Nonparametric two-sample tests based on RKHS distances (Eric et al., 2008; Fromont et al., 2012;

We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of high-dimensional piecewise continuous functions. DJGP overcomes the limitations of conventional Jump Gaussian Processes in high-dimensional input spaces by adding a locally linear projection layer to Jump Gaussian Processes. This projection uses region-specific matrices to capture local subspace structures, naturally complementing the localized nature of JGP, a variant of local Gaussian Processes. To control model complexity, we place a Gaussian Process prior on the projection matrices, allowing them to evolve smoothly across the input space. The projected inputs are then modeled with a JGP to capture piecewise continuous relationships with the response. This yields a distinctive two-layer deep learning of GP/JGP. We further develop a scalable variational inference algorithm to jointly learn the projection matrices and JGP hyperparameters. Experiments on synthetic and benchmark datasets demonstrate that DJGP delivers superior predictive accuracy and more reliable uncertainty quantification compared to existing approaches.

Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties.

We thank the reviewers for their thorough reading of our work. Mean Discrepancy (MMD) when the dimensionality goes to infinity. MMD provided that the summation of discrepancies between marginal univariate distributions is large enough. Our work is complementary and differs on several aspects. We will try to add a mention of this weakness in the manuscript.

Wildlife monitoring via camera traps has become an essential tool in ecology, but the deployment of machine learning models for on-device animal classification faces significant challenges due to domain shifts and resource constraints. This paper introduces WildFit, a novel approach that reconciles the conflicting goals of achieving high domain generalization performance and ensuring efficient inference for camera trap applications. WildFit leverages continuous background-aware model fine-tuning to deploy ML models tailored to the current location and time window, allowing it to maintain robust classification accuracy in the new environment without requiring significant computational resources. This is achieved by background-aware data synthesis, which generates training images representing the new domain by blending background images with animal images from the source domain. We further enhance fine-tuning effectiveness through background drift detection and class distribution drift detection, which optimize the quality of synthesized data and improve generalization performance. Our extensive evaluation across multiple camera trap datasets demonstrates that WildFit achieves significant improvements in classification accuracy and computational efficiency compared to traditional approaches.

We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the distribution over extrema. To this end, we devise a non-parametric conjugate prior based on a kernel regressor.

Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the distinguishability of the distributions, by optimizing a lower bound on test power for a statistical test using these features. The result is a parsimonious and interpretable indication of how and where two distributions differ locally. We show that the empirical estimate of the test power criterion converges with increasing sample size, ensuring the quality of the returned features. In real-world benchmarks on highdimensional text and image data, linear-time tests using the proposed semimetrics achieve comparable performance to the state-of-the-art quadratic-time maximum mean discrepancy test, while returning human-interpretable features that explain the test results.

Combining multi-spectral satellite data and machine learning has been suggested as a method for monitoring plastic pollutants in the ocean environment. Recent studies have made theoretical progress regarding the identification of marine plastic via machine learning. However, no study has assessed the application of these methods for mapping and monitoring marine-plastic density. As such, this paper comprised of three main components: (1) the development of a machine learning model, (2) the construction of the MAP-Mapper, an automated tool for mapping marine-plastic density, and finally (3) an evaluation of the whole system for out-of-distribution test locations. The findings from this paper leverage the fact that machine learning models need to be high-precision to reduce the impact of false positives on results. The developed MAP-Mapper architectures provide users choices to reach high-precision ($\textit{abbv.}$ -HP) or optimum precision-recall ($\textit{abbv.}$ -Opt) values in terms of the training/test data set. Our MAP-Mapper-HP model greatly increased the precision of plastic detection to 95\%, whilst MAP-Mapper-Opt reaches precision-recall pair of 87\%-88\%. The MAP-Mapper contributes to the literature with the first tool to exploit advanced deep/machine learning and multi-spectral imagery to map marine-plastic density in automated software. The proposed data pipeline has taken a novel approach to map plastic density in ocean regions. As such, this enables an initial assessment of the challenges and opportunities of this method to help guide future work and scientific study.