Approximate Confidence and Prediction Intervals for Least Squares Support Vector Regression

Brabanter, Kris De; Brabanter, Jos De; Suykens, Johan A. K.; Moor, Bart De

doi:10.1109/tnn.2010.2087769

Cited by 119 publications

(55 citation statements)

References 30 publications

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“…Once G , A, R and are determined, optimal values of fixed effects, random effects and the Lagrange multipliers are determined from Eq. (20) , and plugged into Eq. (17) .…”

Section: Regression Equationmentioning

confidence: 99%

“…De Brabanter et al [20] proposed a method for approximating 100(1-a )% confidence and prediction intervals for conditional expectation from a least squares support vector machine, that does not require explicit calculation of the bias. Assuming that the observations can be written as a mean function f ( x ) and a standard deviation function σ ( x ),…”

Section: Pointwise Confidence and Prediction Intervalsmentioning

confidence: 99%

“…denotes probability. It can be shown that (see [20] ) the least squares kernel machine model given in Eq. (8) …”

Section: Pointwise Confidence and Prediction Intervalsmentioning

confidence: 99%

See 2 more Smart Citations

A kernel-based mixed effect regression model for earthquake ground motions

Tezcan

Hazirbaba

Cheng

2018

Advances in Engineering Software

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“…Once G , A, R and are determined, optimal values of fixed effects, random effects and the Lagrange multipliers are determined from Eq. (20) , and plugged into Eq. (17) .…”

Section: Regression Equationmentioning

confidence: 99%

Section: Pointwise Confidence and Prediction Intervalsmentioning

confidence: 99%

See 1 more Smart Citation

A kernel-based mixed effect regression model for earthquake ground motions

Tezcan

Hazirbaba

Cheng

2018

Advances in Engineering Software

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“…Distribution free decomposition of multivariate data. Pattern Analysis and Applications, 2(1): [22][23][24][25][26][27][28][29][30]1999.…”

Section: Monolithic Detectionmentioning

confidence: 99%

Crowd Counting and Profiling: Methodology and Evaluation

Loy

Chen

Gong

et al. 2013

The International Series in Video Computing

175

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Video imagery based crowd analysis for population profiling and density estimation in public spaces can be a highly effective tool for establishing global situational awareness. Different strategies such as counting by detection and counting by clustering have been proposed, and more recently counting by regression has also gained considerable interest due to its feasibility in handling relatively more crowded environments. However, the scenarios studied by existing regression-based techniques are rather diverse in terms of both evaluation data and experimental settings. It can be difficult to compare them in order to draw general conclusions on their effectiveness. In addition, contributions of individual components in the processing pipeline such as feature extraction and perspective normalisation remain unclear and less well studied. This study describes and compares the state-of-the-art methods for video imagery based crowd counting, and provides a systematic evaluation of different methods using the same protocol. Moreover, we evaluate critically each processing component to identify potential bottlenecks encountered by existing techniques. Extensive evaluation is conducted on three public scene datasets, including a new shopping centre environment with labelled ground truth for validation. Our study reveals new insights into solving the problem of crowd analysis for population profiling and density estimation, and considers open questions for future studies.

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“…With the estimated bias and variance given in De Brabanter et al (2011a), an approximate 100(1 − α)% pointwise confidence interval for m ism…”

Section: Pointwise Confidence Intervalsmentioning

confidence: 99%

Nonparametric Regression viaStatLSSVM

Brabanter¹,

Suykens²,

Moor³

2013

J. Stat. Soft.

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We present a new MATLAB toolbox under Windows and Linux for nonparametric regression estimation based on the statistical library for least squares support vector machines (StatLSSVM). The StatLSSVM toolbox is written so that only a few lines of code are necessary in order to perform standard nonparametric regression, regression with correlated errors and robust regression. In addition, construction of additive models and pointwise or uniform confidence intervals are also supported. A number of tuning criteria such as classical cross-validation, robust cross-validation and cross-validation for correlated errors are available. Also, minimization of the previous criteria is available without any user interaction.

show abstract

Approximate Confidence and Prediction Intervals for Least Squares Support Vector Regression

Cited by 119 publications

References 30 publications

A kernel-based mixed effect regression model for earthquake ground motions

A kernel-based mixed effect regression model for earthquake ground motions

Crowd Counting and Profiling: Methodology and Evaluation

Nonparametric Regression viaStatLSSVM

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