Forward modeling and inverse estimation for nonlinear filtering

Annealed cooperative–competitive learning of Mahalanobis-NRBF neural modules for nonlinear and chaotic differential function approximation

Prediction of jet impingement solar thermal air collector thermohydraulic performance using soft computing techniques

Given an orthonormal basis and a certain class X of vectors in a Hilbert space H, consider the following nonlinear approximation process: approach a vector $x\in X$ by keeping only its N largest coordinates, and let N go to infinity. In this paper, we study the accuracy of this process in the case where $H=L^2(I)$, and we use either the trigonometric system or a wavelet basis to expand this space. The class of function that we are interested in is described by a stochastic process. We focus on the case of "piecewise stationary processes" that describe functions which are smooth except at isolated points. We show that the nonlinear wavelet approximation is optimal in terms of mean square error and that this optimality is lost either by using the trigonometric system or by using any type of linear approximation method, i.e., keeping the N first coordinates. The main motivation of this work is the search for a suitable mathematical model to study the compression of images and of certain types of signals.

An extended model-based observer for state estimation in nonlinear hysteretic structural systems

Gaussian Process Metamodeling in Bayesian Value of Information Analysis: A Case of the Complex Health Economic Model for Breast Cancer Screening

Innovation by homologous recombination

The ensemble Kalman filter has become a popular data assimilation technique in the geosciences. However, little is known theoretically about its long term stability and accuracy. In this paper, we investigate the behavior of an ensemble Kalman--Bucy filter applied to continuous-time filtering problems. We derive mean field limiting equations as the ensemble size goes to infinity as well as uniform-in-time accuracy and stability results for finite ensemble sizes. The later results require that the process is fully observed and that the measurement noise is small. We also demonstrate that our ensemble Kalman--Bucy filter is consistent with the classic Kalman--Bucy filter for linear systems and Gaussian processes. We finally verify our theoretical findings for the Lorenz-63 system.

ObjectivesRecently, pattern recognition approaches have been used to classify patterns of brain activity elicited by sensory or cognitive processes. In the clinical context, these approaches have been mainly applied to classify groups of individuals based on structural magnetic resonance imaging (MRI) data. Only a few studies have applied similar methods to functional MRI (fMRI) data.MethodsWe used a novel analytic framework to examine the extent to which unipolar and bipolar depressed individuals differed on discrimination between patterns of neural activity for happy and neutral faces. We used data from 18 currently depressed individuals with bipolar I disorder (BD) and 18 currently depressed individuals with recurrent unipolar depression (UD), matched on depression severity, age, and illness duration, and 18 age- and gender ratio-matched healthy comparison subjects (HC). fMRI data were analyzed using a general linear model and Gaussian process classifiers.ResultsThe accuracy for discriminating between patterns of neural activity for happy versus neutral faces overall was lower in both patient groups relative to HC. The predictive probabilities for intense and mild happy faces were higher in HC than in BD, and for mild happy faces were higher in HC than UD (all p < 0.001). Interestingly, the predictive probability for intense happy faces was significantly higher in UD than BD (p = 0.03).ConclusionsThese results indicate that patterns of whole-brain neural activity to intense happy faces were significantly less distinct from those for neutral faces in BD than in either HC or UD. These findings indicate that pattern recognition approaches can be used to identify abnormal brain activity patterns in patient populations and have promising clinical utility as techniques that can help to discriminate between patients with different psychiatric illnesses.

We deal with an important problem in the field of anesthesiology known as automatic segmentation of nerve structures depicted in ultrasound images. This is important to aid the experts in anesthesiology, in order to carry out Peripheral Nerve Blocking (PNB). Ultrasound imaging has gained recent interest for performing PNB procedures since it offers a non-invasive visualization of the nerve and the anatomical structures around it. However, the location of these nerves in ultrasound images is a difficult task for the specialist due to the artifacts (i.e. speckle noise) that affect the intelligibility of a given image. In this paper, we present a probabilistic approach based on Simple Linear Iterative Clustering (SLIC-superpixels) and Gaussian processes for automatic segmentation of peripheral nerves. First, we use Graph cuts segmentation to define a region of interest (ROI). Such a ROI is divided into several correlated regions using SLIC-superpixels, then, a nonlinear Wavelet transform is applied as feature extraction stage. Finally, we use a classification scheme based on Gaussian Processes in order to predict the label of each parametrized superpixel (the label can be "nerve" or "background"). The accuracy of the proposed method is measured in terms of the Dice coefficient. Results obtained show performances with a Dice coefficient of 0.6524±0.0085 which brings accurate performances in nerve segmentation processes.

