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Motivated by the need for computationally tractable spatial methods in neuroimaging studies, we develop a distributed and integrated framework for estimation and inference of Gaussian process model parameters with ultra-high-dimensional likelihoods. We propose a shift in viewpoint from whole to local data perspectives that is rooted in distributed model building and integrated estimation and inference. The framework's backbone is a computationally and statistically efficient integration procedure that simultaneously incorporates dependence within and between spatial resolutions in a recursively partitioned spatial domain. Statistical and computational properties of our distributed approach are investigated theoretically and in simulations. The proposed approach is used to extract new insights on autism spectrum disorder from the Autism Brain Imaging Data Exchange.

Multi-fidelity models provide a framework for integrating computational models of varying complexity, allowing for accurate predictions while optimizing computational resources. These models are especially beneficial when acquiring high-accuracy data is costly or computationally intensive. This review offers a comprehensive analysis of multi-fidelity models, focusing on their applications in scientific and engineering fields, particularly in optimization and uncertainty quantification. It classifies publications on multi-fidelity modeling according to several criteria, including application area, surrogate model selection, types of fidelity, combination methods and year of publication. The study investigates techniques for combining different fidelity levels, with an emphasis on multi-fidelity surrogate models. This work discusses reproducibility, open-sourcing methodologies and benchmarking procedures to promote transparency. The manuscript also includes educational toy problems to enhance understanding. Additionally, this paper outlines best practices for presenting multi-fidelity-related savings in a standardized, succinct and yet thorough manner. The review concludes by examining current trends in multi-fidelity modeling, including emerging techniques, recent advancements, and promising research directions.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at //github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target. Recent literature has focused extensively on assessing the error between the target and estimated distributions, gauging the generative quality through the Kullback-Leibler (KL) divergence and Wasserstein distances. All existing results have been obtained so far for time-homogeneous speed of the noise schedule. Under mild assumptions on the data distribution, we establish an upper bound for the KL divergence between the target and the estimated distributions, explicitly depending on any time-dependent noise schedule. Assuming that the score is Lipschitz continuous, we provide an improved error bound in Wasserstein distance, taking advantage of favourable underlying contraction mechanisms. We also propose an algorithm to automatically tune the noise schedule using the proposed upper bound. We illustrate empirically the performance of the noise schedule optimization in comparison to standard choices in the literature.

The Spatial AutoRegressive model (SAR) is commonly used in studies involving spatial and network data to estimate the spatial or network peer influence and the effects of covariates on the response, taking into account the spatial or network dependence. While the model can be efficiently estimated with a Quasi maximum likelihood approach (QMLE), the detrimental effect of covariate measurement error on the QMLE and how to remedy it is currently unknown. If covariates are measured with error, then the QMLE may not have the $\sqrt{n}$ convergence and may even be inconsistent even when a node is influenced by only a limited number of other nodes or spatial units. We develop a measurement error-corrected ML estimator (ME-QMLE) for the parameters of the SAR model when covariates are measured with error. The ME-QMLE possesses statistical consistency and asymptotic normality properties. We consider two types of applications. The first is when the true covariate cannot be measured directly, and a proxy is observed instead. The second one involves including latent homophily factors estimated with error from the network for estimating peer influence. Our numerical results verify the bias correction property of the estimator and the accuracy of the standard error estimates in finite samples. We illustrate the method on a real dataset related to county-level death rates from the COVID-19 pandemic.

Graph representation learning (GRL) is critical for extracting insights from complex network structures, but it also raises security concerns due to potential privacy vulnerabilities in these representations. This paper investigates the structural vulnerabilities in graph neural models where sensitive topological information can be inferred through edge reconstruction attacks. Our research primarily addresses the theoretical underpinnings of cosine-similarity-based edge reconstruction attacks (COSERA), providing theoretical and empirical evidence that such attacks can perfectly reconstruct sparse Erdos Renyi graphs with independent random features as graph size increases. Conversely, we establish that sparsity is a critical factor for COSERA's effectiveness, as demonstrated through analysis and experiments on stochastic block models. Finally, we explore the resilience of (provably) private graph representations produced via noisy aggregation (NAG) mechanism against COSERA. We empirically delineate instances wherein COSERA demonstrates both efficacy and deficiency in its capacity to function as an instrument for elucidating the trade-off between privacy and utility.

Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input may strongly differ from the true underlying data. However, recent works suggest that this bias is low in the context of high-dimensional linear predictors when data is supposed to be missing completely at random (MCAR). This paper completes the picture for linear predictors by confirming the intuition that the bias is negligible and that surprisingly naive imputation also remains relevant in very low dimension.To this aim, we consider a unique underlying random features model, which offers a rigorous framework for studying predictive performances, whilst the dimension of the observed features varies.Building on these theoretical results, we establish finite-sample bounds on stochastic gradient (SGD) predictors applied to zero-imputed data, a strategy particularly well suited for large-scale learning.If the MCAR assumption appears to be strong, we show that similar favorable behaviors occur for more complex missing data scenarios.

We consider the estimation of the cumulative hazard function, and equivalently the distribution function, with censored data under a setup that preserves the privacy of the survival database. This is done through a $\alpha$-locally differentially private mechanism for the failure indicators and by proposing a non-parametric kernel estimator for the cumulative hazard function that remains consistent under the privatization. Under mild conditions, we also prove lowers bounds for the minimax rates of convergence and show that estimator is minimax optimal under a well-chosen bandwidth.

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the curse of dimensionality whenever the number of variables increases. This challenge is generally addressed by assuming additional structure in theproblem, the preferred options being either additivity or low intrinsic dimensionality. Our contribution for high-dimensional Gaussian process modeling is to combine them with a multi-fidelity strategy, showcasing the advantages through experiments on synthetic functions and datasets.