Gaussian Process Framework Research Articles

Towards a Complete 3D Morphable Model of the Human Head

Three-dimensional morphable models (3DMMs) are powerful statistical tools for representing the 3D shapes and textures of an object class. Here we present the most complete 3DMM of the human head to date that includes face, cranium, ears, eyes, teeth and tongue. To achieve this, we propose two methods for combining existing 3DMMs of different overlapping head parts: (i). use a regressor to complete missing parts of one model using the other, and (ii). use the Gaussian Process framework to blend covariance matrices from multiple models. Thus, we build a new combined face-and-head shape model that blends the variability and facial detail of an existing face model (the LSFM) with the full head modelling capability of an existing head model (the LYHM). Then we construct and fuse a highly-detailed ear model to extend the variation of the ear shape. Eye and eye region models are incorporated into the head model, along with basic models of the teeth, tongue and inner mouth cavity. The new model achieves state-of-the-art performance. We use our model to reconstruct full head representations from single, unconstrained images allowing us to parameterize craniofacial shape and texture, along with the ear shape, eye gaze and eye color.

Data-driven nonparametric Li-ion battery ageing model aiming at learning from real operation data – Part A: Storage operation

• A calendar ageing model is developed under the Gaussian process framework. • A new covariance function is composed, tailored to Li-ion battery ageing prediction. • Especial emphasis on the ability of the model to learn from new data observations. • Sensitivity analysis of the model, and analysis of the uncertainty quantification. • Validation with 32 cells, for broad range of static and dynamic storage conditions. Conventional Li-ion battery ageing models, such as electrochemical, semi-empirical and empirical models, require a significant amount of time and experimental resources to provide accurate predictions under realistic operating conditions. At the same time, there is significant interest from industry in the introduction of new data collection telemetry technology. This implies the forthcoming availability of a significant amount of real-world battery operation data. In this context, the development of ageing models able to learn from in-field battery operation data is an interesting solution to mitigate the need for exhaustive laboratory testing. In a series of two papers, a data-driven ageing model is developed for Li-ion batteries under the Gaussian Process framework. A special emphasis is placed on illustrating the ability of the Gaussian Process model to learn from new data observations, providing more accurate and confident predictions, and extending the operating window of the model. This first paper focusses on the systematic modelling and experimental verification of cell degradation through calendar ageing. A specific covariance function is composed, tailored for use in a battery ageing application. Over an extensive dataset involving 32 cells tested during more than three years, different training possibilities are contemplated in order to quantify the minimal number of laboratory tests required for the design of an accurate ageing model. A model trained with only 18 tested cells achieves an overall mean-absolute-error of 0.53% in the capacity curves prediction, after being validated under a broad window of both dynamic and static temperature and SOC storage conditions.

Detection of Na, K, and H2O in the hazy atmosphere of WASP-6b

ABSTRACT We present new observations of the transmission spectrum of the hot Jupiter WASP-6b both from the ground with the Very Large Telescope FOcal Reducer and Spectrograph (FORS2) from 0.45 to 0.83 μm, and space with the Transiting Exoplanet Survey Satellite from 0.6 to 1.0 μm and the Hubble Space Telescope (HST) Wide Field Camera 3 from 1.12 to 1.65 μm. Archival data from the HST Space Telescope Imaging Spectrograph (STIS) and Spitzer are also re-analysed on a common Gaussian process framework, of which the STIS data show a good overall agreement with the overlapping FORS2 data. We also explore the effects of stellar heterogeneity on our observations and its resulting implications towards determining the atmospheric characteristics of WASP-6b. Independent of our assumptions for the level of stellar heterogeneity we detect Na i, K i, and H2O absorption features and constrain the elemental oxygen abundance to a value of [O/H] ≃ −0.9 ± 0.3 relative to solar. In contrast, we find that the stellar heterogeneity correction can have significant effects on the retrieved distributions of the [Na/H] and [K/H] abundances, primarily through its degeneracy with the sloping optical opacity of scattering haze species within the atmosphere. Our results also show that despite this presence of haze, WASP-6b remains a favourable object for future atmospheric characterization with upcoming missions such as the James Webb Space Telescope.

