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 27 for “"High dimensional statistics"”.
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Geometric aspects of uncertainty quantification in high-dimensional statistics
In high-dimensional statistics, uncertainty quantification is often of its own mathematical interest and complexity. We discuss phenomena that are particular to high-dimensional inference tasks, which closely relate to the need to `adapt' to hidden lower-dimensional structures that are not directly …
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High-Dimensional Statistics for Causal Inference and Panel Data
… a focus on addressing key biases that arise in high-dimensional and dynamic environments. While this dissertation is motivated by the need to flexibly measure the economic impacts of climate change, the methods I develop are much more general. They apply broadly to panel data problems across …
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Algorithms and Algorithmic Barriers in High-Dimensional Statistics and Random Combinatorial Structures
… models arising from modern machine learning and high-dimensional statistical inference tasks. • Our first set of results to this direction establishes self-regularity for two-layer NNs with sigmoid, binary step, rectified linear unit (ReLU) activation functions and non-negative output weights in …
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Topics in Sparsity and Compression: From High dimensional statistics to Overparametrized Neural Networks
This thesis presents applications of sparsity in three different areas: covariance estimation in time-series data, linear regression with categorical variables, and neural network compression. In the first chapter, motivated by problems in computational finance, we consider a framework for jointly …
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Theory and Algorithms for Penalization, Graphical Models, and Surrogate Marker Evaluation
… we study three problems: oracle inequality in high-dimensional statistics theory, graphical models, and surrogate measures in clinical trials. First, we introduce a general slow rate bound for maximum regularized likelihood estimators in Kullback-Leibler divergence. The result applies to a wide …
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Essays on Algorithmic Learning and Uncertainty Quantification
… have found extensive use in machine learning and high-dimensional statistics, motivating a more thorough analysis of their limitations in high-dimensional problems.
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Statistical Learning with Discrete Structures: Statistical and Computational Perspectives
… explore statistical and computational aspects of statistics estimators (some classical and some new) that can be formulated as discrete optimization problems. In Chapters 2 and 3, we study two well-known problems in high-dimensional statistics: sparse Principal Component Analysis (PCA) and …
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Model selection and estimation in high dimensional settings
… and this complexity can be attributed to the high dimensionality of the space containing the inputs and the outputs; the existence of a structural prior knowledge within the inputs or the outputs that if ignored may lead to inefficient estimates of the parameters; and the presence of a …
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High Dimensional Inference for Semiparametric Models
In the literature, high dimensional inference refers to statistical inference when
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Statistical inference in high-dimensional matrix models
Matrix models are ubiquitous in modern statistics. For instance, they are used in finance to assess interdependence of assets, in genomics to impute missing data and in movie recommender systems to model the relationship between users and movie ratings. Typically such models are either …
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Approximate Message Passing for Matrix Regression
… have become popular in various structured high-dimensional statistical problems. Previous AMP algorithms for generalized linear models (GLM) typically require the signal to be in the form of a vector, and the design matrix to have independent and identically distributed Gaussian entries. In …
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Optimization Methods for Machine Learning under Structural Constraints
… a focus on shape constraints in nonparametric statistics and sparsity in high-dimensional statistics. In the first chapter, we consider the subgradient regularized convex regression problem, which aims to fit a convex function between the target variable and covariates. We propose novel …
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Nonparametric testing in modern statistics: A personal journey
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-08-01
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On inference about rare events
… with the number of samples, in a manner akin to high-dimensional statistics. In that context, we propose an approach that allows us to easily establish consistent estimators for a large class of canonical estimation problems. These include estimating entropy, the size of the alphabet, and the …
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Joint Network Modeling of Omics Data for Understanding Complex Diseases
… data sources, stemming from advancements in high-throughput genomic technologies, encourages the development of more sophisticated models. Through the simultaneous analysis of multiple data sets or types, joint network approaches enhance statistical power and provide a route towards a deeper …
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Natural gradient methods in statistics and machine learning
… used for modelling correlation structure in high-dimensional statistics; and various mixture distributions, which represent complex probability distributions as combinations of simpler distributions, allowing for features such as multimodality, which may not be possible to represent in the …
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Sparse Learning using Discrete Optimization: Scalable Algorithms and Statistical Insights
… concept in interpretable machine learning and high-dimensional statistics. While sparse learning problems can be naturally modeled using discrete optimization, computational challenges have historically shifted the focus towards alternatives based on continuous optimization and heuristics. …
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Message Passing Algorithms for Statistical Estimation and Communication
This thesis studies two high-dimensional statistical estimation problems: matrix sketching, and communication over many-user channels. Efficient recovery schemes, based on belief propagation (BP) and Approximate Message Passing (AMP), are developed for these problems. We first consider matrix …
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Topics in high-dimensional linear bandits and approximate Bayesian sampling
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01
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Change point detection for high dimensional data and valid inference for Bayesian linear models
We propose statistical methodologies for high dimensional change point detection and inference for Bayesian linear models. In the first project, we propose a change point detection method testing mean shift for high dimensional observations with unknown heteroscedasticity. The proposed tests target …
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