Recent advancements in Text-to-Speech (TTS) models, particularly in voice cloning, have intensified the demand for adaptable and efficient deepfake detection methods. As TTS systems continue to evolve, detection models must be able to efficiently adapt to previously unseen generation models with minimal data. This paper introduces ADD-GP, a few-shot adaptive framework based on a Gaussian Process (GP) classifier for Audio Deepfake Detection (ADD). We show how the combination of a powerful deep embedding model with the Gaussian processes flexibility can achieve strong performance and adaptability. Additionally, we show this approach can also be used for personalized detection, with greater robustness to new TTS models and one-shot adaptability. To support our evaluation, a benchmark dataset is constructed for this task using new state-of-the-art voice cloning models.
A longstanding goal in safe reinforcement learning (RL) is a method to ensure the safety of a policy throughout the entire process, from learning to operation. However, existing safe RL paradigms inherently struggle to achieve this objective. We propose a method, called Provably Lifetime Safe RL (PLS), that integrates offline safe RL with safe policy deployment to address this challenge. Our proposed method learns a policy offline using return-conditioned supervised learning and then deploys the resulting policy while cautiously optimizing a limited set of parameters, known as target returns, using Gaussian processes (GPs). Theoretically, we justify the use of GPs by analyzing the mathematical relationship between target and actual returns. We then prove that PLS finds near-optimal target returns while guaranteeing safety with high probability. Empirically, we demonstrate that PLS outperforms baselines both in safety and reward performance, thereby achieving the longstanding goal to obtain high rewards while ensuring the safety of a policy throughout the lifetime from learning to operation.
Kernels are key to encoding prior beliefs and data structures in Gaussian process (GP) models. The design of expressive and scalable kernels has garnered significant research attention. Deep kernel learning enhances kernel flexibility by feeding inputs through a neural network before applying a standard parametric form. However, this approach remains limited by the choice of base kernels, inherits high inference costs, and often demands sparse approximations. Drawing on Mercer's theorem, we introduce a fully data-driven, scalable deep kernel representation where a neural network directly represents a low-rank kernel through a small set of basis functions. This construction enables highly efficient exact GP inference in linear time and memory without invoking inducing points. It also supports scalable mini-batch training based on a principled variational inference framework. We further propose a simple variance correction procedure to guard against overconfidence in uncertainty estimates. Experiments on synthetic and real-world data demonstrate the advantages of our deep kernel GP in terms of predictive accuracy, uncertainty quantification, and computational efficiency.
Cell boundary information is crucial for analyzing cell behaviors from time-lapse microscopy videos. Existing supervised cell segmentation tools, such as ImageJ, require tuning various parameters and rely on restrictive assumptions about the shape of the objects. While recent supervised segmentation tools based on convolutional neural networks enhance accuracy, they depend on high-quality labelled images, making them unsuitable for segmenting new types of objects not in the database. We developed a novel unsupervised cell segmentation algorithm based on fast Gaussian processes for noisy microscopy images without the need for parameter tuning or restrictive assumptions about the shape of the object. We derived robust thresholding criteria adaptive for heterogeneous images containing distinct brightness at different parts to separate objects from the background, and employed watershed segmentation to distinguish touching cell objects. Both simulated studies and real-data analysis of large microscopy images demonstrate the scalability and accuracy of our approach compared with the alternatives.
Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on multi-output Gaussian processes (MOGP), to capture both the correlation between vertices and the correlation between associated data. The proposed formulation is built on the definition of MOGP. This allows it to be applied to a wide range of data configurations and scenarios. Moreover, it has high expressive capability due to its flexibility in kernel design. It includes existing methods of Gaussian processes for graph-structured data as special cases and is possible to remove restrictions on data configurations, model selection, and inference scenarios in the existing methods. The performance of extensions achievable by the proposed formulation is evaluated through computer experiments with synthetic and real data.
The increasing integration of renewable energy sources (RESs) and distributed energy resources (DERs) has significantly heightened operational complexity and uncertainty in modern power systems. Concurrently, the widespread deployment of smart meters, phasor measurement units (PMUs) and other sensors has generated vast spatiotemporal data streams, enabling advanced data-driven analytics and decision-making in grid operations. In this context, Gaussian processes (GPs) have emerged as a powerful probabilistic framework, offering uncertainty quantification, non-parametric modeling, and predictive capabilities to enhance power system analysis and control. This paper presents a comprehensive review of GP techniques and their applications in power system operation and control. GP applications are reviewed across three key domains: GP-based modeling, risk assessment, and optimization and control. These areas serve as representative examples of how GP can be utilized in power systems. Furthermore, critical challenges in GP applications are discussed, and potential research directions are outlined to facilitate future power system operations.
Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden changes, or "jumps" in the output variable. The "jump GP" (JGP) was developed for modeling data from such processes, combining local GPs and latent "level" variables under a joint inferential framework. But joint modeling can be fraught with difficulty. We aim to simplify by suggesting a more modular setup, eschewing joint inference but retaining the main JGP themes: (a) learning optimal neighborhood sizes that locally respect manifolds of discontinuity; and (b) a new cluster-based (latent) feature to capture regions of distinct output levels on both sides of the manifold. We show that each of (a) and (b) separately leads to dramatic improvements when modeling processes with jumps. In tandem (but without requiring joint inference) that benefit is compounded, as illustrated on real and synthetic benchmark examples from the recent literature.
Gaussian processes (GPs) play an essential role in biostatistics, scientific machine learning, and Bayesian optimization for their ability to provide probabilistic predictions and model uncertainty. However, GP inference struggles to scale to large datasets (which are common in modern applications), since it requires the solution of a linear system whose size scales quadratically with the number of samples in the dataset. We propose an approximate, distributed, accelerated sketch-and-project algorithm ($\texttt{ADASAP}$) for solving these linear systems, which improves scalability. We use the theory of determinantal point processes to show that the posterior mean induced by sketch-and-project rapidly converges to the true posterior mean. In particular, this yields the first efficient, condition number-free algorithm for estimating the posterior mean along the top spectral basis functions, showing that our approach is principled for GP inference. $\texttt{ADASAP}$ outperforms state-of-the-art solvers based on conjugate gradient and coordinate descent across several benchmark datasets and a large-scale Bayesian optimization task. Moreover, $\texttt{ADASAP}$ scales to a dataset with $> 3 \cdot 10^8$ samples, a feat which has not been accomplished in the literature.
Multi-agent simulations enables the modeling and analyses of the dynamic behaviors and interactions of autonomous entities evolving in complex environments. Agent-based models (ABM) are widely used to study emergent phenomena arising from local interactions. However, their high computational cost poses a significant challenge, particularly for large-scale simulations requiring extensive parameter exploration, optimization, or uncertainty quantification. The increasing complexity of ABM limits their feasibility for real-time decision-making and large-scale scenario analysis. To address these limitations, surrogate models offer an efficient alternative by learning approximations from sparse simulation data. These models provide cheap-to-evaluate predictions, significantly reducing computational costs while maintaining accuracy. Various machine learning techniques, including regression models, neural networks, random forests and Gaussian processes, have been applied to construct robust surrogates. Moreover, uncertainty quantification and sensitivity analysis play a crucial role in enhancing model reliability and interpretability. This article explores the motivations, methods, and applications of surrogate modeling for ABM, emphasizing the trade-offs between accuracy, computational efficiency, and interpretability. Through a case study on a segregation model, we highlight the challenges associated with building and validating surrogate models, comparing different approaches and evaluating their performance. Finally, we discuss future perspectives on integrating surrogate models within ABM to improve scalability, explainability, and real-time decision support across various fields such as ecology, urban planning and economics.
Healthcare data, particularly in critical care settings, presents three key challenges for analysis. First, physiological measurements come from different sources but are inherently related. Yet, traditional methods often treat each measurement type independently, losing valuable information about their relationships. Second, clinical measurements are collected at irregular intervals, and these sampling times can carry clinical meaning. Finally, the prevalence of missing values. Whilst several imputation methods exist to tackle this common problem, they often fail to address the temporal nature of the data or provide estimates of uncertainty in their predictions. We propose using deep Gaussian process emulation with stochastic imputation, a methodology initially conceived to deal with computationally expensive models and uncertainty quantification, to solve the problem of handling missing values that naturally occur in critical care data. This method leverages longitudinal and cross-sectional information and provides uncertainty estimation for the imputed values. Our evaluation of a clinical dataset shows that the proposed method performs better than conventional methods, such as multiple imputations with chained equations (MICE), last-known value imputation, and individually fitted Gaussian Processes (GPs).
