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 20 of 70 for “"Sum of squares"”.
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Statistical Inference and the Sum of Squares Method
… and noisy data is a central concern of modern computer science. Often, the main challenges are inherently computational: the problems are well understood from a purely statistical perspective, but key statistical primitives -- likelihood ratios, Bayes-optimal estimators, etc. -- are …
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Low rank decompositions for sum of squares optimization
… investigate theoretical and numerical advantages of a novel representation for Sum of Squares (SOS) decomposition of univariate and multivariate polynomials. This representation formulates a SOS problem by interpolating a polynomial at a finite set of sampling points. As compared to the …
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OPTIMAL CONTROL DESIGN FOR POLYNOMIAL NONLINEAR SYSTEMS USING SUM OF SQUARES TECHNIQUE WITH GUARANTEED LOCAL OPTIMALITY
… implementation for nonlinear systems is a topic of much interest. However, unlike for linear systems, for nonlinear systems explicit analytical solution for optimal feedback control is not available. Numerical techniques, on the other hand, can be used to approximate the solution of the HJB …
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Nonnegative Polynomials, Sums of Squares and the Cayley-Bacharach Theorem
… polynomial is non-negative is to express it as a sum of squares, however not all non-negative polynomials can be written as a sum of squares. The fundamental reason that there exist non-negative polynomials that cannot be written as sums of squares is that these polynomials satisfy linear …
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Using dimensional analysis in building statistical response models
The method of dimensional analysis has been used for almost a century with experimental methods to obtain, among other things, prediction equations in the physical sciences and engineering. Only recently has the method been considered in the statistical sense. A thorough literature research is …
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Analysis of variance of a group divisible singular design with two associate classes with missing observations
… discussed in this paper is the estimation of a single missing observation, two missing observations and several missing observations in a Group Visible (Singular) for Shirley balanced incomplete blocks design with two associate classes. Subsequently the analysis of variance, of the data …
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Analysis of variance of a balanced incomplete block design with missing observations
The problem considered in this paper is that of estimating several missing values and analyzing the resulting augmented data in a balanced incomplete block design. The estimates are obtained by Yates' procedure of minimizing the error sum of squares. Explicit formulae are obtained for all cases …
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A Computational Tsirelson's Theorem for All Compiled Nonlocal Games
… have been a foundational tool in the study of quantum advantage and have been useful in classically verifying quantum computations. To address the challenge posed by the spatial separation assumption, Kalai et al. (STOC' 23) introduced a compilation procedure that compiles any nonlocal game …
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Minimum description length, regularisation and multi-modal data
… feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of …
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Competitive regression.
… is about investigating the predictive complexity of online regression. In essence, supervised learning from a data sequence consisting of n-dimensional input and the corresponding output is considered. In this work online learning scenario considered consists of sequential arrival of data, without …
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Principled approaches to robust machine learning and beyond
… such noise in high dimensional settings for some of the most fundamental statistical tasks for over sixty years of research. In this thesis we devise two novel, but similarly inspired, algorithmic paradigms for estimation in high dimensions in the presence of a small number of adversarially added …
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Algebraic relaxations and hardness results in polynomial optimization and Lyapunov analysis
The contributions of the first half of this thesis are on the computational and algebraic aspects of convexity in polynomial optimization. We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree …
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The curve through the expected values of order statistics with special reference to problems in nonparametric tests of hypotheses
… population with probability density f(x) occurs often in the statistical literature and especially in the theory of nonparametric statistics. A new expression for this value will be obtained tor any underlying density f(x) but emphasis will be placed on normal scores. A finite series …
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Control Theoretic Methods In Analysis And Design Of Optimization Algorithms
Recently, there has been a surge of interest in incorporating tools from dynamical systems and control theory to analyze and design iterative optimization algorithms. This new perspective provides many insights and new directions of research. In particular, we can study robustness to uncertainties, …
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Analysis of the Projective Re-Normalization method on semidefinite programming feasibility problems
… and study the advantages and disadvantages of a Hit & Run random walk with Dikin ball dilation. We perform this procedure on an ill-conditioned two dimensional simplex to show the Dikin ball Hit & Run random walk mixes much faster than standard Hit & Run random walk. In the last part of this …
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Analysis of variance of a randomized block design with missing observations
The estimation of several missing values in a randomized block design ls considered. The method used ls that of minimizing the error sum of squares, proposed originally by Yates (1933). Explicit equation for each absent value are derived for all cases in which not more than three values are …
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Robust stability and contraction analysis of nonlinear systems via semidefinite optimization
A wide variety of stability and performance problems for linear and certain classes of nonlinear dynamical systems can be formulated as convex optimization problems involving linear matrix inequalities (LMIs). These formulations can be solved numerically with computationally-effcient interior-point …
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Convex Relaxations: Beyond Polynomials, Splitting Methods and Average Case Analysis
The first part of this thesis concerns the use of semidefinite programming for solving optimisation problems involving non-polynomial and non-semialgebraic functions. We start with the problem of determining the logarithmic Sobolev constant of a finite Markov chain, which can be framed as a …
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Polynomial Optimization and the Moment Problem
There are a wide variety of mathematical problems in different areas which are classified under the title of Moment Problem. We are interested in the moment problem with polynomial data and its relation to real algebra and real algebraic geometry. In this direction, we consider two different …
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