High spatial resolution wind data are essential for a wide range of applications in climate, oceanographic and meteorological studies. Large-scale spatial interpolation or downscaling of bivariate wind fields having velocity in two dimensions is a challenging task because wind data tend to be non-Gaussian with high spatial variability and heterogeneity. In spatial statistics, cokriging is commonly used for predicting bivariate spatial fields. However, the cokriging predictor is not optimal except for Gaussian processes. Additionally, cokriging is computationally prohibitive for large datasets. In this paper, we propose a method, called bivariate DeepKriging, which is a spatially dependent deep neural network (DNN) with an embedding layer constructed by spatial radial basis functions for bivariate spatial data prediction. We then develop a distribution-free uncertainty quantification method based on bootstrap and ensemble DNN. Our proposed approach outperforms the traditional cokriging predictor with commonly used covariance functions, such as the linear model of co-regionalization and flexible bivariate Mat\'ern covariance. We demonstrate the computational efficiency and scalability of the proposed DNN model, with computations that are, on average, 20 times faster than those of conventional techniques. We apply the bivariate DeepKriging method to the wind data over the Middle East region at 506,771 locations. The prediction performance of the proposed method is superior over the cokriging predictors and dramatically reduces computation time.

Bayesian inference has many advantages in robotic motion planning over four perspectives: The uncertainty quantification of the policy, safety (risk-aware) and optimum guarantees of robot motions, data-efficiency in training of reinforcement learning, and reducing the sim2real gap when the robot is applied to real-world tasks. However, the application of Bayesian inference in robotic motion planning is lagging behind the comprehensive theory of Bayesian inference. Further, there are no comprehensive reviews to summarize the progress of Bayesian inference to give researchers a systematic understanding in robotic motion planning. This paper first provides the probabilistic theories of Bayesian inference which are the preliminary of Bayesian inference for complex cases. Second, the Bayesian estimation is given to estimate the posterior of policies or unknown functions which are used to compute the policy. Third, the classical model-based Bayesian RL and model-free Bayesian RL algorithms for robotic motion planning are summarized, while these algorithms in complex cases are also analyzed. Fourth, the analysis of Bayesian inference in inverse RL is given to infer the reward functions in a data-efficient manner. Fifth, we systematically present the hybridization of Bayesian inference and RL which is a promising direction to improve the convergence of RL for better motion planning. Sixth, given the Bayesian inference, we present the interpretable and safe robotic motion plannings which are the hot research topic recently. Finally, all algorithms reviewed in this paper are summarized analytically as the knowledge graphs, and the future of Bayesian inference for robotic motion planning is also discussed, to pave the way for data-efficient, explainable, and safe robotic motion planning strategies for practical applications.

Deep learning (DL) models have emerged as a promising solution for the Internet of Things (IoT). However, due to their computational complexity, DL models consume significant amounts of energy, which can rapidly drain the battery and compromise the performance of IoT devices. For sustainable operation, we consider an edge device with a rechargeable battery and energy harvesting (EH) capabilities. In addition to the stochastic nature of the ambient energy source, the harvesting rate is often insufficient to meet the inference energy requirements, leading to drastic performance degradation in energy-agnostic devices. To mitigate this problem, we propose energy-adaptive dynamic early exiting (EE) to enable efficient and accurate inference in an EH edge intelligence system. Our approach derives an energy-aware EE policy that determines the optimal amount of computational processing on a per-sample basis. The proposed policy balances the energy consumption to match the limited incoming energy and achieves continuous availability. Numerical results show that accuracy and service rate are improved up to 25% and 35%, respectively, in comparison with an energy-agnostic policy.

Ensemble Kalman inversion (EKI) is a sequential Monte Carlo method used to solve inverse problems within a Bayesian framework. Unlike backpropagation, EKI is a gradient-free optimization method that only necessitates the evaluation of artificial neural networks in forward passes. In this study, we examine the effectiveness of EKI in training neural ordinary differential equations (neural ODEs) for system identification and control tasks. To apply EKI to optimal control problems, we formulate inverse problems that incorporate a Tikhonov-type regularization term. Our numerical results demonstrate that EKI is an efficient method for training neural ODEs in system identification and optimal control problems, with runtime and quality of solutions that are competitive with commonly used gradient-based optimizers.

The problem of model selection is considered for the setting of interpolating estimators, where the number of model parameters exceeds the size of the dataset. Classical information criteria typically consider the large-data limit, penalizing model size. However, these criteria are not appropriate in modern settings where overparameterized models tend to perform well. For any overparameterized model, we show that there exists a dual underparameterized model that possesses the same marginal likelihood, thus establishing a form of Bayesian duality. This enables more classical methods to be used in the overparameterized setting, revealing the Interpolating Information Criterion, a measure of model quality that naturally incorporates the choice of prior into the model selection. Our new information criterion accounts for prior misspecification, geometric and spectral properties of the model, and is numerically consistent with known empirical and theoretical behavior in this regime.