Stress-based topology optimization under uncertainty via simulation-based Gaussian process

Gaussian processes (GP) form a well-established predictive tool which provides a natural platform for tackling high-dimensional random input data in challenging simulations. This paper introduces a generic framework for integrating Gaussian Processes with risk-based structural optimization. We solve robust and reliability-based design problems in the context of stress-based topology optimization under imperfections in geometry and material properties, and loading variability. We construct independent GPs for primal and adjoint quantities, namely the global maximum von Mises stress and its sensitivity where we enhance the computational efficiency by leveraging the information from multiresolution finite element simulations. The GP framework naturally lends itself to modeling noise in data. We investigate the effect of numerical modeling error in high-fidelity simulations via a noisy GP emulator and provide a pareto curve that shows the robustness of optimal design with respect to the noise level. We provide a posteriori error estimates that quantify the discrepancy between the noisy emulator and true simulations, and verify them with a numerical study. We demonstrate our approach on a benchmark L-shape structure which exhibits stress concentration, a compliant mechanism design and a heat sink design. We also provide practical guidelines for estimation of failure probability and its sensitivity to facilitate reliability-based topology optimization.

Evolving control of human-exoskeleton system using Gaussian process with local model

Significant application breakthrough has not been achieved in human-exoskeleton systems due to the lack of transparent human-exoskeleton interaction. An evolving learning control strategy based on Gaussian process with local model (GPLM) is proposed to realize transparent control of a human-exoskeleton system. As a data driven technique, Gaussian process (GP) serves as a mathematical foundation to learn the dynamics of human lower limbs. Local model is incorporated into the GP framework to improve the prediction results and reduce the computation cost. The GPLM integrates the white-box model and block-box strategy and make use of their benefits. A knowledge base is developed to achieve evolving of the system structure and hyper-parameters. The proposed method can figure out the unspecific kinematics and dynamics of human-exoskeleton systems and cope with the emerging dynamics in new operation regions by system evolving. Surface electromyography (sEMG) signals are processed by a novel method, and are treated as one of the inputs of the model. The proposed sEMG signals processing method is expected to grasp the human muscle activation levels and improve the computational efficiency which can meet the requirements of real-time control. Experimental results show that the interactive force, human effort and interaction damping are reduced greatly compared with traditional force control. The proposed algorithm makes huge improvements on the transparent human-exoskeleton interaction by system evolving, while ensuring the safety of users by risk-based control.

Approximate GP Inference for Nonlinear Dynamical System Identification Using Data-Driven Basis Set

We address the problem of nonlinear dynamical system identification in state space formulation using an approximate Gaussian process (GP) regression framework where the basis for GP are learned from data. Approximate GP inference is used to address the high computational cost of exact GP frameworks, and is based on basis function expansion concept. We address the design of these basis functions using data and eigenvalue decomposition framework. The need for such design arises in practical applications where the collected data has outliers, discontinuities and other non-stationary characteristics which limit not only the applicability but also the performance of traditional GP framework with inherent stationary assumptions. Using the available data set, a kernel eigenvalue problem is formulated which is solved using Monte Carlo techniques to construct basis functions. Then, a low-rank approximation to the exact GP is obtained by an approach similar to kernel principle component analysis (k-PCA). The coefficients in the basis function expansion and other unknown parameters are learned from data using sequential Monte Carlo technique. The proposed GP framework for dynamical system identification is tested and validated against fixed basis framework using simulations and experimental data.

