scholarly journals Skew Gaussian processes for classification

2020 ◽  
Vol 109 (9-10) ◽  
pp. 1877-1902
Author(s):  
Alessio Benavoli ◽  
Dario Azzimonti ◽  
Dario Piga
Keyword(s):  
Gaussian Processes ◽  
Probabilistic Model ◽  
Marginal Likelihood ◽  
Predictive Distribution ◽  
Skewed Distribution ◽  
Expectation Propagation ◽  
Nonparametric Approach ◽  
Finite Dimensional ◽  
The Mean ◽  
Conjugate Model

Abstract Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a symmetric distribution with respect to its mean is an unreasonable model. This implies, for instance, that the mean and the median coincide, while the mean and median in an asymmetric (skewed) distribution can be different numbers. In this paper, we propose skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions. A SkewGP extends the multivariate unified skew-normal distribution over finite dimensional vectors to a stochastic processes. The SkewGP class of distributions includes GPs and, therefore, SkewGPs inherit all good properties of GPs and increase their flexibility by allowing asymmetry in the probabilistic model. By exploiting the fact that SkewGP and probit likelihood are conjugate model, we derive closed form expressions for the marginal likelihood and predictive distribution of this new nonparametric classifier. We verify empirically that the proposed SkewGP classifier provides a better performance than a GP classifier based on either Laplace’s method or expectation propagation.

Bayesian Nonparametric Approach to Average Annual Daily Traffic Estimation for Bridges

2021 ◽  
pp. 036119812199459
Author(s):  
Grace Ashley ◽  
Nii Attoh-Okine
Keyword(s):  
Performance Indicators ◽  
Federal Funding ◽  
Percentage Error ◽  
Bayesian Nonparametric ◽  
Transportation Services ◽  
Nonparametric Approach ◽  
Nonparametric Models ◽  
Bayesian Nonparametric Models ◽  
Average Annual Daily Traffic ◽  
The Mean

Every year, the U.S. government provides several billions of dollars in the form of federal funding for transportation services in the U.S.A. Decision making with regard to the use of these funds largely depends on performance indicators like average annual daily traffic (AADT). In this paper, Bayesian nonparametric models are developed through machine learning for the estimation of AADT on bridges. The effect of hyperparameter choice on the accuracy of estimations produced by Bayesian nonparametric models is also assessed. The predictions produced using the Bayesian nonparametric approach are then compared with predictions from a popular Frequentist approach for the selected bridges. Evaluation metrics like the mean absolute percentage error are subsequently employed in model evaluation. Based on the results, the best methods for AADT forecasting for the selected bridges are recommended.

scholarly journals Quantifying the closeness to a set of random curves via the mean marginal likelihood

2020 ◽  
Author(s):  
Cédric Rommel ◽  
Joseph Frédéric Bonnans ◽  
Baptiste Gregorutti ◽  
Pierre Martinon
Keyword(s):  
Marginal Likelihood ◽  
Marginal Density ◽  
Random Curves ◽  
Practical Applications ◽  
Random Functions ◽  
Practical Usefulness ◽  
Class Of Estimators ◽  
The Mean ◽  
Multivariate Density ◽  
Aircraft Trajectories

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

scholarly journals Gaussian Process Autoregression for Joint Angle Prediction Based on sEMG Signals

2021 ◽  
Vol 9 ◽  
Author(s):  
Jie Liang ◽  
Zhengyi Shi ◽  
Feifei Zhu ◽  
Wenxin Chen ◽  
Xin Chen ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Probabilistic Model ◽  
Autoregressive Model ◽  
Process Model ◽  
Joint Angle ◽  
Gaussian Process Model ◽  
The Mean ◽  
Test Scenarios ◽  
Semg Signals ◽  
Non Parametric

