Bayesian Linear Regression — Different Conjugate Models and Their (In)Sensitivity to Prior-Data Conflict

Walter, GM Gero; Augustin, Thomas

doi:10.1007/978-3-7908-2413-1_4

Cited by 12 publications

(7 citation statements)

References 23 publications

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“…Regression analysis is a vital tool in applied statistics as well as in machine learning. It aims to investigate the influence of certain variables X on a certain outcome y (Walter and Augustin 2010).…”

Section: Introductionmentioning

confidence: 99%

Over-Fitting in Model Selection with Gaussian Process Regression

Mohammed

Cawley

2017

Lecture Notes in Computer Science

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Model selection in Gaussian Process Regression (GPR) seeks to determine the optimal values of the hyper-parameters governing the covariance function, which allows flexible customization of the GP to the problem at hand. An oft-overlooked issue that is often encountered in the model process is over-fitting the model selection criterion, typically the marginal likelihood. The over-fitting in machine learning refers to the fitting of random noise present in the model selection criterion in addition to features improving the generalisation performance of the statistical model. In this paper, we construct several Gaussian process regression models for a range of high-dimensional datasets from the UCI machine learning repository. Afterwards, we compare both MSE on the test dataset and the negative log marginal likelihood (nlZ), used as the model selection criteria, to find whether the problem of overfitting in model selection also affects GPR. We found that the squared exponential covariance function with Automatic Relevance Determination (SEard) is better than other kernels including squared exponential covariance function with isotropic distance measure (SEiso) according to the nLZ, but it is clearly not the best according to MSE on the test data, and this is an indication of over-fitting problem in model selection.

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Section: Introductionmentioning

confidence: 99%

Over-Fitting in Model Selection with Gaussian Process Regression

Mohammed

Cawley

2017

Lecture Notes in Computer Science

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“…Prior-data conflict (Evans & Moshonov, 2006;Nott, Wang, et al, 2020;Walter & Augustin, 2009) can arise due to intentionally or unintentionally informative priors disagreeing with, but not being dominated by, the likelihood. When this is the case, the posterior will be sensitive to scaling both the prior and the likelihood, as illustrated in Figure 5.…”

Section: Diagnosing Sensitivitymentioning

confidence: 99%

Detecting and diagnosing prior and likelihood sensitivity with power-scaling

Kallioinen¹,

Paananen²,

Bürkner³

et al. 2021

Preprint

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Determining the sensitivity of the posterior to perturbations of the prior and likelihood is an important part of the Bayesian workflow. We introduce a practical and computationally efficient sensitivity analysis approach that is applicable to a wide range of models, based on power-scaling perturbations. We suggest a diagnostic based on this that can indicate the presence of prior-data conflict or likelihood noninformativity. The approach can be easily included in Bayesian workflows with minimal work by the model builder. We present the implementation of the approach in our new R package priorsense and demonstrate the workflow on case studies of real data.

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“…Generally, Bayesian approaches are hampered by a computation burden, given that no general analytic solution exists and therefore numerical approaches are taken. Fortunately, an analytic solution was proposed for an additive linear model, using a conjugated prior approach [14]. A python library [15] that implements the method within the framework of numpy and sklearn python modules is available.…”

Section: Models Fittingmentioning

confidence: 99%

Bayesian Harmonic Modelling of Sparse and Irregular Satellite Remote Sensing Time Series of Vegetation Indexes: A Story of Clouds and Fires

et al. 2019

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Vegetation index time series from Landsat and Sentinel-2 have great potential for following the dynamics of ecosystems and are the key to develop essential variables in the realm of biodiversity. Unfortunately, the removal of pixels covered mainly by clouds reduces the temporal resolution, producing irregularity in time series of satellite images. We propose a Bayesian approach based on a harmonic model, fitted on an annual base. To deal with data sparsity, we introduce hierarchical prior distribution that integrate information across the years. From the model, the mean and standard deviation of yearly Ecosystem Functional Attributes (i.e., mean, standard deviation, and peak’s day) plus the inter-year standard deviation are calculated. Accuracy is evaluated with a simulation that uses real cloud patterns found in the Peneda-Gêres National Park, Portugal. Sensitivity to the model’s abrupt change is evaluated against a record of multiple forest fires in the Bosco Difesa Grande Regional Park in Italy and in comparison with the BFAST software output. We evaluated the sensitivity in dealing with mixed patch of land cover by comparing yearly statistics from Landsat at 30m resolution, with a 2m resolution land cover of Murgia Alta National Park (Italy) using FAO Land Cover Classification System 2.

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Bayesian Linear Regression — Different Conjugate Models and Their (In)Sensitivity to Prior-Data Conflict

Cited by 12 publications

References 23 publications

Over-Fitting in Model Selection with Gaussian Process Regression

Over-Fitting in Model Selection with Gaussian Process Regression

Detecting and diagnosing prior and likelihood sensitivity with power-scaling

Bayesian Harmonic Modelling of Sparse and Irregular Satellite Remote Sensing Time Series of Vegetation Indexes: A Story of Clouds and Fires

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