17,800 research outputs found
Smoothing Dynamic Systems with State-Dependent Covariance Matrices
Kalman filtering and smoothing algorithms are used in many areas, including
tracking and navigation, medical applications, and financial trend filtering.
One of the basic assumptions required to apply the Kalman smoothing framework
is that error covariance matrices are known and given. In this paper, we study
a general class of inference problems where covariance matrices can depend
functionally on unknown parameters. In the Kalman framework, this allows
modeling situations where covariance matrices may depend functionally on the
state sequence being estimated. We present an extended formulation and
generalized Gauss-Newton (GGN) algorithm for inference in this context. When
applied to dynamic systems inference, we show the algorithm can be implemented
to preserve the computational efficiency of the classic Kalman smoother. The
new approach is illustrated with a synthetic numerical example.Comment: 8 pages, 1 figur
Bibliographic Review on Distributed Kalman Filtering
In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud
The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area
A Unifying review of linear gaussian models
Factor analysis, principal component analysis, mixtures of gaussian clusters, vector quantization, Kalman filter models, and hidden Markov models can all be unified as variations of unsupervised learning under a single basic generative model. This is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity. Through the use of other nonlinearities, we show how independent component analysis is also a variation of the same basic generative model.We show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term. We introduce a new model for static data, known as sensible principal component analysis, as well as a novel concept of spatially adaptive observation noise. We also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models
A 4D-Var Method with Flow-Dependent Background Covariances for the Shallow-Water Equations
The 4D-Var method for filtering partially observed nonlinear chaotic
dynamical systems consists of finding the maximum a-posteriori (MAP) estimator
of the initial condition of the system given observations over a time window,
and propagating it forward to the current time via the model dynamics. This
method forms the basis of most currently operational weather forecasting
systems. In practice the optimization becomes infeasible if the time window is
too long due to the non-convexity of the cost function, the effect of model
errors, and the limited precision of the ODE solvers. Hence the window has to
be kept sufficiently short, and the observations in the previous windows can be
taken into account via a Gaussian background (prior) distribution. The choice
of the background covariance matrix is an important question that has received
much attention in the literature. In this paper, we define the background
covariances in a principled manner, based on observations in the previous
assimilation windows, for a parameter . The method is at most times
more computationally expensive than using fixed background covariances,
requires little tuning, and greatly improves the accuracy of 4D-Var. As a
concrete example, we focus on the shallow-water equations. The proposed method
is compared against state-of-the-art approaches in data assimilation and is
shown to perform favourably on simulated data. We also illustrate our approach
on data from the recent tsunami of 2011 in Fukushima, Japan.Comment: 32 pages, 5 figure
Network estimation in State Space Model with L1-regularization constraint
Biological networks have arisen as an attractive paradigm of genomic science
ever since the introduction of large scale genomic technologies which carried
the promise of elucidating the relationship in functional genomics. Microarray
technologies coupled with appropriate mathematical or statistical models have
made it possible to identify dynamic regulatory networks or to measure time
course of the expression level of many genes simultaneously. However one of the
few limitations fall on the high-dimensional nature of such data coupled with
the fact that these gene expression data are known to include some hidden
process. In that regards, we are concerned with deriving a method for inferring
a sparse dynamic network in a high dimensional data setting. We assume that the
observations are noisy measurements of gene expression in the form of mRNAs,
whose dynamics can be described by some unknown or hidden process. We build an
input-dependent linear state space model from these hidden states and
demonstrate how an incorporated regularization constraint in an
Expectation-Maximization (EM) algorithm can be used to reverse engineer
transcriptional networks from gene expression profiling data. This corresponds
to estimating the model interaction parameters. The proposed method is
illustrated on time-course microarray data obtained from a well established
T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4,
CASP4, CD69, and C3X1 to have higher number of inwards directed connections and
FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed
connections. We recommend these genes to be object for further investigation.
Caspase 4 is also found to activate the expression of JunD which in turn
represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359
Estimating effective connectivity in linear brain network models
Contemporary neuroscience has embraced network science to study the complex
and self-organized structure of the human brain; one of the main outstanding
issues is that of inferring from measure data, chiefly functional Magnetic
Resonance Imaging (fMRI), the so-called effective connectivity in brain
networks, that is the existing interactions among neuronal populations. This
inverse problem is complicated by the fact that the BOLD (Blood Oxygenation
Level Dependent) signal measured by fMRI represent a dynamic and nonlinear
transformation (the hemodynamic response) of neuronal activity. In this paper,
we consider resting state (rs) fMRI data; building upon a linear population
model of the BOLD signal and a stochastic linear DCM model, the model
parameters are estimated through an EM-type iterative procedure, which
alternately estimates the neuronal activity by means of the Rauch-Tung-Striebel
(RTS) smoother, updates the connections among neuronal states and refines the
parameters of the hemodynamic model; sparsity in the interconnection structure
is favoured using an iteratively reweighting scheme. Experimental results using
rs-fMRI data are shown demonstrating the effectiveness of our approach and
comparison with state of the art routines (SPM12 toolbox) is provided
Factorial graphical lasso for dynamic networks
Dynamic networks models describe a growing number of important scientific
processes, from cell biology and epidemiology to sociology and finance. There
are many aspects of dynamical networks that require statistical considerations.
In this paper we focus on determining network structure. Estimating dynamic
networks is a difficult task since the number of components involved in the
system is very large. As a result, the number of parameters to be estimated is
bigger than the number of observations. However, a characteristic of many
networks is that they are sparse. For example, the molecular structure of genes
make interactions with other components a highly-structured and therefore
sparse process.
Penalized Gaussian graphical models have been used to estimate sparse
networks. However, the literature has focussed on static networks, which lack
specific temporal constraints. We propose a structured Gaussian dynamical
graphical model, where structures can consist of specific time dynamics, known
presence or absence of links and block equality constraints on the parameters.
Thus, the number of parameters to be estimated is reduced and accuracy of the
estimates, including the identification of the network, can be tuned up. Here,
we show that the constrained optimization problem can be solved by taking
advantage of an efficient solver, logdetPPA, developed in convex optimization.
Moreover, model selection methods for checking the sensitivity of the inferred
networks are described. Finally, synthetic and real data illustrate the
proposed methodologies.Comment: 30 pp, 5 figure
On optimal and suboptimal linear smoothing
Orthogonality principle and covariance equations for optimal and suboptimal linear smoothin
Semiparametric Approaches to the Prediction of Conditional Correlation Matrices in Finance
We consider the problem of ex-ante forecasting conditional correlation patterns using ultra high frequency data. Flexible semiparametric predictors referring to the class of dynamic panel and dynamic factor models are adopted for daily forecasts. The parsimonious set up of our approach allows to forecast correlations exploiting both estimated realized correlation matrices and exogenous factors. The Fisher-z transformation guarantees robustness of correlation estimators under elliptically constrained departures from normality. For the purpose of performance comparison we contrast our methodology with prominent parametric and nonparametric alternatives to correlation modeling. Based on economic performance criteria, we distinguish dynamic factor models as having the highest predictive content. --Correlation forecasting,Epps effect,Fourier method,Dynamic panel model,Dynamic factor model
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