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Gaussian processes (GPs) are a popular class of Bayesian nonparametric models, but its training can be computationally burdensome for massive training datasets. While there has been notable work on scaling up these models for big data, existing methods typically rely on a stationary GP assumption for approximation, and can thus perform poorly when the underlying response surface is non-stationary, i.e., it has some regions of rapid change and other regions with little change. Such non-stationarity is, however, ubiquitous in real-world problems, including our motivating application for surrogate modeling of computer experiments. We thus propose a new Product of Sparse GP (ProSpar-GP) method for scalable GP modeling with massive non-stationary data. The ProSpar-GP makes use of a carefully-constructed product-of-experts formulation of sparse GP experts, where different experts are placed within local regions of non-stationarity. These GP experts are fit via a novel variational inference approach, which capitalizes on mini-batching and GPU acceleration for efficient optimization of inducing points and length-scale parameters for each expert. We further show that the ProSpar-GP is Kolmogorov-consistent, in that its generative distribution defines a valid stochastic process over the prediction space; such a property provides essential stability for variational inference, particularly in the presence of non-stationarity. We then demonstrate the improved performance of the ProSpar-GP over the state-of-the-art, in a suite of numerical experiments and an application for surrogate modeling of a satellite drag simulator.

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based brain models.

We present USLR, a computational framework for longitudinal registration of brain MRI scans to estimate nonlinear image trajectories that are smooth across time, unbiased to any timepoint, and robust to imaging artefacts. It operates on the Lie algebra parameterisation of spatial transforms (which is compatible with rigid transforms and stationary velocity fields for nonlinear deformation) and takes advantage of log-domain properties to solve the problem using Bayesian inference. USRL estimates rigid and nonlinear registrations that: (i) bring all timepoints to an unbiased subject-specific space; and (i) compute a smooth trajectory across the imaging time-series. We capitalise on learning-based registration algorithms and closed-form expressions for fast inference. A use-case Alzheimer's disease study is used to showcase the benefits of the pipeline in multiple fronts, such as time-consistent image segmentation to reduce intra-subject variability, subject-specific prediction or population analysis using tensor-based morphometry. We demonstrate that such approach improves upon cross-sectional methods in identifying group differences, which can be helpful in detecting more subtle atrophy levels or in reducing sample sizes in clinical trials. The code is publicly available in //github.com/acasamitjana/uslr

A significant limitation of the LTE-V2X and NR-V2X sidelink scheduling mechanisms is their difficulty coping with variations in inter packet arrival times, also known as aperiodic packets. This conflicts with the fundamental characteristics of most V2X services which are triggered based on an event. e.g. ETSI Cooperative Awareness Messages (CAMs) - vehicle kinematics, Cooperative Perception Messages (CPMs) - object sensing and Decentralised Event Notification Messages (DENMs) - event occurrences. Furthermore, network management techniques such as congestion control mechanisms can result in varied inter packet arrival times. To combat this, NR-V2X introduced a dynamic grant mechanism, which we show is ineffective unless there is background periodic traffic to stabilise the sensing history upon which the scheduler makes it decisions. The characteristics of V2X services make it implausible that such periodic application traffic will exist. To overcome this significant drawback, we demonstrate that the standardised scheduling algorithms can be made effective if the event triggered arrival rate of packets can be accurately predicted. These predictions can be used to tune the Resource Reservation Interval (RRI) parameter of the MAC scheduler to negate the negative impact of aperiodicity. Such an approach allows the scheduler to achieve comparable performance to a scenario where packets arrive periodically. To demonstrate the effectiveness of our approach, an ML model has been devised for the prediction of cooperative awareness messages, but the same principle can be abstracted to other V2X service types.

This study addresses the significant challenge of developing efficient decoding algorithms for classifying steady-state visual evoked potentials (SSVEPs) in scenarios characterized by extreme scarcity of calibration data, where only one calibration is available for each stimulus target. To tackle this problem, we introduce a novel cross-subject dual-domain fusion network (CSDuDoFN) incorporating task-related and task-discriminant component analysis (TRCA and TDCA) for one-shot SSVEP classification. The CSDuDoFN framework is designed to comprehensively transfer information from source subjects, while TRCA and TDCA are employed to exploit the single available calibration of the target subject. Specifically, we develop multi-reference least-squares transformation (MLST) to map data from both source subjects and the target subject into the domain of sine-cosine templates, thereby mitigating inter-individual variability and benefiting transfer learning. Subsequently, the transformed data in the sine-cosine templates domain and the original domain data are separately utilized to train a convolutional neural network (CNN) model, with the adequate fusion of their feature maps occurring at distinct network layers. To further capitalize on the calibration of the target subject, source aliasing matrix estimation (SAME) data augmentation is incorporated into the training process of the ensemble TRCA (eTRCA) and TDCA models. Ultimately, the outputs of the CSDuDoFN, eTRCA, and TDCA are combined for SSVEP classification. The effectiveness of our proposed approach is comprehensively evaluated on three publicly available SSVEP datasets, achieving the best performance on two datasets and competitive performance on one. This underscores the potential for integrating brain-computer interface (BCI) into daily life.

