arXiv subjects

Gabriel Riutort-Mayol

Publications and source records attributed to Gabriel Riutort-Mayol.

4 recordsLinked to original sources

arXiv2022

Practical Hilbert space approximate Bayesian Gaussian processes for probabilistic programming

Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially when estimated with fully Bayesian methods such as Markov chain Monte Carlo. In this paper, we focus on a low-rank approximate Bayesian Gaussian processes, based on a basis function approximation via Laplace eigenfunctions for stationary covariance functions. The main contribution of this paper is a detailed analysis of the performance, and practical recommendations for how to select the number of basis functions and the boundary factor. Intuitive visualizations and recommendations, make it easier for users to improve approximation accuracy and computational performance. We also propose diagnostics for checking that the number of basis functions and the boundary factor are adequate given the data. The approach is simple and exhibits an attractive computational complexity due to its linear structure, and it is easy to implement in probabilistic programming frameworks. Several illustrative examples of the performance and applicability of the method in the probabilistic programming language Stan are presented together with the underlying Stan model code.

stat.CO↗

arXiv2020

A Bayesian Multilevel Random-Effects Model for Estimating Noise in Image Sensors

Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging with digital cameras. A Bayesian probabilistic model based on the (theoretical) model for noise sources in image sensing is fitted to a set of a time-series of images with different reflectance and wavelengths under controlled lighting conditions. The image sensing model is a complex model, with several interacting components dependent on reflectance and wavelength. The properties of the Bayesian approach of defining conditional dependencies among parameters in a fully probabilistic model, propagating all sources of uncertainty in inference, makes the Bayesian modeling framework more attractive and powerful than classical methods for approaching the image sensing model. A feasible correspondence of noise parameters to their expected theoretical behaviors and well calibrated posterior predictive distributions with a small root mean square error for model predictions have been achieved in this study, thus showing that the proposed model accurately approximates the image sensing model. The Bayesian approach could be extended to formulate further components aimed at identifying even more specific parameters of the imaging process.

stat.AP↗

arXiv2019

Gaussian process with derivative information for the analysis of the sunlight adverse effects on color of rock art paintings

Microfading Spectrometry (MFS) is a method for assessing light sensitivity color (spectral) variations of cultural heritage objects. The MFS technique provides measurements of the surface under study, where each point of the surface gives rise to a time-series that represents potential spectral (color) changes due to sunlight exposition over time. Color fading is expected to be non-decreasing as a function of time and stabilize eventually. These properties can be expressed in terms of the partial derivatives of the functions. We propose a spatio-temporal model that takes this information into account by jointly modeling the spatio-temporal process and its derivative process using Gaussian processes (GPs). We fitted the proposed model to MFS data collected from the surface of prehistoric rock art paintings. A multivariate covariance function in a GP allows modeling trichromatic image color variables jointly with spatial distances and time points variables as inputs to evaluate the covariance structure of the data. We demonstrated that the colorimetric variables are useful for predicting the color fading time-series for new unobserved spatial locations. Furthermore, constraining the model using derivative sign observations for monotonicity was shown to be beneficial in terms of both predictive performance and application-specific interpretability.

stat.AP↗

arXiv2019

Correlated functional models with derivative information for modeling MFS data on rock art paintings

Microfading Spectrometry (MFS) is a method for assessing light sensitivity color (spectral) variations of cultural heritage objects. Each measured point on the surface gives rise to a time-series of stochastic observations that represents color fading over time. Color degradation is expected to be non-decreasing as a function of time and stabilize eventually. These properties can be expressed in terms of the derivatives of the functions. In this work, we propose spatially correlated splines-based time-varying functions and their derivatives for modeling and predicting MFS data collected on the surface of rock art paintings. The correlation among the splines models is modeled using Gaussian process priors over the spline coefficients across time-series. A multivariate covariance function in a Gaussian process allows the use of trichromatic image color variables jointly with spatial locations as inputs to evaluate the correlation among time-series, and demonstrated the colorimetric variables as useful for predicting new color fading time-series. Furthermore, modeling the derivative of the model and its sign demonstrated to be beneficial in terms of both predictive performance and application-specific interpretability.

stat.AP↗