422 research outputs found
Inferring hidden states in Langevin dynamics on large networks: Average case performance
We present average performance results for dynamical inference problems in
large networks, where a set of nodes is hidden while the time trajectories of
the others are observed. Examples of this scenario can occur in signal
transduction and gene regulation networks. We focus on the linear stochastic
dynamics of continuous variables interacting via random Gaussian couplings of
generic symmetry. We analyze the inference error, given by the variance of the
posterior distribution over hidden paths, in the thermodynamic limit and as a
function of the system parameters and the ratio {\alpha} between the number of
hidden and observed nodes. By applying Kalman filter recursions we find that
the posterior dynamics is governed by an "effective" drift that incorporates
the effect of the observations. We present two approaches for characterizing
the posterior variance that allow us to tackle, respectively, equilibrium and
nonequilibrium dynamics. The first appeals to Random Matrix Theory and reveals
average spectral properties of the inference error and typical posterior
relaxation times, the second is based on dynamical functionals and yields the
inference error as the solution of an algebraic equation.Comment: 20 pages, 5 figure
Adaptive Evolutionary Clustering
In many practical applications of clustering, the objects to be clustered
evolve over time, and a clustering result is desired at each time step. In such
applications, evolutionary clustering typically outperforms traditional static
clustering by producing clustering results that reflect long-term trends while
being robust to short-term variations. Several evolutionary clustering
algorithms have recently been proposed, often by adding a temporal smoothness
penalty to the cost function of a static clustering method. In this paper, we
introduce a different approach to evolutionary clustering by accurately
tracking the time-varying proximities between objects followed by static
clustering. We present an evolutionary clustering framework that adaptively
estimates the optimal smoothing parameter using shrinkage estimation, a
statistical approach that improves a naive estimate using additional
information. The proposed framework can be used to extend a variety of static
clustering algorithms, including hierarchical, k-means, and spectral
clustering, into evolutionary clustering algorithms. Experiments on synthetic
and real data sets indicate that the proposed framework outperforms static
clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox
available at http://tbayes.eecs.umich.edu/xukevin/affec
Recursive neuro fuzzy techniques for online identification and control
Dissertação para obtenção do Grau de Mestre em
Engenharia Electrotécnica e de ComputadoresThe main goal of this thesis will be focused on developing an adaptative closed loop
control solution, using fuzzy methodologies. A positive theoretical and experimental
contribution, regarding modelling and control of fuzzy and neuro fuzzy systems, is expected
to be achieved.
Proposed non-linear identification solution will use for modelling and control, a recurrent
neuro fuzzy architecture. Regarding model solution, a state space approach will be
considered during fuzzy consequent local models design. Developed controller will be
based on model parameters, being expected not only a stable closed loop solution, but
also a static error with convergence towards zero. Model and controller fuzzy subspaces,
will be partitioned throughout process dynamical universe, allowing fuzzy local models
and controllers commutation and aggregation.
With the aim of capturing process under control dynamics using a real time approach,
the use of recursive optimization techniques are to be adopted. Such methods will be
applied during parameter and state estimation, using a dual decoupled Kalman filter extended
with unscented transformation.
Two distinct processes one single-input (SISO) other multi-input (MIMO), will be used
during experimentation. It is expected from experiments, a practical validation of proposed
solution capabilities for control and identification. Presented work will not be
completed, without first presenting a global analysis of adopted concepts and methods,
describing new perspectives for future investigations
Modeling and Estimation of Biological Plants
Estimating the state of a dynamic system is an essential task for achieving important objectives such as process monitoring, identification, and control. Unlike linear systems, no systematic method exists for the design of observers for nonlinear systems. Although many researchers have devoted their attention to these issues for more than 30 years, there are still many open questions. We envisage that estimation plays a crucial role in biology because of the possibility of creating new avenues for biological studies and for the development of diagnostic, management, and treatment tools. To this end, this thesis aims to address two types of nonlinear estimation techniques, namely, the high-gain observer and the moving-horizon estimator with application to three different biological plants.
