Aerospace Control Laboratory
http://hdl.handle.net/1721.1/37332
2014-11-21T02:37:12ZLearning Sparse Gaussian Graphical Model with l0-regularization
http://hdl.handle.net/1721.1/88969
Learning Sparse Gaussian Graphical Model with l0-regularization
Mu, Beipeng; How, Jonathan
For the problem of learning sparse Gaussian graphical models, it is desirable to obtain both sparse structures as well as good parameter estimates. Classical techniques, such as optimizing the l1-regularized maximum likelihood or Chow-Liu algorithm, either focus on parameter estimation or constrain to speci c structure. This paper proposes an alternative that is based on l0-regularized maximum likelihood and employs a greedy algorithm to solve the optimization problem. We show that, when the graph is acyclic, the greedy solution finds the optimal acyclic graph. We also show it can update the parameters in constant time when connecting two sub-components, thus work efficiently on sparse graphs. Empirical results are provided to demonstrate this new algorithm can learn sparse structures with cycles efficiently and that it dominates l1-regularized approach on graph likelihood.
2014-08-22T00:00:00ZSupplementary material for nonparameteric adaptive control of time varying systems using gaussian processes
http://hdl.handle.net/1721.1/77933
Supplementary material for nonparameteric adaptive control of time varying systems using gaussian processes
Chowdhary, Girish; Kingravi, Hassan A.; How, Jonathan P.; Vela, Patricio A.
Real-world dynamical variations make adaptive control of time-varying systems highly relevant. However, most adaptive control literature focuses on analyzing systems where the uncertainty is represented as a weighted linear combination of fixed number of basis functions, with constant weights. One approach to modeling time variations is to assume time varying ideal weights, and use difference integration to accommodate weight variation. However, this approach reactively suppresses the uncertainty, and has little ability to predict system behavior locally. We present an alternate formulation by leveraging Bayesian nonparametric Gaussian Process adaptive elements. We show that almost surely bounded adaptive controllers for a class of nonlinear time varying system can be formulated by incorporating time as an additional input to the Gaussian kernel. Analysis and simulations show that the learning-enabled local predictive ability of our adaptive controllers significantly improves performance.
This technical report has supplementary material for "Bayesian Nonparametric Adaptive Control of Time-varying Systems using Gaussian Processes" American Control Conference paper
2013-03-15T00:00:00ZBayesian Nonparametric Adaptive Control using Gaussian Processes
http://hdl.handle.net/1721.1/77931
Bayesian Nonparametric Adaptive Control using Gaussian Processes
Chowdhary, Girish; Kingravi, Hassan A.; How, Jonathan P.; Vela, Patricio A.
Most current Model Reference Adaptive Control
(MRAC) methods rely on parametric adaptive elements, in
which the number of parameters of the adaptive element are
fixed a priori, often through expert judgment. An example of
such an adaptive element are Radial Basis Function Networks
(RBFNs), with RBF centers pre-allocated based on the expected
operating domain. If the system operates outside of the expected
operating domain, this adaptive element can become
non-effective in capturing and canceling the uncertainty, thus
rendering the adaptive controller only semi-global in nature.
This paper investigates a Gaussian Process (GP) based Bayesian
MRAC architecture (GP-MRAC), which leverages the power and
flexibility of GP Bayesian nonparametric models of uncertainty.
GP-MRAC does not require the centers to be preallocated, can
inherently handle measurement noise, and enables MRAC to
handle a broader set of uncertainties, including those that are
defined as distributions over functions. We use stochastic stability
arguments to show that GP-MRAC guarantees good closed loop
performance with no prior domain knowledge of the uncertainty.
Online implementable GP inference methods are compared in
numerical simulations against RBFN-MRAC with preallocated
centers and are shown to provide better tracking and improved
long-term learning.
This technical report is a preprint of an article submitted to a journal.
2013-03-15T00:00:00ZEfficient Distributed Sensing Using Adaptive Censoring-Based Inference
http://hdl.handle.net/1721.1/77915
Efficient Distributed Sensing Using Adaptive Censoring-Based Inference
Mu, Beipeng; Chowdhary, Girish; How, Jonathan P.
In many distributed sensing applications it is likely that only a few agents will have valuable information at any given time. Since
wireless communication between agents is resource-intensive, it is important to ensure that the communication effort is focused on
communicating valuable information from informative agents. This paper presents communication efficient distributed sensing algorithms
that avoid network cluttering by having only agents with high Value of Information (VoI) broadcast their measurements to the network,
while others censor themselves. A novel contribution of the presented distributed estimation algorithm is the use of an adaptively adjusted
VoI threshold to determine which agents are informative. This adaptation enables the team to better balance between the communication
cost incurred and the long-term accuracy of the estimation. Theoretical results are presented establishing the almost sure convergence of
the communication cost and estimation error to zero for distributions in the exponential family. Furthermore, validation through numerical
simulations and real datasets show that the new VoI-based algorithms can yield improved parameter estimates than those achieved by
previously published hyperparameter consensus algorithms while incurring only a fraction of the communication cost.
This technical report is a preprint of work submitted to a journal.
2013-03-15T00:00:00Z