with independent errors. We derive asymptotic variances of our estimators when the underlying causal structure is partly known, as well as high-dimensional consistency when the causal st...
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作者：Balakrishnan, Sivaraman; Wainwrightt, Martin J.; Yu, Bin
作者单位：University of California System; University of California Berkeley; Carnegie Mellon University
摘要：The EM algorithm is a widely used tool in maximum-likelihood estimation in incomplete data problems. Existing theoretical work has focused on conditions under which the iterates or likelihood values converge, and the associated rates of convergence. Such guarantees do not distinguish whether the ultimate fixed point is a near global optimum or a bad local optimum of the sample likelihood, nor do they relate the obtained fixed point to the global optima of the idealized population likelihood (o...
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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：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：Mousavi, Ali; Maleki, Arian; Baraniuk, Richard G.
作者单位：Rice University; Columbia University
摘要：This paper studies the optimal tuning of the regularization parameter in LASSO or the threshold parameters in approximate message passing (AMP). Considering a model in which the design matrix and noise are zero-mean i.i.d. Gaussian, we propose a data-driven approach for estimating the regularization parameter of LASSO and the threshold parameters in AMP. Our estimates are consistent, that is, they converge to their asymptotically optimal values in probability as n, the number of observations, ...
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作者：Fallat, Shaun; Lauritzen, Steffen; Sadeghi, Kayvan; Uhler, Caroline; Wermuth, Nanny; Zwiernik, Piotr
作者单位：University of Regina; University of Copenhagen; University of Cambridge; Massachusetts Institute of Technology (MIT); Institute of Science & Technology - Austria; Chalmers University of Technology; Johannes Gutenberg University of Mainz; Pompeu Fabra University
摘要：We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional semi-graphoid which is upward-stable and singletontransitive. In addition, we prove that any MTP2 distribution satisfying an appropriate support condition is faithful to its concentration graph. Finally, we analyze factorization properties of MTP2 distributio...
