Global ETD Search
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Showing 1 to 11 of 11 for “"Minimax rates"”.
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Sparse functional regression models: minimax rates and contamination
… in estimating the sensitive point. The minimax rate of convergence for estimating the parameters in sparse functional linear regression is derived. It is shown that the optimal rate for estimating the sensitive point depends on the roughness of the predictor function, which is quantified …
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Modern challenges in distribution testing
… regime, with interest in sample complexities and minimax rates. Our understanding of many fundamental problems is now quite mature, but there are several questions which have arisen over the last decade, which have not yet received adequate attention. The goal of this dissertation is to identify …
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Statistical problems in transport and alignment
… on an arbitrary metric space. We prove sharp rates of convergence for empirical measures in Wasserstein distance on sufficiently regular compact metric spaces, improving on a line of work going back to Dudley (1969). We give the first nearly-optimal minimax lower bounds for the problem of …
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Private and Provably Efficient Federated Decision-Making
… setting, where a group of agents collaborates to improve their collective reward by communicating over a network. We first study the multi-armed bandit problem in a decentralized environment. We study federated bandit learning under several real-world environmental constraints, such as …
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Asymptotic theory for Bayesian nonparametric procedures in inverse problems
… setting. In the mildly ill-posed setting, minimax optimal rates are obtained, with sieve priors being rate adaptive over Sobolev classes. In the severely ill-posed setting, oversmoothing the prior yields minimax rates. Previously established results in the conjugate setting are obtained …
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Minimax estimation with structured data : shape constraints, causal models, and optimal transport
… optimization. For TV denoising, we provide fast rates that are adaptive to the underlying edge sparsity of the image, as well as generalizations to other graph structures, including higher-dimensional grid-graphs. For the estimation of Monge matrices, we give near minimax rates for their …
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Matrix estimation with latent permutations
… unimodal. We study both global and adaptive rates of estimation for this model, and introduce an efficient algorithm for the monotone case. Next, we move on to ranking from pairwise comparisons, and consider the noisy sorting model. We establish the minimax rates of estimation for noisy …
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The Limits of Recovering Planted Subgraphs
… novel graph decomposition of H as well as a new minimax theorem which may be of independent interest. Our results generalize to the setting of minimax rates of recovering arbitrary monotone boolean properties planted in random noise, where the statistician observes the union of a planted minimal …
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Contributions to statistical learning and its applications in personalized medicine
… that regardless the generality of the method, minimax optimal convergence rates are achieved. In order to derive the asymptotic analysis of the estimator, we developed a simultaneous diagonalization tool for two positive definite operators: the kernel operator and the operator defined by the …
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Contributions to asymptotic theory in nonparametric statistics
… parameter in order to achieve fast convergence rates. We show that the DGP prior does indeed consistently solve the inverse problem, proving a posterior contraction rate result; this contraction rate depends on the compositional structure of the true parameter, and the DGP prior is able to adapt …
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Consistent community detection in uni-layer and multi-layer networks
… and through simulations. We also derived minimax error rates and thresholds for achieving consistency of community detection in MLSBM, which were then used to show the advantage of the multi-layer model over a traditional alternative, the aggregate stochastic block model. In simulations …