Spatiotemporal Multitask Learning for 3-D Dynamic Field Modeling

3-D dynamic field modeling using data acquired from sensor networks is typically complex due to the data sparsity and missing problem. In this article, we consider the ubiquitous missing data problem in current sensor networks and aim to take complete advantage of the existing sensor data for thermal field modeling. In the common scenario, data from the target network are not always obtainable, but data from other neighboring networks with homogeneous fields are accessible. Thus, a novel method that captures the information acquired from these neighboring networks is proposed. To achieve accurate thermal field estimation using limited sensor observations, we develop a mixed-effect model framework in which the dynamic field is decomposed into a mean profile and local variability. In particular, we establish a spatiotemporal field multitask learning (FML) approach to identify the spatiotemporal correlation by integrating a multitask Gaussian process (MGP) framework into an autoregressive (AR) model using neighboring data sources from homogeneous fields. Our proposed method is verified through a real case study of thermal field estimation during grain storage. Note to Practitioners —The proposed method aims to obtain an accurate estimation of a thermal field when certain sensor data are inaccessible. To better implement this method in practice, three things are noteworthy: First, the mean profile of the thermal field should be extracted using the thermodynamic model, so that the remaining data are able to follow a Gaussian process. Second, the FML approach considers neighboring data sources from homogeneous thermal fields to achieve an accurate estimation of the target thermal field. Thus, the target thermal field and other thermal fields should be under similar external conditions, e.g., environmental surroundings, geographical location, and field size. Third, the proposed method can not only process the data from grid-based sensor networks, but also can be extended to other topological structures of sensor networks for field estimation.

Radial velocity confirmation of K2-100b: a young, highly irradiated, and low-density transiting hot Neptune

ABSTRACT We present a detailed analysis of HARPS-N radial velocity observations of K2-100, a young and active star in the Praesepe cluster, which hosts a transiting planet with a period of 1.7 d. We model the activity-induced radial velocity variations of the host star with a multidimensional Gaussian Process framework and detect a planetary signal of 10.6 ± 3.0 ${\rm m\, s^{-1}}$, which matches the transit ephemeris, and translates to a planet mass of 21.8 ± 6.2 M⊕. We perform a suite of validation tests to confirm that our detected signal is genuine. This is the first mass measurement for a transiting planet in a young open cluster. The relatively low density of the planet, $2.04 _{ - 0.61 } ^ { + 0.66 }$ ${\rm g\, cm^{-3}}$, implies that K2-100b retains a significant volatile envelope. We estimate that the planet is losing its atmosphere at a rate of $10^{11}\!-\!10^{12}\, {\rm g\, s^{-1}}$ due to the high level of radiation it receives from its host star.

Optimally Balanced Gaussian Process Propensity Scores for Estimating Treatment Effects.

Propensity scores are commonly employed in observational study settings where the goal is to estimate average treatment effects. This paper introduces a flexible propensity score modeling approach, where the probability of treatment is modeled through a Gaussian process framework. To evaluate the effectiveness of the estimated propensity score, a metric of covariate imbalance is developed that quantifies the discrepancy between the distributions of covariates in the treated and control groups. It is demonstrated that this metric is ultimately a function of the hyperparameters of the covariance matrix of the Gaussian process and therefore it is possible to select the hyperparameters to optimize the metric and minimize overall covariate imbalance. The effectiveness of the GP method is compared in a simulation against other methods of estimating the propensity score and the method is applied to data from Dehejia and Wahba (1999) to demonstrate benchmark performance within a relevant policy application.

A Gaussian Process Framework for Overlap and Causal Effect Estimation with High-Dimensional Covariates

Abstract A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and revisits the standard assumptions made in causal inference. We show that by employing a flexible Gaussian process framework, the assumption of strict overlap leads to very restrictive assumptions about the distribution of covariates, results for which can be characterized using classical results from Gaussian random measures as well as reproducing kernel Hilbert space theory. In addition, we propose a strategy for data-adaptive causal effect estimation that does not rely on the strict overlap assumption. These findings reveal under a focused framework the stringency that accompanies the use of the treatment positivity assumption in high-dimensional settings.

Collective Online Learning of Gaussian Processes in Massive Multi-Agent Systems

This paper presents a novel Collective Online Learning of Gaussian Processes (COOL-GP) framework for enabling a massive number of GP inference agents to simultaneously perform (a) efficient online updates of their GP models using their local streaming data with varying correlation structures and (b) decentralized fusion of their resulting online GP models with different learned hyperparameter settings and inducing inputs. To realize this, we exploit the notion of a common encoding structure to encapsulate the local streaming data gathered by any GP inference agent into summary statistics based on our proposed representation, which is amenable to both an efficient online update via an importance sampling trick as well as multi-agent model fusion via decentralized message passing that can exploit sparse connectivity among agents for improving efficiency and enhance the robustness of our framework against transmission loss. We provide a rigorous theoretical analysis of the approximation loss arising from our proposed representation to achieve efficient online updates and model fusion. Empirical evaluations show that COOL-GP is highly effective in model fusion, resilient to information disparity between agents, robust to transmission loss, and can scale to thousands of agents.

