Search results for "Gaussia"
showing 10 items of 653 documents
Learning Structures in Earth Observation Data with Gaussian Processes
2020
Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems consistently. This paper reviews the main theoretical GP developments in the field. We review new algorithms that respect the signal and noise characteristics, that provide feature rankings automatically, and that allow applicability of associated uncertainty intervals to transport GP models in space and time. All these developments are illustrated in the field of geoscience and remote sensing at a local and global scales through a set of illustrative exa…
Joint Gaussian Processes for Biophysical Parameter Retrieval
2017
Solving inverse problems is central to geosciences and remote sensing. Radiative transfer models (RTMs) represent mathematically the physical laws which govern the phenomena in remote sensing applications (forward models). The numerical inversion of the RTM equations is a challenging and computationally demanding problem, and for this reason, often the application of a nonlinear statistical regression is preferred. In general, regression models predict the biophysical parameter of interest from the corresponding received radiance. However, this approach does not employ the physical information encoded in the RTMs. An alternative strategy, which attempts to include the physical knowledge, co…
Randomized Rx For Target Detection
2018
This work tackles the target detection problem through the well-known global RX method. The RX method models the clutter as a multivariate Gaussian distribution, and has been extended to nonlinear distributions using kernel methods. While the kernel RX can cope with complex clutters, it requires a considerable amount of computational resources as the number of clutter pixels gets larger. Here we propose random Fourier features to approximate the Gaussian kernel in kernel RX and consequently our development keep the accuracy of the nonlinearity while reducing the computational cost which is now controlled by an hyperparameter. Results over both synthetic and real-world image target detection…
Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes
2017
Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by prevalently redundant or sy…
Local Granger causality
2021
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes. We exploit such equivalence and calculate exactly the 'local Granger causality', i.e. the profile of the information transfer at each discrete time point in Gaussian processes; in this frame Granger causality is the average of its local version. Our approach offers a robust and computationally fast method to follow the information transfer along the time history of linear stochastic processes, as well as of nonlinear …
Adaptive independent sticky MCMC algorithms
2018
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively based on previously drawn samples. The algorithm's efficiency is ensured by a test that controls the evolution of the set of support points. This extra stage controls the computational cost and the converge…
Bayesian Unification of Gradient and Bandit-based Learning for Accelerated Global Optimisation
2017
Bandit based optimisation has a remarkable advantage over gradient based approaches due to their global perspective, which eliminates the danger of getting stuck at local optima. However, for continuous optimisation problems or problems with a large number of actions, bandit based approaches can be hindered by slow learning. Gradient based approaches, on the other hand, navigate quickly in high-dimensional continuous spaces through local optimisation, following the gradient in fine grained steps. Yet, apart from being susceptible to local optima, these schemes are less suited for online learning due to their reliance on extensive trial-and-error before the optimum can be identified. In this…
The Recycling Gibbs sampler for efficient learning
2018
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary sample…
Multispectral image denoising with optimized vector non-local mean filter
2016
Nowadays, many applications rely on images of high quality to ensure good performance in conducting their tasks. However, noise goes against this objective as it is an unavoidable issue in most applications. Therefore, it is essential to develop techniques to attenuate the impact of noise, while maintaining the integrity of relevant information in images. We propose in this work to extend the application of the Non-Local Means filter (NLM) to the vector case and apply it for denoising multispectral images. The objective is to benefit from the additional information brought by multispectral imaging systems. The NLM filter exploits the redundancy of information in an image to remove noise. A …
Fractional Spectral Moments for Digital Simulation of Multivariate Wind Velocity Fields
2012
In this paper, a method for the digital simulation of wind velocity fields by Fractional Spectral Moment function is proposed. It is shown that by constructing a digital filter whose coefficients are the fractional spectral moments, it is possible to simulate samples of the target process as superposition of Riesz fractional derivatives of a Gaussian white noise processes. The key of this simulation technique is the generalized Taylor expansion proposed by the authors. The method is extended to multivariate processes and practical issues on the implementation of the method are reported.