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作者：Pensky, Marianna
作者单位：State University System of Florida; University of Central Florida
摘要：In the present paper, we consider the application of overcomplete dictionaries to the solution of general ill-posed linear inverse problems. In the context of regression problems, there has been an enormous amount of effort to recover an unknown function using an overcomplete dictionary. One of the most popular methods, Lasso and its variants, is based on maximizing the likelihood, and relies on stringent assumptions on the dictionary, the so-called compatibility conditions, for a proof of its...
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作者：Sadeghi, Kayvan
作者单位：University of Cambridge
摘要：In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs aft...
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作者：Cai, T. Tony; Eldar, Yonina C.; Li, Xiaodong
作者单位：University of Pennsylvania; Technion Israel Institute of Technology; University of California System; University of California Davis
摘要：In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the rareness and weakness of the complex sinusoids hidden in the series. The OPHC test is shown to be asymptotically powerful in the detectable region. Numerical simulations illustrate and verify the effectiveness of the proposed test. Furthermore, the periodogram ov...
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作者：Han, Xiao; Pan, Guangming; Zhang, Bo
作者单位：Nanyang Technological University
摘要：Let A(p) = YY*/m and B-p = XX*/n be two independent random matrices where X = (X-ij)(pxn) and Y = (Y-ij)(pxm) respectively consist of real (or complex) independent random variables with EXij = EYij = 0, E vertical bar X-ij vertical bar(2) = E vertical bar Y-ij vertical bar(2) = 1. Denote by lambda(1) the largest root of the determinantal equation det(lambda A(p) - B-p) = 0. We establish the Tracy-Widom type universality for lambda(1) under some moment conditions on X-ij and Y-ij when p/m and p...
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作者：Li, Ke
作者单位：International Business Machines (IBM); IBM USA; Massachusetts Institute of Technology (MIT)
摘要：We consider the problem of testing multiple quantum hypotheses {rho(circle times n)(1) ,..., rho(circle times n)(r)},where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state. It is known that the minimal average error probability P-e decays exponentially to zero, that is, P-e = exp{-xi n + o(n)}. However, this error exponent xi is generally unknown, except for the case that r = 2. In this paper, we solve the long-standing open problem of identi...
