Abstract
dc:description.abstractThis 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 × 5Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- vt_gsexam:4457
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/51263