Gaussian processes (GPs) are a class of Kernel methods that have shown to be very useful in geoscience and remote sensing applications for parameter retrieval, model inversion, and emulation. They are widely used because they are simple, flexible, and provide accurate estimates. GPs are based on a Bayesian statistical framework which provides a posterior probability function for each estimation. Therefore, besides the usual prediction (given in this case by the mean function), GPs come equipped with the possibility to obtain a predictive variance (i.e., error bars, confidence intervals) for each prediction. Unfortunately, the GP formulation usually assumes that there is no noise in the inputs, only in the observations. However, this is often not the case in earth observation problems where an accurate assessment of the measuring instrument error is typically available, and where there is huge interest in characterizing the error propagation through the processing pipeline. In this letter, we demonstrate how one can account for input noise estimates using a GP model formulation which propagates the error terms using the derivative of the predictive mean function. We analyze the resulting predictive variance term and show how they more accurately represent the model error in a temperature prediction problem from infrared sounding data.
Ludwig-Maximilians-Universität München (LMU)（慕尼黑大学）
Bayesian optimization (BO) with Gaussian processes (GP) as surrogate models is widely used to optimize analytically unknown and expensive-to-evaluate functions. In this paper, we propose Prior-mean-RObust Bayesian Optimization (PROBO) that outperforms classical BO on specific problems. First, we study the effect of the Gaussian processes' prior specifications on classical BO's convergence. We find the prior's mean parameters to have the highest influence on convergence among all prior components. In response to this result, we introduce PROBO as a generalization of BO that aims at rendering th…
This paper introduces deep Gaussian processes (DGPs) for geophysical parameter retrieval. Unlike the standard full GP model, the DGP accounts for complicated (modular, hierarchical) processes, provides an efficient solution that scales well to large datasets, and improves prediction accuracy over standard full and sparse GP models. We give empirical evidence of performance for estimation of surface dew point temperature from infrared sounding data.
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…
University of Manchester（曼彻斯特大学）；Aalto University（阿尔托大学）
Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem of learning from many short, low-noise trajectories, but learning from a small number of long, noisy trajectories, whilst accounting for model uncertainty has not been addressed. In this work, we present a Gaussian process model for Hamiltonian systems with efficient decoupled parameterisation, and introduce an energy-conserving shooting method that allows ro…
University of Liverpool（利物浦大学）；Universidad Antonio de Nebrija（安东尼奥·德·内布里哈大学）；Aalto University（阿尔托大学）
This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the conditional mean of the labels and accounting for the linearisation error. PL has some theoretical advantages over expectation propagation (EP): all calculated covariance matrices are positive definite and there is a local convergence theorem. In experimental data, PL has better performance than EP with the noisy threshold likelihood and the parallel implementa…
University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦·图灵研究所）
Learning in Gaussian Process models occurs through the adaptation of hyperparameters of the mean and the covariance function. The classical approach entails maximizing the marginal likelihood yielding fixed point estimates (an approach called \textit{Type II maximum likelihood} or ML-II). An alternative learning procedure is to infer the posterior over hyperparameters in a hierarchical specification of GPs we call \textit{Fully Bayesian Gaussian Process Regression} (GPR). This work considers two approximation schemes for the intractable hyperparameter posterior: 1) Hamiltonian Monte Carlo (HMC…
Bayesian optimisation (BO) is widely used to optimise stochastic black box functions. While most BO approaches focus on optimising conditional expectations, many applications require risk-averse strategies and alternative criteria accounting for the distribution tails need to be considered. In this paper, we propose new variational models for Bayesian quantile and expectile regression that are well-suited for heteroscedastic noise settings. Our models consist of two latent Gaussian processes accounting respectively for the conditional quantile (or expectile) and the scale parameter of an asymm…