There is uncertainty in the neuromusculoskeletal system, and deterministic models cannot describe this significant presence of uncertainty, affecting the accuracy of model predictions. In this paper, a knee joint angle prediction model based on surface electromyography (sEMG) signals is proposed. To address the instability of EMG signals and the uncertainty of the neuromusculoskeletal system, a non-parametric probabilistic model is developed using a Gaussian process model combined with the physiological properties of muscle activation. Since the neuromusculoskeletal system is a dynamic system, the Gaussian process model is further combined with a non-linear autoregressive with eXogenous inputs (NARX) model to create a Gaussian process autoregression model. In this paper, the normalized root mean square error (NRMSE) and the correlation coefficient (CC) are compared between the joint angle prediction results of the Gaussian process autoregressive model prediction and the actual joint angle under three test scenarios: speed-dependent, multi-speed and speed-independent. The mean of NRMSE and the mean of CC for all test scenarios in the healthy subjects dataset and the hemiplegic patients dataset outperform the results of the Gaussian process model, with significant differences (p < 0.05 and p < 0.05, p < 0.05 and p < 0.05). From the perspective of uncertainty, a non-parametric probabilistic model for joint angle prediction is established by using Gaussian process autoregressive model to achieve accurate prediction of human movement.

scholarly journals Performance and reliability of multimodel hydrological ensemble simulations based on seventeen lumped models and a thousand catchments

2010 ◽  
Vol 14 (11) ◽  
pp. 2303-2317 ◽  
Author(s):  
J. A. Velázquez ◽  
F. Anctil ◽  
C. Perrin
Keyword(s):  
Predictive Distribution ◽  
Added Value ◽  
Average Error ◽  
Hydrological Models ◽  
Relative Operating Characteristic ◽  
Probability Score ◽  
Ensemble Simulations ◽  
Continuous Ranked Probability Score ◽  
The Mean ◽  
Improved Performance

Abstract. This work investigates the added value of ensembles constructed from seventeen lumped hydrological models against their simple average counterparts. It is thus hypothesized that there is more information provided by all the outputs of these models than by their single aggregated predictors. For all available 1061 catchments, results showed that the mean continuous ranked probability score of the ensemble simulations were better than the mean average error of the aggregated simulations, confirming the added value of retaining all the components of the model outputs. Reliability of the simulation ensembles is also achieved for about 30% of the catchments, as assessed by rank histograms and reliability plots. Nonetheless this imperfection, the ensemble simulations were shown to have better skills than the deterministic simulations at discriminating between events and non-events, as confirmed by relative operating characteristic scores especially for larger streamflows. From 7 to 10 models are deemed sufficient to construct ensembles with improved performance, based on a genetic algorithm search optimizing the continuous ranked probability score. In fact, many model subsets were found improving the performance of the reference ensemble. This is thus not essential to implement as much as seventeen lumped hydrological models. The gain in performance of the optimized subsets is accompanied by some improvement of the ensemble reliability in most cases. Nonetheless, a calibration of the predictive distribution is still needed for many catchments.

scholarly journals Limit theorems for hitting times of 1-dimensional generalized diffusions

1998 ◽  
Vol 152 ◽  
pp. 1-37
Author(s):  
Matsuyo Tomisaki ◽  
Makoto Yamazato
Keyword(s):  
Limit Theorems ◽  
Bessel Functions ◽  
Diffusion Processes ◽  
Hitting Times ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Starting Point ◽  
Self Similar ◽  
The Mean ◽  
The One

Abstract.Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting points tend to boundaries under an assumption which is slightly stronger than that the existence of limits γ + 1 of the ratio of the mean and the variance of the hitting time. Laplace transforms of limit distributions are modifications of Bessel functions. Results are classified by the one parameter {γ}, each of which is the degree of corresponding Bessel function. In case the limit distribution is degenerate to one point, by changing the normalization, we obtain convergence to the normal distribution. Regarding the starting point as a time parameter, we obtain convergence in finite dimensional distributions to self-similar processes with independent increments under slightly stronger assumption.

Limit theorem for continuous-time random walks with two time scales

2004 ◽  
Vol 41 (2) ◽  
pp. 455-466 ◽  
Author(s):  
Peter Becker-Kern ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Time Scales ◽  
Waiting Time ◽  
Continuous Time ◽  
Fractional Partial Differential Equations ◽  
Finite Dimensional ◽  
Mean Waiting Time ◽  
Continuous Time Random Walks ◽  
Random Jumps ◽  
The Mean

Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.