Gaussian Process based Bayesian Optimization is a widely applied algorithm to learn and optimize under uncertainty, well-known for its sample efficiency. However, recently -- and more frequently -- research studies have empirically demonstrated that the Gaussian Process fitting procedure at its core could be its most relevant weakness. Fitting a Gaussian Process means tuning its kernel's hyperparameters to a set of observations, but the common Maximum Likelihood Estimation technique, usually appropriate for learning tasks, has shown different criticalities in Bayesian Optimization, making theoretical analysis of this algorithm an open challenge. Exploiting the analogy between Gaussian Processes and Gaussian Distributions, we present a new approach which uses a prefixed set of hyperparameters values to fit as many Gaussian Processes and then combines them into a unique model as a Wasserstein Barycenter of Gaussian Processes. We considered both "easy" test problems and others known to undermine the \textit{vanilla} Bayesian Optimization algorithm. The new method, namely Wasserstein Barycenter Gausssian Process based Bayesian Optimization (WBGP-BO), resulted promising and able to converge to the optimum, contrary to vanilla Bayesian Optimization, also on the most "tricky" test problems.
Predicting the labels of graph-structured data is crucial in scientific applications and is often achieved using graph neural networks (GNNs). However, when data is scarce, GNNs suffer from overfitting, leading to poor performance. Recently, Gaussian processes (GPs) with graph-level inputs have been proposed as an alternative. In this work, we extend the Gaussian process framework to simplicial complexes (SCs), enabling the handling of edge-level attributes and attributes supported on higher-order simplices. We further augment the resulting SC representations by considering their Hodge decompositions, allowing us to account for homological information, such as the number of holes, in the SC. We demonstrate that our framework enhances the predictions across various applications, paving the way for GPs to be more widely used for graph and SC-level predictions.
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is large or when the underlying function contains multi-scale features that are difficult to represent by a stationary kernel. To address the former, training of GPs with large-scale data is often performed through inducing point approximations (also known as sparse GP regression (GPR)), where the size of the covariance matrices in GPR is reduced considerably through a greedy search on the data set. To aid the latter, deep GPs have gained traction as hierarchical models that resolve multi-scale features by combining multiple GPs. Posterior inference in deep GPs requires a sampling or, more usual, a variational approximation. Variational approximations lead to large-scale stochastic, non-convex optimisation problems and the resulting approximation tends to represent uncertainty incorrectly. In this work, we combine variational learning with MCMC to develop a particle-based expectation-maximisation method to simultaneously find inducing points within the large-scale data (variationally) and accurately train the GPs (sampling-based). The result is a highly efficient and accurate methodology for deep GP training on large-scale data. We test our method on standard benchmark problems.
Constrained Bayesian optimization (CBO) methods have seen significant success in black-box optimization with constraints, and one of the most commonly used CBO methods is the constrained expected improvement (CEI) algorithm. CEI is a natural extension of the expected improvement (EI) when constraints are incorporated. However, the theoretical convergence rate of CEI has not been established. In this work, we study the convergence rate of CEI by analyzing its simple regret upper bound. First, we show that when the objective function $f$ and constraint function $c$ are assumed to each lie in a reproducing kernel Hilbert space (RKHS), CEI achieves the convergence rates of $\mathcal{O} \left(t^{-\frac{1}{2}}\log^{\frac{d+1}{2}}(t) \right) \ \text{and }\ \mathcal{O}\left(t^{\frac{-\nu}{2\nu+d}} \log^{\frac{\nu}{2\nu+d}}(t)\right)$ for the commonly used squared exponential and Mat\'{e}rn kernels, respectively. Second, we show that when $f$ and $c$ are assumed to be sampled from Gaussian processes (GPs), CEI achieves the same convergence rates with a high probability. Numerical experiments are performed to validate the theoretical analysis.
Kernel-based conditional independence (KCI) testing is a powerful nonparametric method commonly employed in causal discovery tasks. Despite its flexibility and statistical reliability, cubic computational complexity limits its application to large datasets. To address this computational bottleneck, we propose \textit{FastKCI}, a scalable and parallelizable kernel-based conditional independence test that utilizes a mixture-of-experts approach inspired by embarrassingly parallel inference techniques for Gaussian processes. By partitioning the dataset based on a Gaussian mixture model over the conditioning variables, FastKCI conducts local KCI tests in parallel, aggregating the results using an importance-weighted sampling scheme. Experiments on synthetic datasets and benchmarks on real-world production data validate that FastKCI maintains the statistical power of the original KCI test while achieving substantial computational speedups. FastKCI thus represents a practical and efficient solution for conditional independence testing in causal inference on large-scale data.
Algorithmic fairness has become a central topic in machine learning, and mitigating disparities across different subpopulations has emerged as a rapidly growing research area. In this paper, we systematically study the classification of functional data under fairness constraints, ensuring the disparity level of the classifier is controlled below a pre-specified threshold. We propose a unified framework for fairness-aware functional classification, tackling an infinite-dimensional functional space, addressing key challenges from the absence of density ratios and intractability of posterior probabilities, and discussing unique phenomena in functional classification. We further design a post-processing algorithm, Fair Functional Linear Discriminant Analysis classifier (Fair-FLDA), which targets at homoscedastic Gaussian processes and achieves fairness via group-wise thresholding. Under weak structural assumptions on eigenspace, theoretical guarantees on fairness and excess risk controls are established. As a byproduct, our results cover the excess risk control of the standard FLDA as a special case, which, to the best of our knowledge, is first time seen. Our theoretical findings are complemented by extensive numerical experiments on synthetic and real datasets, highlighting the practicality of our designed algorithm.
