Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 18 of 18 for “"asymptotic bounds"”.
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Non-asymptotic bounds for prediction problems and density estimation.
… two parts: first, we provide the minimax lower bounds for the performance of active learning methods. Second, we propose an active learning algorithm which attains nearly optimal rates over a broad class of underlying distributions and is adaptive with respect to the unknown parameters of the …
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Asymptotic bounds and values for the norm of the Laplace operator and other partial differential operators on spaces of polynomials
In der vorliegenden Dissertation werden endlichdimensionale Räume multivariater Polynome in N Variablen mit der Laguerre-, Hermite- bzw. Legendrenorm versehen. Dabei sei der Höchstgrad der Polynome oder die Summe der Grade der Variablen durch eine natürliche Zahl n nach oben beschränkt. Wir …
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Non-asymptotic Behavior in Massive Multiple Access and Streaming System Identification
Non-asymptotic understanding of information theoretic and algorithmic limits of estimation in statistical problems is indispensable for practical applications in engineering. There are two broad approaches to this end. The first: tools and advances in modern probability theory aid in deriving fully …
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Compressive Sensing
… techniques. Although theoretical performance bounds for these techniques can be found scattered throughout the published literature, there are few practical rules for concrete problems. This thesis helps fill this gap by experimenting on the asymptotic bounds of the number of measurements …
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Topics in combinatorics and combinatorial algorithms
… studied and so are one-point removal theorems. Asymptotic bounds on the interval number of almost every poset are derived, as well as results concerning the computational complexity of this parameter.
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Some topics in sequential density estimation
… Error (MIAE). Devroye and Gyorfi (1985) obtained asymptotic bounds for the MIAE in estimating f by a kernel estimate $\ f\sb{n}.$ Using these bounds one can identify an appropriate sample size such that the MIAE is smaller than some pre-assigned quantity w $>$ 0. Hence there is no fixed sample …
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An Intermediate Representation for Expressing and Optimizing Computations in Lattice Quantum Chromodynamics
… the algorithmic approach in search of better asymptotic bounds. Our approaches lead to up to 5x speedups and at worse 2x slowdowns for our most important problem, but with a better development cycle, requiring only 100s of SLOC compared to 1000s of SLOC.
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Probabilistic Models and Algorithmic Analysis of Network Problems
… first problem, we aim to improve upon the known bounds of some fundamental distributed algorithms, Minimum Spanning Tree (MST) in particular. We propose the Smoothed Analysis, where the key is to randomly and slightly alter the input, and show new asymptotic bounds. For the MST problem, we also …
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Learning hypertrees with shortest path queries
… For various classes H of hypertrees, we present bounds on the number of queries required to learn an unknown hypertree from H. Matching upper and lower asymptotic bounds are presented for learning hyperpaths and hyperstars. Moreover, inspired by Hein’s algorithm for learning evolutionary trees …
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Asymptotic Behavior of Homology and Intersection Multiplicity
… one, also the most important one, deals with the asymptotic length of homology for complexes of finitely generated free modules, under the iteration of the Frobenius functor. We first obtain asymptotic bounds on such length functions in lower dimensional cases, which generalizes a result of Dutta. …
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Non-Asymptotic 𝑡-Wise Independence of Substitution-Permutation Networks
… against cryptanalytic attacks and show non-asymptotic bounds for two widely-used ciphers. There are two main contributions of this thesis. In the first part of this thesis, we study the pairwise independence of AES. Replacing the INV 𝑆-box with an ‘ideal’ variant, we are able to compute …
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Theoretical study of two prediction-centric problems : graphical model learning and recommendations
… the prediction task of interest. We derive non-asymptotic bounds on the number of samples needed to get a distribution (from the same class) with small ssTV relative to the one generating the samples. An implication is that far fewer samples are needed for accurate predictions than for …
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Topological and geometric inference of data
… attention owing to its conceptual elegance, and asymptotic bounds are obtained on the admissible level of noise such that the manifold can be recovered up to homotopy equivalence. Attention is turned on how to accomplish this in practice. Following ideas from topological data analysis, simplicial …
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Efficient secure computation enabled by blockchain technology
… protocol (for up to 64-bit integers) and better asymptotic bounds for fixed-point division.
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Message Passing Algorithms for Statistical Estimation and Communication
… structure of the matrix. We derive a non-asymptotic bound on the probability of exact recovery, which holds for any *n*<sub>1</sub> x *n*<sub>2</sub> sparse, low-rank matrix. We also show how to adapt the scheme to tackle matrices that are approximately sparse and low-rank. The theoretical …
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On congruence function fields with many rational places
… places, namely maximal function fields and asymptotically good towers of function fields. The third part concerns Selmer groups of elliptic curves over the rational function field. Let $\mathcal{H}$ be the Hermitian function field, and $\mathcal{C}$ be a maximal function field, both over the …
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New methods for econometric inference
… These methods yield tests that have correct asymptotic size and are asymptotically nonconservative. It is also shown how to obtain an adaptive rate optimal test that has the best attainable rate of uniform consistency against models whose regression function has Lipschitz-continuous …
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Resource Allocation in Cellular Networks with Coexisting Femtocells and Macrocells
… probability. Using this model, we establish asymptotic bounds on the minimum number of resource blocks required to make interference-free resource assignments for all the users in the network. We assess these bounds using a simple greedy resource allocation algorithm to demonstrate that the …