Explainable artificial intelligence (XAI) focuses on creating methods to provide transparency in how complex machine learning models make decisions. A key approach in XAI is feature attribution, which breaks down the model's predictions into the contributions of individual input features. In this presentation, we address feature attribution within the framework of Gaussian process regression (GPR). We present a principled approach that incorporates model uncertainty into the attribution process, expanding existing methods. Despite the GPR's flexibility and non-parametric nature, we demonstrate that interpretable, closed-form expressions for feature attributions can still be derived. Using integrated gradients as the attribution technique, we show that these attributions follow a Gaussian process distribution, effectively capturing the uncertainty inherent in the model. Through both theoretical and experimental validations, we show the robustness and versatility of this approach. Moreover, in applicable cases, the exact GPR attributions are not only more precise but also computationally more efficient than commonly used approximation methods.

Bayesian optimization is a commonly employed method for optimizing expensive, black-box functions, leveraging statistical surrogate models to identify optimal query points while maintaining a balance between exploration and exploitation in the search space. Traditionally, this approach assumes the target function remains constant over time. However, recent advancements have introduced a framework for time-varying Bayesian optimization, capable of addressing dynamic, non-stationary functions. In this presentation, we explore a time-varying approach using dynamic random feature-based Gaussian processes that evolve a linear model's parameters to capture function changes over time. Our proposed mechanism enables the acquisition function to dynamically adjust the exploration-exploitation trade-off in response to these changes. We demonstrate the effectiveness of our method through comparisons with baseline time-varying Bayesian optimization algorithms on both a synthetic example and a localization problem based on simulated data.

Space-based remote sensing facilitates the determination of greenhouse gas concentrations, enhancing the comprehension of carbon fluxes at the Earth’s surface in the context of climate change. High-resolution spectrometers, such as the CNES/UKSA MicroCarb and the upcoming ESA Copernicus Carbon Dioxide Monitoring (CO2M) spectrometers, are crucial tools for this purpose. These instruments require a precise calibration, especially regarding the relative approximation errors of the Instrument Spectral Response Functions (ISRFs). To ease ISRF estimation, parametric models such as Gaussian and Super-Gaussian models have been investigated. However, these models cannot always take into account the diversity of ISRF shapes that are encountered in practical applications. For example, in MicroCarb simulations, the expected performance is not always achieved by these two conventional ISRF estimation methods, even when there is no spectral and radiometric errors. This paper investigates a novel approach based on the sparse representation of ISRFs in a dictionary. This method decomposes the spectral responses of interest as sparse linear combinations of atoms belonging to a dictionary, which are built using representative ISRFs. This new method can be applied both for on-ground ISRF denoising, and in-flight ISRF estimation through the resolution of an appropriate inverse problem. Experiments conducted using realistic simulated datasets associated with the MicroCarb instrument are used to evaluate the performance of the proposed method for on-ground and in-flight ISRF estimation, yielding promising estimation performance compared to the state of the art.

Forests worldwide have undergone significant transformations due to forest loss, highlighting the critical need for real-time forest monitoring to prevent further vegetation loss and facilitate prompt interventions. Traditionally, forest loss monitoring relied on optical imagery, which is obstructed by its susceptibility to cloud coverage, especially in tropical regions. In recent times, Synthetic Aperture Radar (SAR)-based systems have emerged to enable all-weather operability. However, SAR-based approaches encounter challenges, such as the alterations in backscatter caused by factors like soil moisture variations. Moreover, accurately detecting small-scale disturbances remains problematic for SAR systems, partly due to the spatial filtering techniques employed to mitigate the effects of speckle. Additionally, monitoring forest loss in regions characterized by pronounced seasonality in backscatter signals, such as dry forests and savannas, poses limitations, resulting in substantial under-monitoring of these extensive carbon sinks. This study introduces an unsupervised SAR-based method for detecting forest loss, employing Bayesian inference through an infinite state Markov chain.

In this article, the principles of robust estimation are applied to the standard basic time scale equation to obtain a new method of assigning weights to clocks. Specifically, the Student’s t-distribution is introduced as a new statistical model for an ensemble of clocks that are experiencing phase jumps, frequency jumps or anomalies in their measurement links. The proposed robust time scale is designed to mitigate the effects of these anomalies without necessarily identifying them, but through applying a method of robust estimation for the parameters of a Student’s t-distribution. The proposed time scale algorithm using the Student’s t-distribution (ATST) is shown to achieve comparable robustness to phase jumps, frequency jumps, and anomalies in the measurements with respect to the AT1 oracle time scale. The AT1 oracle is a special realization of the AT1 time scale which corrects all anomalies by having prior knowledge of their occurrences. The similar performance of ATST and AT1 oracle suggests that the ATST algorithm is efficient for obtaining robustness with no prior knowledge or detection of the occurrences of anomalies.

Hyperbolic geometry has recently garnered considerable attention in machine learning due to its ability to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework to detect local outliers for datasets grounded in hyperbolic 2-space, which is referred to as Hyperbolic Local Outlier Probability (HLoOP). Within a Euclidean space, well-known techniques for local outlier detection are based on the Local Outlier Factor (LOF) and its variant, the LoOP (Local Outlier Probability), which incorporates probabilistic concepts to model the outlier level of a data vector. The proposed HLoOP combines the notion of finding nearest neighbors, density-based outlier scoring with a probabilistic, statistically oriented approach. Therefore, the method computes the Riemmanian distance of a data point to its nearest neighbors following a Gaussian probability density function expressed in a hyperbolic space. This is achieved by defining a Gaussian cumulative distribution in this space. The proposed HLoOP algorithm is tested on the WordNet dataset and desmonstrated promising results. The code and data will be made available upon request for reproducibility.

Robust estimation methods are useful in mitigating the impact of anomalies in clock data. Such anomalous clock data is assumed to be well modeled by a Student’s t-distribution. This paper derives a lower bound on the performance of the misspecified Gaussian model using the theory of the Misspecified Cram´er-Rao bound (MCRB). The results of these derivations are verified by analyzing the Mean Square Error (MSE) of the misspecified Gaussian Maximum Likelihood Estimator (MLE) when using data generated by the Student’s t-distribution. The derived MCRB indicates a constraint on the MSE when assuming a Gaussian distribution. The MLE for the mean of the Student’s t-distribution is obtained with an Expectation maximization algorithm and is shown to obtain a lower MSE than the MCRB and hence, the misspecified estimator. This indicates an improvement in performance if anomalous clock data is appropriately accounted for in the statistical model.