We consider two applications where we study how dependence structure between many variables is linked to external network data. We first study the interplay between social media connectedness and the co-evolution of the COVID-19 pandemic across USA counties. We next study study how the dependence between stock market returns across firms relates to similarities in economic and policy indicators from text regulatory filings. Both applications are modelled via Gaussian graphical models where one has external network data. We develop spike-and-slab and graphical LASSO frameworks to integrate the network data, both facilitating the interpretation of the graphical model and improving inference. The goal is to detect when the network data relates to the graphical model and, if so, explain how. We found that counties strongly connected on Facebook are more likely to have similar COVID-19 evolution (positive partial correlations), accounting for various factors driving the mean. We also found that the association in stock market returns depends in a stronger fashion on economic than on policy indicators. The examples show that data integration can improve interpretation, statistical accuracy, and out-of-sample prediction, in some instances using significantly sparser graphical models.

Topological signal processing (TSP) over simplicial complexes typically assumes observations associated with the simplicial complexes are real scalars. In this paper, we develop TSP theories for the case where observations belong to general abelian groups, including function spaces that are commonly used to represent time-varying signals. Our approach generalizes the Hodge decomposition and allows for signal processing tasks to be performed on these more complex observations. We propose a unified and flexible framework for TSP that expands its applicability to a wider range of signal processing applications. Numerical results demonstrate the effectiveness of this approach and provide a foundation for future research in this area.

Traditional perturbative statistical disclosure control (SDC) approaches such as microaggregation, noise addition, rank swapping, etc, perturb the data in an ``ad-hoc" way in the sense that while they manage to preserve some particular aspects of the data, they end up modifying others. Synthetic data approaches based on the fully conditional specification data synthesis paradigm, on the other hand, aim to generate new datasets that follow the same joint probability distribution as the original data. These synthetic data approaches, however, rely either on parametric statistical models, or non-parametric machine learning models, which need to fit well the original data in order to generate credible and useful synthetic data. Another important drawback is that they tend to perform better when the variables are synthesized in the correct causal order (i.e., in the same order as the true data generating process), which is often unknown in practice. To circumvent these issues, we propose a fully non-parametric and model free perturbative SDC approach that approximates the joint distribution of the original data via sequential applications of restricted permutations to the numerical microdata (where the restricted permutations are guided by the joint distribution of a discretized version of the data). Empirical comparisons against popular SDC approaches, using both real and simulated datasets, suggest that the proposed approach is competitive in terms of the trade-off between confidentiality and data utility.

Numerical simulations of kinetic problems can become prohibitively expensive due to their large memory footprint and computational costs. A method that has proven to successfully reduce these costs is the dynamical low-rank approximation (DLRA). One key question when using DLRA methods is the construction of robust time integrators that preserve the invariances and associated conservation laws of the original problem. In this work, we demonstrate that the augmented basis update & Galerkin integrator (BUG) preserves solution invariances and the associated conservation laws when using a conservative truncation step and an appropriate time and space discretization. We present numerical comparisons to existing conservative integrators and discuss advantages and disadvantages

Nowadays, deep-learning image coding solutions have shown similar or better compression efficiency than conventional solutions based on hand-crafted transforms and spatial prediction techniques. These deep-learning codecs require a large training set of images and a training methodology to obtain a suitable model (set of parameters) for efficient compression. The training is performed with an optimization algorithm which provides a way to minimize the loss function. Therefore, the loss function plays a key role in the overall performance and includes a differentiable quality metric that attempts to mimic human perception. The main objective of this paper is to study the perceptual impact of several image quality metrics that can be used in the loss function of the training process, through a crowdsourcing subjective image quality assessment study. From this study, it is possible to conclude that the choice of the quality metric is critical for the perceptual performance of the deep-learning codec and that can vary depending on the image content.