Radboud University Medical Centre（拉德堡德大学医学中心）；Radboud University（拉德堡德大学）
Normative modeling has recently been proposed as an alternative for the case-control approach in modeling heterogeneity within clinical cohorts. Normative modeling is based on single-output Gaussian process regression that provides coherent estimates of uncertainty required by the method but does not consider spatial covariance structure. Here, we introduce a scalable multi-task Gaussian process regression (S-MTGPR) approach to address this problem. To this end, we exploit a combination of a low-rank approximation of the spatial covariance matrix with algebraic properties of Kronecker product …
Universitat de València（瓦伦西亚大学）；University of Granada（格拉纳达大学）
Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel…
University of Electronic Science and Technology of China（电子科技大学）；China Academy of Engineering Physics（中国工程物理研究院）
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to promote the low-rankness of the matrix. Based on the proposed hierarchical model, a variational expectation-maximization (EM) algorithm is developed. The proposed method is less sensitive to the choice of the initialization point and works well with random initialization. Simulat…
Universitat de València（瓦伦西亚大学）；CICESE；Israel Institute of Technology, Technion（以色列理工学院（Technion））
With current and upcoming imaging spectrometers, automated band analysis techniques are needed to enable efficient identification of most informative bands to facilitate optimized processing of spectral data into estimates of biophysical variables. This paper introduces an automated spectral band analysis tool (BAT) based on Gaussian processes regression (GPR) for the spectral analysis of vegetation properties. The GPR-BAT procedure sequentially backwards removes the least contributing band in the regression model for a given variable until only one band is kept. GPR-BAT is implemented within …
Helmholtz-Zentrum Geesthacht（亥姆霍兹盖斯特哈赫特中心）；Finnish Environment Institute SYKE（芬兰环境研究所（SYKE））
The coloured dissolved organic matter (CDOM) concentration is the standard measure of humic substance in natural waters. CDOM measurements by remote sensing is calculated using the absorption coefficient (a) at a certain wavelength (e.g. 440nm). This paper presents a comparison of four machine learning methods for the retrieval of CDOM from remote sensing signals: regularized linear regression (RLR), random forest (RF), kernel ridge regression (KRR) and Gaussian process regression (GPR). Results are compared with the established polynomial regression algorithms. RLR is revealed as the simplest…
Individual Privacy Accounting with Gaussian Differential Privacy
Nokia Bell Labs（诺基亚贝尔实验室）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所）；University of Helsinki（赫尔辛基大学）；Department of Computer Science, University of Helsinki（赫尔辛基大学计算机科学系）
Rice University（莱斯大学）；The Ohio State University（俄亥俄州立大学）
Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise. Progress has been made recently on more robust algorithms using signal priors, but at the expense of limiting the range of supported measurement models (e.g., to Gaussian or coded diffraction patterns). In this work we leverage the re…
UC Santa Barbara（加州大学圣巴巴拉分校）；Northwestern University（西北大学）
Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, $f$-DP and the PLD formalism) via the \emph{characteristic function} ($ϕ$-function) of a certain \emph{dominating} privacy loss random variable. We show that our approach allows \emph{natural} adaptive composition like Renyi DP, provides \emph{exactly tight} privacy accounting like PLD, and can be (o…
Conditional Diffusion-Based Retrieval of Atmospheric CO2 from Earth Observing Spectroscopy
University of Oklahoma（俄克拉荷马大学）；Jet Propulsion Laboratory（喷气推进实验室）；California Institute of Technology（加州理工学院）；LumenUs Scientific（LumenUs科学公司）；Cooperative Institute for Atmospheric Research（大气研究合作研究所）；Colorado State University（科罗拉多州立大学）
Ultrasonic guided waves are commonly used to localize structural damage in infrastructures such as buildings, airplanes, bridges. Damage localization can be viewed as an inverse problem. Physical model based techniques are popular for guided wave based damage localization. The performance of these techniques depend on the degree of faithfulness with which the physical model describes wave propagation. External factors such as environmental variations and random noise are a source of uncertainty in wave propagation. The physical modeling of uncertainty in an inverse problem is still a challengi…
