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.
Results
Showing 1 to 9 of 9 for “"Concentration inequalities"”.
-
Concentration Inequalities for Dependent Random Variables on Bayesian Networks
The thesis presents a theoretical study of the concentration results for the function defined on the random variables on a Bayesian Network. In this work, we provide several concentration inequality results under the assumption that the function is Lipshitz or bounded difference. In addition, we …
-
Applications of empirical processes in learning theory : algorithmic stability and generalization bounds
… To analyze these properties, we focus on concentration inequalities and tools from empirical process theory. We obtain theoretical results and demonstrate their applications to machine learning. First, we show how various notions of stability upper- and lower-bound the bias and variance of …
-
Risk Aware Planning and Probabilistic Prediction for Autonomous Systems under Uncertain Environments
… and non-Gaussian uncertainty. We utilize concentration inequalities, higher order moments, and risk contours to handle non-Gaussian uncertainties. Without considering dynamics, we use RRT to plan trajectories together with SOS programming to verify the safety of the trajectory. Considering …
-
A concentration inequality based statistical methodology for inference on covariance matrices and operators
… this manuscript, we propose using tools from the concentration of measure literature–a theory that arose in the latter half of the 20th century from connections between geometry, probability, and functional analysis–to construct rigorous descriptive and inferential statistical methodology for …
-
Magnitude, concentration, and metric complexity in phylogenetics and information theory
… results about consistency in the classical case, concentration inequalities for independent random variables are used. However, when k << n, the dependencies between the observations cannot be ignored. So in Chapter 3, we show some McDiarmid-type concentration inequalities for leaf marginals of …
-
Functional inequalities in quantum information theory
Functional inequalities constitute a very powerful toolkit in studying various problems arising in classical information theory, statistics and many-body systems. Extensions of these tools to the noncommutative setting have been introduced in the beginning of the 90's in order to study the …
-
System identification for the bar model: Algorithms, consistency and sample complexity
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01
-
Essays in Econometrics
… The paper addresses this issue by providing concentration inequalities designed to detect patterns of model misspecification. The associated bounds can be used to identify subsets of individual characteristics that are not consistent with the moment restrictions. These results are applied to …
-
Consistency of nonparametric Bayesian methods for two statistical inverse problems arising from partial differential equations
Partial differential equations (PDEs) govern many natural phenomena. When trying to understand the parameters driving these phenomena, we must be aware of the inevitable errors in our measurements; in statistical inverse problems these measurement errors are modelled by statistical noise. One …