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作者：Najafi, Amir; Ilchi, Saeed; Saberi, Amir Hossein; Motahari, Seyed Abolfazl; Khalaj, Babak H.; Rabiee, Hamid R.
作者单位：Sharif University of Technology; Sharif University of Technology; Sharif University of Technology
摘要：We study the sample complexity of learning a high-dimensional simplex from a set of points uniformly sampled from its interior. Learning of simplices is a long studied problem in computer science and has applications in computational biology and remote sensing, mostly under the name of spectral unmixing. We theoretically show that a sufficient sample complexity for reliable learning of a K-dimensional simplex up to a total-variation error of is an element of is O(K-2/epsilon log K/epsilon), wh...
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作者：Montanari, Andrea; Venkataramanan, Ramji
作者单位：Stanford University; Stanford University; University of Cambridge
摘要：Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise, a setting that is also known as spiked model or deformed random matrix. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic accuracy of Bayes-optimal estimators in the high-dimensional limit. In this paper, we present a practical alg...
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作者：Koltchinskii, Vladimir; Zhilova, Mayya
作者单位：University System of Georgia; Georgia Institute of Technology
摘要：Let X1,..., X-n be i.i.d. random variables sampled from a normal distribution N(mu, Sigma) in R-d with unknown parameter theta = (mu, Sigma) is an element of Theta := R-d x C-+(d), where C-+(d) is the cone of positively definite covariance operators in R-d. Given a smooth functional f : Theta 1 bar right arrow R-1, the goal is to estimate f (theta) based on X-1,.., X-n. Let Theta(a; d) := R-d x {Sigma is an element of C-+(d) : sigma(Sigma) subset of [1/a, a]}, a >= 1, where sigma(Sigma) is the...
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作者：Samworth, Richard J.; Yuan, Ming
作者单位：University of Cambridge; Columbia University
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作者：Chen, Yuxin; Cheng, Chen; Fan, Jianqing
作者单位：Princeton University; Stanford University; Princeton University
摘要：This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix M* is an element of R-n(xn), yet only a randomly perturbed version M is observed. The noise matrix M - M* is composed of independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise if, for example, when we have two independent samples for each entry of M* and arrange them in...
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作者：Obloj, Jan; Wiesel, Johannes
作者单位：University of Oxford; University of Oxford
摘要：We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with d traded assets. We introduce a plug-in estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this, we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale densities. We then ext...
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作者：Tang, Yu; Xu, Hongquan
作者单位：Soochow University - China; University of California System; University of California Los Angeles
摘要：While the minimum aberration criterion is popular for selecting good designs with qualitative factors under an ANOVA model, the minimum beta-aberration criterion is more suitable for selecting designs with quantitative factors under a polynomial model. In this paper, we propose the concept of wordlength enumerator to unify these two criteria. The wordlength enumerator is defined as an average similarity of contrasts among all possible pairs of runs. The wordlength enumerator is easy and fast t...
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作者：Fisher, Nicholas, I; Smith, Adrian F. M.
作者单位：University of Sydney; Alan Turing Institute
摘要：Bill van Zwet's contributions to his profession are, in their own way, comparable to his very substantial research, research supervision and teaching contributions. He had several leadership roles in professional societies, edited leading theoretical journals, started up or revived important conference series, founded a research center and played a huge role in providing colleagues in Central and Eastern Europe access to the western world of probability and statistics. And to each of these sev...
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作者：Sherlock, Chris; Thiery, Alexandre H.; Golightly, Andrew
作者单位：Lancaster University; National University of Singapore; Newcastle University - UK
摘要：Delayed-acceptance Metropolis-Hastings and delayed-acceptance pseudo-marginal Metropolis-Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a computationally cheap deterministic approximation is available. An initial accept-reject stage uses the cheap approximation for computing the Metropolis-Hastings ratio; proposals which are accepted at this stage are subjected to a further accept-reje...
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作者：Hanneke, Steve; Kontorovich, Aryeh; Sabato, Sivan; Weiss, Roi
作者单位：Toyota Technological Institute - Chicago; Ben-Gurion University of the Negev; Ariel University
摘要：We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes consistent in all metric spaces admitting any such learner, making it an optimistically universal Bayes-consistent learner. This is the first learning algorithm known to enjoy this property; by comparison, the k-NN classifier and its variants are not generally universally Bayes consistent, except under additional structural assumptions, such as an i...