Accurate probabilistic forecasting of wind power is essential for maintaining grid stability and enabling efficient integration of renewable energy sources. Gaussian Process (GP) models offer a principled framework for quantifying uncertainty; however, conventional approaches rely on stationary kernels, which are inadequate for modeling the inherently non-stationary nature of wind speed and power output. We propose a non-stationary GP framework that incorporates the generalized spectral mixture (GSM) kernel, enabling the model to capture time-varying patterns and heteroscedastic behaviors in wind speed and wind power data. We evaluate the performance of the proposed model on real-world SCADA data across short\mbox{-,} medium-, and long-term forecasting horizons. Compared to standard radial basis function and spectral mixture kernels, the GSM-based model outperforms, particularly in short-term forecasts. These results highlight the necessity of modeling non-stationarity in wind power forecasting and demonstrate the practical value of non-stationary GP models in operational settings.
Gaussian process regression is a popular model in the small data regime due to its sound uncertainty quantification and the exploitation of the smoothness of the regression function that is encountered in a wide range of practical problems. However, Gaussian processes perform sub-optimally when the degree of smoothness is non-homogeneous across the input domain. Random forest regression partially addresses this issue by providing local basis functions of variable support set sizes that are chosen in a data-driven way. However, they do so at the expense of forgoing any degree of smoothness, which often results in poor performance in the small data regime. Here, we aim to combine the advantages of both models by applying a kernel-based smoothing mechanism to a learned random forest or any other piecewise constant prediction function. As we demonstrate empirically, the resulting model consistently improves the predictive performance of the underlying random forests and, in almost all test cases, also improves the log loss of the usual uncertainty quantification based on inter-tree variance. The latter advantage can be attributed to the ability of the smoothing model to take into account the uncertainty over the exact tree-splitting locations.
Telling apart the cause and effect between two random variables with purely observational data is a challenging problem that finds applications in various scientific disciplines. A key principle utilized in this task is the algorithmic Markov condition, which postulates that the joint distribution, when factorized according to the causal direction, yields a more succinct codelength compared to the anti-causal direction. Previous approaches approximate these codelengths by relying on simple functions or Gaussian processes (GPs) with easily evaluable complexity, compromising between model fitness and computational complexity. To overcome these limitations, we propose leveraging the variational Bayesian learning of neural networks as an interpretation of the codelengths. Consequently, we can enhance the model fitness while promoting the succinctness of the codelengths, while avoiding the significant computational complexity of the GP-based approaches. Extensive experiments on both synthetic and real-world benchmarks in cause-effect identification demonstrate the effectiveness of our proposed method, surpassing the overall performance of related complexity-based and structural causal model regression-based approaches.
Motivation: Understanding the spatial architecture of tissues is essential for decoding the complex interactions within cellular ecosystems and their implications for disease pathology and clinical outcomes. Recent advances in multiplex imaging technologies have enabled high-resolution profiling of cellular phenotypes and their spatial distributions, revealing critical roles of tissue structures such as tertiary lymphoid structures (TLSs) in shaping immune responses and influencing disease progression. However, existing methods for analyzing spatial tissue structures often rely on hard clustering or adjacency-based spatial models, which are limited in capturing the nuanced and overlapping nature of cellular communities. To address these challenges, we develop a novel spatial topic modeling framework for the unsupervised discovery of spatial tissue structures in multiplex imaging data. Results: We propose TopSpace, a novel Bayesian spatial topic model that integrates Gaussian processes into latent Dirichlet allocation to flexibly model spatial dependencies in tissue microenvironments. By leveraging the Bayesian framework, TopSpace supports multicellular mixed-membership clustering and offers key inferential advantages, including robust uncertainty quantification and data-driven determination of the number of multicellular microenvironments. We demonstrate the utility of TopSpace through simulations and a case study on non-small cell lung cancer (NSCLC) data. Simulations show that TopSpace accurately recovers latent tissue microenvironments and spatial clustering patterns, outperforming existing methods in scenarios with varying spatial dependencies. Applied to NSCLC data, TopSpace successfully identifies TLS and captures their spatial probability distribution, which strongly correlates with patient survival outcomes.