Particle-based likelihood inference in partially observed diffusion processes using generalised Poisson estimators

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form expressions of the transition densities. Thus, in order to estimate efficiently the EM intermediate quantity we construct, using novel techniques for unbiased estimation of diffusion transition densities, a random weight fixed-lag auxiliary particle smoother, which avoids the well known problem of particle trajectory degeneracy in the smoothing mode. The estimator is justified theoretically and demonstrated on a simulated example

Feature extraction from ear-worn sensor data for gait analysis

Gait analysis has a significant role in assessing human's walking pattern. It is generally used in sports science for understanding body mechanics, and it is also used to monitor patients' neuro-disorder related gait abnormalities. Traditional marker-based systems are well known for tracking gait parameters for gait analysis, however, it requires long set up time therefore very difficult to be applied in everyday realtime monitoring. Nowadays, there is ever growing of interest in developing portable devices and their supporting software with novel algorithms for gait pattern analysis. The aim of this research is to investigate the possibilities of novel gait pattern detection algorithms for accelerometer-based sensors. In particular, we have used e-AR sensor, an ear-worn sensor which registers body motion via its embedded 3-D accelerom-eter. Gait data was given semantic annotation using pressure mat as well as real-time video recording. Important time stamps within a gait cycle, which are essential for extracting meaningful gait parameters, were identified. Furthermore, advanced signal processing algorithm was applied to perform automatic feature extraction by signal decomposition and reconstruction. Analysis on real-word data has demonstrated the potential for an accelerometer-based sensor system and its ability to extract of meaningful gait parameters

Bayesian emulation for optimization in multi-step portfolio decisions

We discuss the Bayesian emulation approach to computational solution of multi-step portfolio studies in financial time series. "Bayesian emulation for decisions" involves mapping the technical structure of a decision analysis problem to that of Bayesian inference in a purely synthetic "emulating" statistical model. This provides access to standard posterior analytic, simulation and optimization methods that yield indirect solutions of the decision problem. We develop this in time series portfolio analysis using classes of economically and psychologically relevant multi-step ahead portfolio utility functions. Studies with multivariate currency, commodity and stock index time series illustrate the approach and show some of the practical utility and benefits of the Bayesian emulation methodology.Comment: 24 pages, 7 figures, 2 table

Kernel methods for detecting coherent structures in dynamical data

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted in terms of kernel transfer operators and that it can be obtained by optimizing the variational approach for Markov processes (VAMP) score. As a result, we show that coherent sets of particle trajectories can be computed by kernel CCA. We demonstrate the efficiency of this approach with several examples, namely the well-known Bickley jet, ocean drifter data, and a molecular dynamics problem with a time-dependent potential. Finally, we propose a straightforward generalization of dynamic mode decomposition (DMD) called coherent mode decomposition (CMD). Our results provide a generic machine learning approach to the computation of coherent sets with an objective score that can be used for cross-validation and the comparison of different methods

Estimation of muscular forces from SSA smoothed sEMG signals calibrated by inverse dynamics-based physiological static optimization

The estimation of muscular forces is useful in several areas such as biomedical or rehabilitation engineering. As muscular forces cannot be measured in vivo non-invasively they must be estimated by using indirect measurements such as surface electromyography (sEMG) signals or by means of inverse dynamic (ID) analyses. This paper proposes an approach to estimate muscular forces based on both of them. The main idea is to tune a gain matrix so as to compute muscular forces from sEMG signals. To do so, a curve fitting process based on least-squares is carried out. The input is the sEMG signal filtered using singular spectrum analysis technique. The output corresponds to the muscular force estimated by the ID analysis of the recorded task, a dumbbell weightlifting. Once the model parameters are tuned, it is possible to obtain an estimation of muscular forces based on sEMG signal. This procedure might be used to predict muscular forces in vivo outside the space limitations of the gait analysis laboratory.Postprint (published version

On the auxiliary particle filter

In this article we study asymptotic properties of weighted samples produced by the auxiliary particle filter (APF) proposed by pitt and shephard (1999). Besides establishing a central limit theorem (CLT) for smoothed particle estimates, we also derive bounds on the Lp error and bias of the same for a finite particle sample size. By examining the recursive formula for the asymptotic variance of the CLT we identify first-stage importance weights for which the increase of asymptotic variance at a single iteration of the algorithm is minimal. In the light of these findings, we discuss and demonstrate on several examples how the APF algorithm can be improved.Comment: 26 page

A critical review of online battery remaining useful lifetime prediction methods.

Lithium-ion batteries play an important role in our daily lives. The prediction of the remaining service life of lithium-ion batteries has become an important issue. This article reviews the methods for predicting the remaining service life of lithium-ion batteries from three aspects: machine learning, adaptive filtering, and random processes. The purpose of this study is to review, classify and compare different methods proposed in the literature to predict the remaining service life of lithium-ion batteries. This article first summarizes and classifies various methods for predicting the remaining service life of lithium-ion batteries that have been proposed in recent years. On this basis, by selecting specific criteria to evaluate and compare the accuracy of different models, find the most suitable method. Finally, summarize the development of various methods. According to the research in this article, the average accuracy of machine learning is 32.02% higher than the average of the other two methods, and the prediction cycle is 9.87% shorter than the average of the other two methods

Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics

A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This ensures eigenvalues with unit norm and thus stable dynamics and training. However this comes at the cost of reduced expressivity due to the limited variety of orthogonal transformations. We propose a novel connectivity structure based on the Schur decomposition and a splitting of the Schur form into normal and non-normal parts. This allows to parametrize matrices with unit-norm eigenspectra without orthogonality constraints on eigenbases. The resulting architecture ensures access to a larger space of spectrally constrained matrices, of which orthogonal matrices are a subset. This crucial difference retains the stability advantages and training speed of orthogonal RNNs while enhancing expressivity, especially on tasks that require computations over ongoing input sequences