A novel approach to computing super observations for probabilistic wave model validation

In the field of wave model validation, the use of super observations is a common strategy to smooth satellite observations and match the simulated spatiotemporal scales. An approach based on averaging along track is widely applied because it is straightforward to implement and adjustable. However, the choice of an appropriate length scale for obtaining the averages can be ambiguous, affecting subsequent analyses. Despite this dilemma, no uncertainty for the validation metric is provided when proceeding with wave model validation. We show that super observations computed from averaging data points applying an inappropriate length scale can lead to a misrepresentation of the wave field which can introduce errors into the wave model validation. Modelling the mean of observations as a Gaussian Process mitigates those errors and reliably identifies outliers by exploiting information hidden in the observational time series. Moreover, the uncertainty accompanying the validation statistic is readily accessible in the Gaussian Process framework. The flexibility of a Gaussian process makes it an attractive candidate for the probabilistic validation of wave models with steadily increasing horizontal resolution. Moreover, this approach can be applied to measurements from other platforms (e.g. buoys) and other variables (e.g. wind).

Wireless Traffic Prediction With Scalable Gaussian Process: Framework, Algorithms, and Verification

The cloud radio access network (C-RAN) is a promising paradigm to meet the stringent requirements of the fifth generation (5G) wireless systems. Meanwhile, wireless traffic prediction is a key enabler for C-RANs to improve both the spectrum efficiency and energy efficiency through load-aware network managements. This paper proposes a scalable Gaussian process (GP) framework as a promising solution to achieve large-scale wireless traffic prediction in a cost-efficient manner. Our contribution is three-fold. First, to the best of our knowledge, this paper is the first to empower GP regression with the alternating direction method of multipliers (ADMM) for parallel hyper-parameter optimization in the training phase, where such a scalable training framework well balances the local estimation in baseband units (BBUs) and information consensus among BBUs in a principled way for large-scale executions. Second, in the prediction phase, we fuse local predictions obtained from the BBUs via a cross-validation based optimal strategy, which demonstrates itself to be reliable and robust for general regression tasks. Moreover, such a cross-validation based optimal fusion strategy is built upon a well acknowledged probabilistic model to retain the valuable closed-form GP inference properties. Third, we propose a C-RAN based scalable wireless prediction architecture, where the prediction accuracy and the time consumption can be balanced by tuning the number of the BBUs according to the real-time system demands. Experimental results show that our proposed scalable GP model can outperform the state-of-the-art approaches considerably, in terms of wireless traffic prediction performance.