In this work, we propose a novel prior learning method for advancing generalization and uncertainty estimation in deep neural networks. The key idea is to exploit scalable and structured posteriors of neural networks as informative priors with generalization guarantees. Our learned priors provide expressive probabilistic representations at large scale, like Bayesian counterparts of pre-trained models on ImageNet, and further produce non-vacuous generalization bounds. We also extend this idea to a continual learning framework, where the favorable properties of our priors are desirable. Major enablers are our technical contributions: (1) the sums-of-Kronecker-product computations, and (2) the derivations and optimizations of tractable objectives that lead to improved generalization bounds. Empirically, we exhaustively show the effectiveness of this method for uncertainty estimation and generalization.

This paper investigates the utility gain of using Iterative Bayesian Update (IBU) for private discrete distribution estimation using data obfuscated with Locally Differentially Private (LDP) mechanisms. We compare the performance of IBU to Matrix Inversion (MI), a standard estimation technique, for seven LDP mechanisms designed for one-time data collection and for other seven LDP mechanisms designed for multiple data collections (e.g., RAPPOR). To broaden the scope of our study, we also varied the utility metric, the number of users n, the domain size k, and the privacy parameter {\epsilon}, using both synthetic and real-world data. Our results suggest that IBU can be a useful post-processing tool for improving the utility of LDP mechanisms in different scenarios without any additional privacy cost. For instance, our experiments show that IBU can provide better utility than MI, especially in high privacy regimes (i.e., when {\epsilon} is small). Our paper provides insights for practitioners to use IBU in conjunction with existing LDP mechanisms for more accurate and privacy-preserving data analysis. Finally, we implemented IBU for all fourteen LDP mechanisms into the state-of-the-art multi-freq-ldpy Python package (https://pypi.org/project/multi-freq-ldpy/) and open-sourced all our code used for the experiments as tutorials.

Model-based disease mapping remains a fundamental policy-informing tool in the fields of public health and disease surveillance. Hierarchical Bayesian models have emerged as the state-of-the-art approach for disease mapping since they are able to both capture structure in the data and robustly characterise uncertainty. When working with areal data, e.g.~aggregates at the administrative unit level such as district or province, current models rely on the adjacency structure of areal units to account for spatial correlations and perform shrinkage. The goal of disease surveillance systems is to track disease outcomes over time. This task is especially challenging in crisis situations which often lead to redrawn administrative boundaries, meaning that data collected before and after the crisis are no longer directly comparable. Moreover, the adjacency-based approach ignores the continuous nature of spatial processes and cannot solve the change-of-support problem, i.e.~when estimates are required to be produced at different administrative levels or levels of aggregation. We present a novel, practical, and easy to implement solution to solve these problems relying on a methodology combining deep generative modelling and fully Bayesian inference: we build on the recently proposed PriorVAE method able to encode spatial priors over small areas with variational autoencoders by encoding aggregates over administrative units. We map malaria prevalence in Kenya, a country in which administrative boundaries changed in 2010.

This paper proposes a Bayesian model to compare multiple algorithms on multiple data sets, on any metric. The model is based on the Bradley-Terry model, that counts the number of times one algorithm performs better than another on different data sets. Because of its Bayesian foundations, the Bayesian Bradley Terry model (BBT) has different characteristics than frequentist approaches to comparing multiple algorithms on multiple data sets, such as Demsar (2006) tests on mean rank, and Benavoli et al. (2016) multiple pairwise Wilcoxon tests with p-adjustment procedures. In particular, a Bayesian approach allows for more nuanced statements regarding the algorithms beyond claiming that the difference is or it is not statistically significant. Bayesian approaches also allow to define when two algorithms are equivalent for practical purposes, or the region of practical equivalence (ROPE). Different than a Bayesian signed rank comparison procedure proposed by Benavoli et al. (2017), our approach can define a ROPE for any metric, since it is based on probability statements, and not on differences of that metric. This paper also proposes a local ROPE concept, that evaluates whether a positive difference between a mean measure across some cross validation to the mean of some other algorithms is should be really seen as the first algorithm being better than the second, based on effect sizes. This local ROPE proposal is independent of a Bayesian use, and can be used in frequentist approaches based on ranks. A R package and a Python program that implements the BBT is available.

Annotating musical beats is a very long and tedious process. In order to combat this problem, we present a new self-supervised learning pretext task for beat tracking and downbeat estimation. This task makes use of Spleeter, an audio source separation model, to separate a song's drums from the rest of its signal. The first set of signals are used as positives, and by extension negatives, for contrastive learning pre-training. The drum-less signals, on the other hand, are used as anchors. When pre-training a fully-convolutional and recurrent model using this pretext task, an onset function is learned. In some cases, this function is found to be mapped to periodic elements in a song. We find that pre-trained models outperform randomly initialized models when a beat tracking training set is extremely small (less than 10 examples). When this is not the case, pre-training leads to a learning speed-up that causes the model to overfit to the training set. More generally, this work defines new perspectives in the realm of musical self-supervised learning. It is notably one of the first works to use audio source separation as a fundamental component of self-supervision.