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Virginia Tech

A Rate of Convergence for Learning Theory with Consensus

Abstract

dc:description.abstract

This thesis poses and solves a distribution free learning problem with consensus that arises in the study of estimation and control strategies for distributed sensor networks. Each node i for i = 1, . . . , n of the sensor network collects independent and identically distributed local measurements {z i} := {z i j}j∈N := {(x i j , yi j )}j∈N ⊆ X × Y := Z that are generated by the probability measure ρ i on Z. Each node i for i = 1, . . . , n of the network constructs a sequence of estimates {f i k }k∈N from its local measurements {z i} and from information functionals whose values are exchanged with other nodes as specified by the communication graph G for the network. The optimal estimate of the distribution free learning problem with consensus is cast as a saddle point problem which characterizes the consensus-constrained optimal estimate. This thesis introduces a two stage learning dynamic wherein local estimation is carried out via local least square approximations based on wavelet constructions and information exchange is associated with the Lagrange multipliers of the saddle point problem. Rates of convergence for the two stage learning dynamic are derived based on certain recent probabilistic bounds derived for wavelet approximation of regressor functions.

Degree

thesis:*
Name thesis:degree_name
Master of Science
Level thesis:degree_level
masters
Discipline thesis:degree_discipline
Mechanical Engineering
Department dc:contributor.department
Mechanical Engineering
Grantor dc:publisher
Virginia Tech
Year dc:date.issued
2015

Author and committee

dc:creator, dc:contributor.*
Author dc:creator
  • Gregory, Jessica G.
Chairs dc:contributor.committeechair
  • Kurdila, Andrew J.
  • Bayandor, Javid
Committee members dc:contributor.committeemember
  • Burns, John A.
  • Leonessa, Alexander

Subjects

dc:subject × 5

Rights

dc:rights
Statement dc:rights
  • In Copyright

Identifiers

dc:identifier.*
Dc Identifier Other
vt_gsexam:4457
OAI identifier oai:identifier
oai:vtechworks.lib.vt.edu:10919/51263

Chain of custody

source
Harvested from
Virginia Tech
Base URL
vtechworks.lib.vt.edu/oai/request
Last updated
2026-07-22
Source record
OAI-PMH GetRecord
citation

Gregory, Jessica G.. A Rate of Convergence for Learning Theory with Consensus. masters thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/51263