Recent Advances in Spatio‐Temporal Methodology

This special issue consists of a collection of articles that describe innovations in spatio-temporal methodology. Spatio-temporal statistics has been developing at a rapid pace over the past 25 years. The topic is briefly covered in Cressie's (1993) comprehensive book on spatial statistics. Subsequently, Cressie and Wikle (2011) provided the first comprehensive book on spatio-temporal statistics, but it focused primarily on linear, univariate, and Gaussian methods. More recently, there have been numerous significant advancements in non-linear, multivariate, and non-Gaussian spatio-temporal methods, particularly those suited for ‘big’ data problems. Yet, each of these topic areas is relatively underdeveloped, and there are still many research challenges. Historically, spatio-temporal statistics methodology has developed more as an extension of spatial statistics rather than time series. That is, the emphasis has been on specification of models through their second-order structure, typically within a Gaussian process framework. Alternatively, dynamic spatio-temporal models (DSTMs) have been used to model processes for which it is more realistic to think of spatial processes evolving through time, that is, when it is more reasonable to think of the process conditionally (in time) rather than marginally (as with the Gaussian process framework). DSTMs often have model forms as in classical multivariate time series models, but they present unique challenges in that the types of relationships between space and time are often driven by mechanistic processes, and the associated statistical models must attempt to accommodate these relationships. In addition, the dimensionality of the spatial components of these models often prohibits the use of classical multivariate time series methods. Although much of the development of spatio-temporal methodology has been driven by environmental, epidemiological, and ecological applications (e.g. pollution monitoring, weather forecasting, climate, oceanography, disease mapping, invasive species, animal movement, etc.), there is an increasing number of novel methodologies that are motivated by the biological sciences (e.g. brain science), federal statistics (e.g. multivariate surveys, non-Gaussian change of support), sociological statistics (e.g. crime analysis), and econometric (e.g. multivariate panel) applications. Indeed, these processes are often multivariate, non-linear, and/or non-Gaussian. The articles in this special issue provide a representative snapshot of innovative work in these areas. Specifically, the articles selected for this issue highlight non-Gaussian spatio-temporal models, computational efficiency, and/or improving parameterizations of DSTMs. In their article ‘Scalable Inference for Space-Time Gaussian Cox Processes’, Shirota and Banerjee show how one can use an efficient data augmentation approach in conjunction with nearest-neighbor log-Gaussian processes to efficiently model count (crime event) data via spatio-temporal Gaussian Cox processes. In ‘Estimating Spatial Changes Over Time of Artic Sea Ice Using Hidden 2 × 2 Tables’, Zhang and Cressie consider non-Gaussian (Bernoulli) data on the presence/absence of sea ice. The model is cast in an efficient manner by using dimension-reduced spatio-temporal processes in an EM algorithm, cleverly describing the process as time-varying 2 × 2 tables. Tagle, Castruccio, Crippa, and Genton, in their article ‘A Non-Gaussian Spatio-Temporal Model for Daily Wind Speeds Based on a Multivariate Skew-T Distribution’, show how to build an efficient and realistic ‘weather generator’ for daily wind speeds that is able to simulate the type of skewed distributions that are often found in weather variables. In their article ‘On a Semiparametric Data-Driven Nonlinear Model with Penalized Spatio-Temporal Lag Interactions’, Al-Sulami, Jiang, Lu, and Zhu consider a non-linear (semiparametric) regression spatio-temporal model that also includes a dynamic interaction term and consider an adaptive lasso approach for selecting the space–time lag interactions that are most useful (in their example, to model US housing price data). Their methodology does not rely on a Gaussian error assumption. In the spirit of efficient modeling of the spatio-temporal terms beyond a trend and seasonality, Gao and Tsay present an efficient structured factor approach for multivariate time series and spatio-temporal data (e.g. PM2.5 pollutant observations) in their article ‘A Structural-Factor Approach to Modeling High-Dimensional Time Series and Space-Time Data’. Finally, in their article ‘Spatio-Temporal Models for Big Multinomial Data Using the Conditional Multivariate Logit-Beta Distribution’, Bradley, Wikle and Holan develop a novel efficient conjugate Bayesian algorithm to model high-dimensional spatio-temporal multinomial data, which includes a spatio-temporal dynamic process. They apply this model to public-use Quarterly Workforce Indicators from the Longitudinal Employer Household Dynamics program of the US Census Bureau. These articles provide excellent examples of how spatio-temporal statistical models can be applied to address complex non-Gaussian, non-linear, and multivariate data with efficient computational algorithms. These problems are by no means ‘solved’, but it is our hope that the readers of the Journal of Time Series Analysis may see connections to their own work that can be applied to this rich set of problems and this growing and important area of statistics. Finally, we would like to end this Editorial by thanking Prof. A. M. R. Taylor for encouraging us to edit this special issue.