Geophysical Inverse Theory and Regularization Problems

Earth observation from satellite sensory data pose challenging problems, where machine learning is currently a key player. In recent years, Gaussian Process (GP) regression and other kernel methods have excelled in biophysical parameter estimation tasks from space. GP regression is based on solid Bayesian statistics, and generally yield efficient and accurate parameter estimates. However, GPs are typically used for inverse modeling based on concurrent observations and in situ measurements only. Very often a forward model encoding the well-understood physical relations is available though. In this work, we review three GP models that respect and learn the physics of the underlying processes in the context of inverse modeling. First, we will introduce a Joint GP (JGP) model that combines in situ measurements and simulated data in a single GP model. Second, we present a latent force model (LFM) for GP modeling that encodes ordinary differential equations to blend data-driven modeling and physical models of the system. The LFM performs multi-output regression, adapts to the signal characteristics, is able to cope with missing data in the time series, and provides explicit latent functions that allow system analysis and evaluation. Finally, we present an Automatic Gaussian Process Emulator (AGAPE) that approximates the forward physical model via interpolation, reducing the number of necessary nodes. Empirical evidence of the performance of these models will be presented through illustrative examples of vegetation monitoring and atmospheric modeling.

In this paper, a novel methodology is proposed to solve the state estimation problem combining the extended Kalman filter (EKF) with a kernel recursive least squares (KRLS) algorithm (EKF-KRLS). The EKF algorithm estimates hidden states in the input space, while the KRLS algorithm estimates the measurement model. The algorithm works well without knowing the linear or nonlinear measurement model. We apply this algorithm to vehicle tracking, and compare the performances with traditional Kalman filter, EKF and KRLS algorithms. Results demonstrate that the performance of the EKF-KRLS algorithm outperforms these existing algorithms. Especially when nonlinear measurement functions are applied, the advantage of the EKF-KRLS algorithm is very obvious.

A multiple conversion approach (MCA) to nonlinear estimation is proposed in this paper. It jointly considers multiple hypotheses on the joint distribution of the quantity to be estimated and its measurement. The overall MCA estimate is a probabilistically weighted sum of the hypothesis conditional estimates. To describe the hypothesized joint distributions used to match the truth, a general distribution form characterized by a (linear or nonlinear) measurement conversion is found. This form is more general than Gaussian and includes Gaussian as a special case. Moreover, the minimum mean square error (MMSE) optimal estimate, given a hypothesized distribution in this form, is simply the linear MMSE (LMMSE) estimate using the converted measurement. LMMSE-based estimators, including the original LMMSE estimator and its generalization—the recently proposed uncorrelated conversion based filter—can all be incorporated into the MCA framework. Given a nonlinear problem, a specific form of the hypothesized distribution can be optimally obtained by quadratic programming using the information in the nonlinear measurement function and the measurement conversion. Then, the MCA estimate can be obtained easily. For dynamic problems, an interacting multiple conversion algorithm is proposed for recursive estimation. The MCA approach has a simple and flexible structure and takes advantage of multiple LMMSE-based nonlinear estimators. The overall estimates are obtained adaptively depending on the performance of the candidate estimators. Simulation results demonstrate the effectiveness of the proposed approach compared with other nonlinear filters.

In this paper, a neural network architecture for non-linear function approximation is proposed. We point out problems in non-linear function approximation with traditional neural networks, that is, difficulty in analyzing internal representation, no reproducibility in function approximation due to the random scheme for weight initialization, and the insufficient generalization ability in learning without enough samples. Based on these considerations, we suggest three main improvements. The first is the design of a sigmoidal function with localized derivative. The second is a deterministic scheme for weight initialization. The third is an updating rule for weight parameters. Simulation results show beneficial characteristics of our proposed method; low approximation error at the beginning of iterative calculation, smooth convergence of error and its improvement for difficulty in analyzing internal representation.

Statistical signal extraction using stable processes