After recalling basic definitions of stability and observability of dynamical systems and giving a bird's-eye survey of the available state estimation techniques, we are interested in the high-gain observers. These observers may be used when the system dynamics can be expressed in specific a coordinate under the so-called observability canonical form with the possibility to assign the rate of convergence arbitrarily by acting on a single parameter called the high-gain parameter. Despite the evident benefits of this class of observers, their use in real applications is questionable due to some drawbacks: numerical problems, the peaking phenomenon, and high sensitivity to measurement noise. The first part of the thesis aims to enrich the theory of high-gain observers with novel techniques to overcome or attenuate these challenging performance issues that arise when implementing such observers. The validity and applicability of our proposed techniques have been shown firstly on a simple one-gene regulatory network, and secondly on an SI epidemic model.
The second part of the thesis studies the problem of state estimation using the moving horizon approach. The main advantage of MHE is that information
about the system can be explicitly considered in the form of constraints
and hence improve the estimates. In this work, we focus on estimation for nonlinear plants that can be rewritten in the form of quasi-linear parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost with respect to both state variables and parameters simultaneously. In the latter, we minimize such a cost with respect to the state variables after picking up the maximum of the parameters. Under suitable assumptions, the stability of the estimation error given by the exponential boundedness is proved in both scenarios.
Finally, the validity of our obtained results has been demonstrated through three different examples from biological and biomedical fields, namely, an example of one gene regulatory network, a two-stage SI epidemic model, and Amnioserosa cell's mechanical behavior during Dorsal closure
Recommended from our members
Modern Statistical/Machine Learning Techniques for Bio/Neuro-imaging Applications
Developments in modern bio-imaging techniques have allowed the routine collection of a vast amount of data from various techniques. The challenges lie in how to build accurate and efficient models to draw conclusions from the data and facilitate scientific discoveries. Fortunately, recent advances in statistics, machine learning, and deep learning provide valuable tools. This thesis describes some of our efforts to build scalable Bayesian models for four bio-imaging applications: (1) Stochastic Optical Reconstruction Microscopy (STORM) Imaging, (2) particle tracking, (3) voltage smoothing, (4) detect color-labeled neurons in c elegans and assign identity to the detections
Challenges in Statistical Theory: Complex Data Structures and Algorithmic Optimization
Technological developments have created a constant incoming stream of complex new data structures that need analysis. Modern statistics therefore means mathematically sophisticated new statistical theory that generates or supports innovative data-analytic methodologies for complex data structures. Inherent in many of these methodologies are challenging numerical optimization methods. The proposed workshop intends to bring together experts from mathematical statistics as well as statisticians involved in serious modern applications and computing. The primary goal of this meeting was to advance the mathematical and methodological underpinnings of modern statistics for complex data. Particular focus was given to the advancement of theory and methods under non-stationarity and complex dependence structures including (multivariate) financial time series, scientific data analysis in neurosciences and bio-physics, estimation under shape constraints, and highdimensional discrimination/classification
Advanced sequential Monte Carlo methods and their applications to sparse sensor network for detection and estimation
The general state space models present a flexible framework for modeling dynamic systems and therefore have vast applications in many disciplines such as engineering, economics, biology, etc. However, optimal estimation problems of non-linear non-Gaussian state space models are analytically intractable in general. Sequential Monte Carlo (SMC) methods become a very popular class of simulation-based methods for the solution of optimal estimation problems. The advantages of SMC methods in comparison with classical filtering methods such as Kalman Filter and Extended Kalman Filter are that they are able to handle non-linear non-Gaussian scenarios without relying on any local linearization techniques. In this thesis, we present an advanced SMC method and the study of its asymptotic behavior. We apply the proposed SMC method in a target tracking problem using different observation models. Specifically, a distributed SMC algorithm is developed for a wireless sensor network (WSN) that incorporates with an informative-sensor detection technique. The novel SMC algorithm is designed to surmount the degeneracy problem by employing a multilevel Markov chain Monte Carlo (MCMC) procedure constructed by engaging drift homotopy and likelihood bridging techniques. The observations are gathered only from the informative sensors, which are sensing useful observations of the nearby moving targets. The detection of those informative sensors, which are typically a small portion of the WSN, is taking place by using a sparsity-aware matrix decomposition technique. Simulation results showcase that our algorithm outperforms current popular tracking algorithms such as bootstrap filter and auxiliary particle filter in many scenarios
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