HADES RV program with HARPS-N at the TNG

Aims.The HArps-n red Dwarf Exoplanet Survey (HADES) is providing a major contribution to the widening of the current statistics of low-mass planets, through the in-depth analysis of precise radial-velocity (RV) measurements in a narrow range of spectral sub-types. Using the HARPS-N spectrograph we reach the precision needed to detect small planets with a few earth masses. Our survey is mainly focused on the M-dwarf population of the northern hemisphere.Methods.As part of that program, we obtained RV measurements of Gl 686, an M1 dwarf atd= 8.2 pc. These measurements show a dispersion much in excess of their internal errors. The analysis of data obtained within an intensive observing campaign demonstrates that the excess dispersion is due to a coherent signal with a period of 15.53 d. Almost simultaneous photometric observations were carried out within the APACHE and EXORAP programs to characterize the stellar activity and to distinguish periodic variations related to activity from signals due to the presence of planetary companions, complemented also with ASAS photometric data. We used a Bayesian framework to estimate the orbital parameters and the planet minimum mass, and to properly treat the activity noise. We took advantage of the available RV measurements for this target from other observing campaigns. The analysis of the RV composite time series from the HIRES, HARPS, and HARPS-N spectrographs, consisting of 198 measurements taken over 20 yr, enabled us to address the nature of periodic signals and also to characterize stellar physical parameters (mass, temperature, and rotation).Results.We report the discovery of a super-Earth orbiting at a distance of 0.092 AU from the host star Gl 686. The planet has a minimum mass of 7.1 ± 0.9M⊕and an orbital period of 15.532 ± 0.002 d. The analysis of the activity indexes, of the correlated noise through a Gaussian process framework, and of the photometry provides an estimate of the stellar rotation period at 37 d, and highlights the variability of the spot configuration during the long timespan covering 20 yr. The observed periodicities around 2000 d likely point to the existence of an activity cycle.

Hierarchical Facial Age Estimation Using Gaussian Process Regression

Automatic age estimation from facial images has attracted increasing attention due to its promising potential in real-life computer vision applications. However, due to uncontrollable environments, insufficient and incomplete training data, strong person-specific and large within- age span variations, age estimation has become a challenging problem. Among published age estimation, hierarchical age estimation methods have achieved comparable performance improvement than single level approaches. Most of the published hierarchical approaches have mainly used support vector machines to classify age groups followed by support vector regression for withina- age group age estimation. In this paper, we present a novel hierarchical Gaussian process framework for automatic age estimation. It consists of multi-class Gaussian process classifier to classify the input images into different age groups followed by a warped Gaussian process regression to model group specific aging patterns. In this paper, we separately tune the hyper-parameters for each age group at the regression stage. Compared with existing single level Gaussian process approaches for age estimation, our approach is computationally efficient at both the levels of hierarchy. Partitioning data into different age groups and learning group-wise hyper-parameters is computationally more efficient than learning complete training data. Misclassifications at the group boundaries are compensated at the regression stage by overlapping the neighboring age ranges. Finally, through extensive experiments on two popular aging datasets, the FG-NET and the Morph-II, we demonstrate the effectiveness of our algorithm in improving age estimation performance.

Efficient Transport Simulation With Restricted Batch-Mode Active Learning

Simulation modeling is a well-known and recurrent approach to study the performance of urban systems. Taking into account the recent and continuous transformations within increasingly complex and multidimensional cities, the use of simulation tools is, in many cases, the only feasible and reliable approach to analyze such dynamic systems. However, simulation models can become very time consuming when detailed input-space exploration is needed. To tackle this problem, simulation metamodels are often used to approximate the simulators’ results. In this paper, we propose an active learning algorithm based on the Gaussian process (GP) framework that gathers the most informative simulation data points in batches, according to both their predictive variances and to the relative distance between them. This allows us to explore the simulators’ input space with fewer data points and in parallel, and thus in a more efficient way, while avoiding computationally expensive simulation runs in the process. We take advantage of the closeness notion encoded into the GP to select batches of points in such a way that they do not belong to the same high-variance neighborhoods. In addition, we also suggest two simple and practical user-defined stopping criteria so that the iterative learning procedure can be fully automated. We illustrate this methodology using three experimental settings. The results show that the proposed methodology is able to improve the exploration efficiency of the simulation input space in comparison with non-restricted batch-mode active learning procedures.