Limit theorem for continuous-time random walks with two time scales

2004 ◽  
Vol 41 (02) ◽  
pp. 455-466 ◽  
Author(s):  
Peter Becker-Kern ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Time Scales ◽  
Waiting Time ◽  
Continuous Time ◽  
Fractional Partial Differential Equations ◽  
Finite Dimensional ◽  
Mean Waiting Time ◽  
Continuous Time Random Walks ◽  
Random Jumps ◽  
The Mean

Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.

scholarly journals Generalized Inferences about the Mean Vector of Several Multivariate Gaussian Processes

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Pilar Ibarrola ◽  
Ricardo Vélez
Keyword(s):  
Gaussian Processes ◽  
Confidence Region ◽  
Confidence Regions ◽  
Covariance Matrices ◽  
Nuisance Parameters ◽  
Vector Parameter ◽  
Multivariate Gaussian ◽  
The Mean ◽  
Unknown Vector ◽  
Mean Vector

We consider in this paper the problem of comparing the means of several multivariate Gaussian processes. It is assumed that the means depend linearly on an unknown vector parameterθand that nuisance parameters appear in the covariance matrices. More precisely, we deal with the problem of testing hypotheses, as well as obtaining confidence regions forθ. Both methods will be based on the concepts of generalizedpvalue and generalized confidence region adapted to our context.

scholarly journals Transcripts for the acetylcholine receptor and acetylcholine esterase show distribution differences in cultured chick muscle cells.

1992 ◽  
Vol 118 (5) ◽  
pp. 1201-1212 ◽  
Author(s):  
K W Tsim ◽  
I Greenberg ◽  
M Rimer ◽  
W R Randall ◽  
M M Salpeter
Keyword(s):  
In Situ Hybridization ◽  
Acetylcholine Receptor ◽  
Gaussian Distribution ◽  
Muscle Cells ◽  
Skewed Distribution ◽  
Alpha Subunit ◽  
Subunit Mrna ◽  
Nuclear Label ◽  
The Mean

In situ hybridization of chick cultured muscle cells using exonic DNA probes for both AChR alpha-sub-unit and the catalytic subunit of AChE, revealed major differences in the distribution of label both over nuclei and in their surrounding cytoplasm, although some overlap in these distributions exists. For the AChR alpha-subunit there is a highly skewed distribution of labeled nuclei, with 35% of the nuclei being relatively inactive (less than 0.25 times the mean label) and approximately 10% being very heavily labeled (greater than 2.5 times the mean label). In contrast the nuclei labeled with the exonic probe for the AChE transcripts had a more Gaussian distribution, yet with some slight skewness in the direction of a few heavily labeled nuclei. There was also a difference in the cytoplasmic distribution of the label. The AChR alpha-subunit mRNA was mainly within 4 microns of labeled nuclei while the AChE mRNA was more widely distributed throughout the cytoplasm, possibly within a 10 microns rim around labeled nuclei. An intronic probe for the AChE gave the identical distribution of nuclear label to that of the exonic probe (but without any cytoplasmic label). In addition, calibration of the technique indicated that per myotube the AChE transcript is about sixfold more abundant than the AChR alpha-subunit transcript.

scholarly journals The consequences of uncertainty for the prediction of the effects of schistosomiasis control programmes

1996 ◽  
Vol 117 (3) ◽  
pp. 537-550 ◽  
Author(s):  
M. S. Chan
Keyword(s):  
Worm Burden ◽  
Skewed Distribution ◽  
Effective Control ◽  
Acquired Immunity ◽  
Treatment Programme ◽  
Chemotherapy Treatment ◽  
Schistosomiasis Control ◽  
Considerable Uncertainty ◽  
Control Programmes ◽  
The Mean

SummaryProgress in the development of schistosomiasis models for use in control programmes is limited by the considerable uncertainty in many of the biological parameters. In this paper, this problem is addressed by a comprehensive sensitivity analysis of a schistosomiasis model using the Latin Hypercube method. Fifty simulations with different parameter contributions are run for 50 years with treatment during the first 20 years and reinfection thereafter. The analysis shows only a relatively small divergence between simulations during the chemotherapy treatment programme but considerable divergence in reinfection levels after treatment is stopped. A skewed distribution of outcomes was seen with most simulations showing effective control and a few where control had less impact. The most important uncertainty source was due to the unknown levels of acquired immunity and also uncertainty in the true worm burden. In particular, the strength of the immune response was most important in determining whether control was effective with higher immunity leading to less effective control. Among those simulations in which control was not very effective, those in which the mean worm burden was high showed the least effective control. Since both these are areas of genuine uncertainty, it is proposed that uncertainty analysis should be an integral part of any projection of control programmes.

Sign in / Sign up

Export Citation Format

Share Document