1,412 research outputs found
Detection of abrupt changes in dynamic systems
Some of the basic ideas associated with the detection of abrupt changes in dynamic systems are presented. Multiple filter-based techniques and residual-based method and the multiple model and generalized likelihood ratio methods are considered. Issues such as the effect of unknown onset time on algorithm complexity and structure and robustness to model uncertainty are discussed
A survey of design methods for failure detection in dynamic systems
A number of methods for the detection of abrupt changes (such as failures) in stochastic dynamical systems were surveyed. The class of linear systems were emphasized, but the basic concepts, if not the detailed analyses, carry over to other classes of systems. The methods surveyed range from the design of specific failure-sensitive filters, to the use of statistical tests on filter innovations, to the development of jump process formulations. Tradeoffs in complexity versus performance are discussed
Bayesian Nonparametric Hidden Semi-Markov Models
There is much interest in the Hierarchical Dirichlet Process Hidden Markov
Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous
Hidden Markov Model for learning from sequential and time-series data. However,
in many settings the HDP-HMM's strict Markovian constraints are undesirable,
particularly if we wish to learn or encode non-geometric state durations. We
can extend the HDP-HMM to capture such structure by drawing upon
explicit-duration semi-Markovianity, which has been developed mainly in the
parametric frequentist setting, to allow construction of highly interpretable
models that admit natural prior information on state durations.
In this paper we introduce the explicit-duration Hierarchical Dirichlet
Process Hidden semi-Markov Model (HDP-HSMM) and develop sampling algorithms for
efficient posterior inference. The methods we introduce also provide new
methods for sampling inference in the finite Bayesian HSMM. Our modular Gibbs
sampling methods can be embedded in samplers for larger hierarchical Bayesian
models, adding semi-Markov chain modeling as another tool in the Bayesian
inference toolbox. We demonstrate the utility of the HDP-HSMM and our inference
methods on both synthetic and real experiments
Dirichlet Posterior Sampling with Truncated Multinomial Likelihoods
We consider the problem of drawing samples from posterior distributions
formed under a Dirichlet prior and a truncated multinomial likelihood, by which
we mean a Multinomial likelihood function where we condition on one or more
counts being zero a priori. Sampling this posterior distribution is of interest
in inference algorithms for hierarchical Bayesian models based on the Dirichlet
distribution or the Dirichlet process, particularly Gibbs sampling algorithms
for the Hierarchical Dirichlet Process Hidden Semi-Markov Model. We provide a
data augmentation sampling algorithm that is easy to implement, fast both to
mix and to execute, and easily scalable to many dimensions. We demonstrate the
algorithm's advantages over a generic Metropolis-Hastings sampling algorithm in
several numerical experiments
Sequential Compressed Sensing
Compressed sensing allows perfect recovery of sparse signals (or signals
sparse in some basis) using only a small number of random measurements.
Existing results in compressed sensing literature have focused on
characterizing the achievable performance by bounding the number of samples
required for a given level of signal sparsity. However, using these bounds to
minimize the number of samples requires a-priori knowledge of the sparsity of
the unknown signal, or the decay structure for near-sparse signals.
Furthermore, there are some popular recovery methods for which no such bounds
are known.
In this paper, we investigate an alternative scenario where observations are
available in sequence. For any recovery method, this means that there is now a
sequence of candidate reconstructions. We propose a method to estimate the
reconstruction error directly from the samples themselves, for every candidate
in this sequence. This estimate is universal in the sense that it is based only
on the measurement ensemble, and not on the recovery method or any assumed
level of sparsity of the unknown signal. With these estimates, one can now stop
observations as soon as there is reasonable certainty of either exact or
sufficiently accurate reconstruction. They also provide a way to obtain
"run-time" guarantees for recovery methods that otherwise lack a-priori
performance bounds.
We investigate both continuous (e.g. Gaussian) and discrete (e.g. Bernoulli)
random measurement ensembles, both for exactly sparse and general near-sparse
signals, and with both noisy and noiseless measurements.Comment: to appear in IEEE transactions on Special Topics in Signal Processin
Learning Gaussian Graphical Models with Observed or Latent FVSs
Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely
used in many applications, and the trade-off between the modeling capacity and
the efficiency of learning and inference has been an important research
problem. In this paper, we study the family of GGMs with small feedback vertex
sets (FVSs), where an FVS is a set of nodes whose removal breaks all the
cycles. Exact inference such as computing the marginal distributions and the
partition function has complexity using message-passing algorithms,
where k is the size of the FVS, and n is the total number of nodes. We propose
efficient structure learning algorithms for two cases: 1) All nodes are
observed, which is useful in modeling social or flight networks where the FVS
nodes often correspond to a small number of high-degree nodes, or hubs, while
the rest of the networks is modeled by a tree. Regardless of the maximum
degree, without knowing the full graph structure, we can exactly compute the
maximum likelihood estimate in if the FVS is known or in
polynomial time if the FVS is unknown but has bounded size. 2) The FVS nodes
are latent variables, where structure learning is equivalent to decomposing a
inverse covariance matrix (exactly or approximately) into the sum of a
tree-structured matrix and a low-rank matrix. By incorporating efficient
inference into the learning steps, we can obtain a learning algorithm using
alternating low-rank correction with complexity per
iteration. We also perform experiments using both synthetic data as well as
real data of flight delays to demonstrate the modeling capacity with FVSs of
various sizes
Control optimization, stabilization and computer algorithms for aircraft applications
The analysis and design of complex multivariable reliable control systems are considered. High performance and fault tolerant aircraft systems are the objectives. A preliminary feasibility study of the design of a lateral control system for a VTOL aircraft that is to land on a DD963 class destroyer under high sea state conditions is provided. Progress in the following areas is summarized: (1) VTOL control system design studies; (2) robust multivariable control system synthesis; (3) adaptive control systems; (4) failure detection algorithms; and (5) fault tolerant optimal control theory
Estimation for bilinear stochastic systems
Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed
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