Bayesian Nonlinear Support Vector Machines for Big Data

Wenzel, Florian; Galy-Fajou, Théo; Deutsch, Matthäus; Kloft, Marius

doi:10.1007/978-3-319-71249-9_19

Cited by 22 publications

(21 citation statements)

References 17 publications

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“…For the analysis, we also used a hybrid system, where the four methods mentioned above were connected, namely RF [40], SVM [41], GP [42], and NN [43] of the intelligent system, into one Euler graph method of machine learning (Figure 8). Ensemble methods are learning algorithms that build a series of classifiers and then classify new data points, summarizing the results of their predictions.…”

Section: Analysis Of Geomorphometric Parametersmentioning

confidence: 99%

Modeling and Classification of Alluvial Fans with DEMs and Machine Learning Methods: A Case Study of Slovenian Torrential Fans

Babič¹,

Petrovič

Sodnik

et al. 2021

Remote Sensing

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Alluvial (torrential) fans, especially those created from debris-flow activity, often endanger built environments and human life. It is well known that these kinds of territories where human activities are favored are characterized by increasing instability and related hydrological risk; therefore, treating the problem of its assessment and management is becoming strongly relevant. The aim of this study was to analyze and model the geomorphological aspects and the physical processes of alluvial fans in relation to the environmental characteristics of the territory for classification and prediction purposes. The main geomorphometric parameters capable of describing complex properties, such as relative fan position depending on the neighborhood, which can affect their formation or shape, or properties delineating specific parts of fans, were identified and evaluated through digital elevation model (DEM) data. Five machine learning (ML) methods, including a hybrid Euler graph ML method, were compared to analyze the geomorphometric parameters and physical characteristics of alluvial fans. The results obtained in 14 case studies of Slovenian torrential fans, validated with data of the empirical model proposed by Bertrand et al. (2013), confirm the validity of the developed method and the possibility to identify alluvial fans that can be considered as debris-flow prone.

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Section: Analysis Of Geomorphometric Parametersmentioning

confidence: 99%

Modeling and Classification of Alluvial Fans with DEMs and Machine Learning Methods: A Case Study of Slovenian Torrential Fans

Babič¹,

Petrovič

Sodnik

et al. 2021

Remote Sensing

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show abstract

“…Polson et al (2013) developed an approach with the logistic likelihood, this work was further expanded by Wenzel et al (2019) to big data. The augmentation done on the Bayesian Support Vector Machine of Polson et al (2011) and scaled up by Wenzel et al (2017), is similar to our method but is based on a different augmentation approach. Note that our method covers all these cases exactly but do not rely on any manual derivations.…”

Section: Related Workmentioning

confidence: 99%

Automated Augmented Conjugate Inference for Non-conjugate Gaussian Process Models

Galy-Fajou,

Wenzel,

Opper

2020

Preprint

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We propose automated augmented conjugate inference, a new inference method for nonconjugate Gaussian processes (GP) models. Our method automatically constructs an auxiliary variable augmentation that renders the GP model conditionally conjugate. Building on the conjugate structure of the augmented model, we develop two inference methods. First, a fast and scalable stochastic variational inference method that uses efficient block coordinate ascent updates, which are computed in closed form. Second, an asymptotically correct Gibbs sampler that is useful for small datasets. Our experiments show that our method are up two orders of magnitude faster and more robust than existing stateof-the-art black-box methods.

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“…whereby the normalization term in the denominator of (4) is omitted. This approximation was also used by Fu et al (2010), Mao et al (2014), Lai et al (2015), and Wenzel et al (2017), where it is argued that it is more computationally feasible than MLE (since it is a concave optimization problem) and that the functional form more closely resembles the SVM problem from which it is derived.…”

Section: Introductionmentioning

confidence: 99%

A binary-response regression model based on support vector machines

Nguyen¹,

Fryer²

2020

Preprint

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The soft-margin support vector machine (SVM) is a ubiquitous tool for prediction of binary-response data. However, the SVM is characterized entirely via a numerical optimization problem, rather than a probability model, and thus does not directly generate probabilistic inferential statements as outputs. We consider a probabilistic regression model for binary-response data that is based on the optimization problem that characterizes the SVM. Under weak regularity assumptions, we prove that the maximum likelihood estimate (MLE) of our model exists, and that it is consistent and asymptotically normal. We further assess the performance of our model via simulation studies, and demonstrate its use in real data applications regarding spam detection and well water access.

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Bayesian Nonlinear Support Vector Machines for Big Data

Cited by 22 publications

References 17 publications

Modeling and Classification of Alluvial Fans with DEMs and Machine Learning Methods: A Case Study of Slovenian Torrential Fans

Modeling and Classification of Alluvial Fans with DEMs and Machine Learning Methods: A Case Study of Slovenian Torrential Fans

Automated Augmented Conjugate Inference for Non-conjugate Gaussian Process Models

A binary-response regression model based on support vector machines

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