Robust Closed-Loop Control of a Cursor in a Person with Tetraplegia using Gaussian Process Regression

Intracortical brain computer interfaces can enable individuals with paralysis to control external devices through voluntarily modulated brain activity. Decoding quality has been previously shown to degrade with signal nonstationarities-specifically, the changes in the statistics of the data between training and testing data sets. This includes changes to the neural tuning profiles and baseline shifts in firing rates of recorded neurons, as well as nonphysiological noise. While progress has been made toward providing long-term user control via decoder recalibration, relatively little work has been dedicated to making the decoding algorithm more resilient to signal nonstationarities. Here, we describe how principled kernel selection with gaussian process regression can be used within a Bayesian filtering framework to mitigate the effects of commonly encountered nonstationarities. Given a supervised training set of (neural features, intention to move in a direction)-pairs, we use gaussian process regression to predict the intention given the neural data. We apply kernel embedding for each neural feature with the standard radial basis function. The multiple kernels are then summed together across each neural dimension, which allows the kernel to effectively ignore large differences that occur only in a single feature. The summed kernel is used for real-time predictions of the posterior mean and variance under a gaussian process framework. The predictions are then filtered using the discriminative Kalman filter to produce an estimate of the neural intention given the history of neural data. We refer to the multiple kernel approach combined with the discriminative Kalman filter as the MK-DKF. We found that the MK-DKF decoder was more resilient to nonstationarities frequently encountered in-real world settings yet provided similar performance to the currently used Kalman decoder. These results demonstrate a method by which neural decoding can be made more resistant to nonstationarities.

Sandwich shield subjected to bird impact: Use of surrogate models for influencing parameter analysis and shield behaviour understanding

In this work, the behaviour of a sandwich shield subjected to a 1.82 kg bird impact at 175 m/s is studied using a finite element model. The 6 most influential design parameters are varied and their effects on the shield behaviour and on the target protection are assessed. First, we try to establish an engineer's visualization by varying parameters 2 × 2 using three 5-levels full-factorial design of experiments. These three 2D design of experiments enable us to visualize precisely the different effects of each parameter. Then a full sensitivity analysis (6D) is performed using a Latin Hypercube sampling to assess the possible interactions between parameters. Surrogate models are constructed using the Gaussian Process framework to follow the variation of the outputs in the 6D design space. These surrogate models are finally studied using two statistical methods: the Sobol′ method and the Morris method. The methodology developed in this study enables to improve the understanding of the behaviour of a shield under a soft body impact, as a first step towards a shield design tool.

Branch-recombinant Gaussian processes for analysis of perturbations in biological time series.

MotivationA common class of behaviour encountered in the biological sciences involves branching and recombination. During branching, a statistical process bifurcates resulting in two or more potentially correlated processes that may undergo further branching; the contrary is true during recombination, where two or more statistical processes converge. A key objective is to identify the time of this bifurcation (branch or recombination time) from time series measurements, e.g. by comparing a control time series with perturbed time series. Gaussian processes (GPs) represent an ideal framework for such analysis, allowing for nonlinear regression that includes a rigorous treatment of uncertainty. Currently, however, GP models only exist for two-branch systems. Here, we highlight how arbitrarily complex branching processes can be built using the correct composition of covariance functions within a GP framework, thus outlining a general framework for the treatment of branching and recombination in the form of branch-recombinant Gaussian processes (B-RGPs).ResultsWe first benchmark the performance of B-RGPs compared to a variety of existing regression approaches, and demonstrate robustness to model misspecification. B-RGPs are then used to investigate the branching patterns of Arabidopsis thaliana gene expression following inoculation with the hemibotrophic bacteria, Pseudomonas syringae DC3000, and a disarmed mutant strain, hrpA. By grouping genes according to the number of branches, we could naturally separate out genes involved in basal immune response from those subverted by the virulent strain, and show enrichment for targets of pathogen protein effectors. Finally, we identify two early branching genes WRKY11 and WRKY17, and show that genes that branched at similar times to WRKY11/17 were enriched for W-box binding motifs, and overrepresented for genes differentially expressed in WRKY11/17 knockouts, suggesting that branch time could be used for identifying direct and indirect binding targets of key transcription factors.Availability and implementation https://github.com/cap76/BranchingGPs Supplementary information Supplementary data are available at Bioinformatics online.