Approximation Of Posterior Distribution Research Articles

Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models

Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, i.e., on large data sets. In this article, we present iterative methods to overcome this drawback. Among other things, we introduce and analyze several preconditioners, derive new convergence results, and propose novel methods for accurately approximating predictive variances. We analyze our proposed methods theoretically and in experiments with simulated and real-world data. In particular, we obtain a speed-up of an order of magnitude compared to Cholesky-based calculations and a threefold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite data set. All methods are implemented in a free C++ software library with high-level Python and R packages. 4

Copula Approximate Bayesian Computation Using Distribution Random Forests

Ongoing modern computational advancements continue to make it easier to collect increasingly large and complex datasets, which can often only be realistically analyzed using models defined by intractable likelihood functions. This Stats invited feature article introduces and provides an extensive simulation study of a new approximate Bayesian computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the parameters of models defined by intractable likelihoods, that unifies and extends previous ABC methods proposed separately. This framework, copulaABCdrf, aims to accurately estimate and describe the possibly skewed and high-dimensional posterior distribution by a novel multivariate copula-based meta-t distribution based on univariate marginal posterior distributions that can be accurately estimated by distribution random forests (drf), while performing automatic summary statistics (covariates) selection, based on robustly estimated copula dependence parameters. The copulaABCdrf framework also provides a novel multivariate mode estimator to perform MLE and posterior mode estimation and an optional step to perform model selection from a given set of models using posterior probabilities estimated by drf. The posterior distribution estimation accuracy of the ABC framework is illustrated and compared with previous standard ABC methods through several simulation studies involving low- and high-dimensional models with computable posterior distributions, which are either unimodal, skewed, or multimodal; and exponential random graph and mechanistic network models, each defined by an intractable likelihood from which it is costly to simulate large network datasets. This paper also proposes and studies a new solution to the simulation cost problem in ABC involving the posterior estimation of parameters from datasets simulated from the given model that are smaller compared to the potentially large size of the dataset being analyzed. This proposal is motivated by the fact that, for many models defined by intractable likelihoods, such as the network models when they are applied to analyze massive networks, the repeated simulation of large datasets (networks) for posterior-based parameter estimation can be too computationally costly and vastly slow down or prohibit the use of standard ABC methods. The copulaABCdrf framework and standard ABC methods are further illustrated through analyses of large real-life networks of sizes ranging between 28,000 and 65.6 million nodes (between 3 million and 1.8 billion edges), including a large multilayer network with weighted directed edges. The results of the simulation studies show that, in settings where the true posterior distribution is not highly multimodal, copulaABCdrf usually produced similar point estimates from the posterior distribution for low-dimensional parametric models as previous ABC methods, but the copula-based method can produce more accurate estimates from the posterior distribution for high-dimensional models, and, in both dimensionality cases, usually produced more accurate estimates of univariate marginal posterior distributions of parameters. Also, posterior estimation accuracy was usually improved when pre-selecting the important summary statistics using drf compared to ABC employing no pre-selection of the subset of important summaries. For all ABC methods studied, accurate estimation of a highly multimodal posterior distribution was challenging. In light of the results of all the simulation studies, this article concludes by discussing how the copulaABCdrf framework can be improved for future research.

Approximate Bayesian Inference Based on Expected Evaluation

Approximate Bayesian computing (ABC) and Bayesian Synthetic likelihood (BSL) are two popular families of methods to evaluate the posterior distribution when the likelihood function is not available or tractable. For existing variants of ABC and BSL, the focus is usually first put on the simulation algorithm, and after that the form of the resulting approximate posterior distribution comes as a consequence of the algorithm. In this paper we turn this around and firstly define a reasonable approximate posterior distribution by studying the distributional properties of the expected discrepancy, or more generally an expected evaluation, with respect to generated samples from the model. The resulting approximate posterior distribution will be on a simple and interpretable form compared to ABC and BSL. Secondly a Markov chain Monte Carlo (MCMC) algorithm is developed to simulate from the resulting approximate posterior distribution. The algorithm was evaluated on a synthetic data example and on the Stepping Stone population genetics model, demonstrating that the proposed scheme has real world applicability. The algorithm demonstrates competitive results with the BSL and sequential Monte Carlo ABC algorithms, but is outperformed by the ABC MCMC.

A graph residual generation network for node classification based on multi-information aggregation

The key to improving the performance of graph convolutional networks (GCN) is to fully explore the correlation between neighboring and distant information. Aiming at the over-smoothing problem of GCN, in order to make full use of the relationship among features, graphs and labels, a graph residual generation network based on multi-information aggregation (MIA-GRGN) is proposed. Firstly, aiming at the defects of GCN, we design a deep initial residual graph convolution network (DIRGCN), which connects the initial input through residuals, so that each layer node retains part of the information of the initial features, ensuring the localization of the graph structure and effectively alleviating the problem of over-smoothing. Secondly, we propose a random graph generation method (RGGM) by utilizing graph edge sampling and negative edge sampling, and optimize the supervision loss function of DIRGCN in the form of generation framework. Finally, applying RGGM and DIRGCN as inference modules for modeling hypotheses and obtaining approximate posterior distributions of unknown labels, an optimized loss function is obtained, we construct a multi-information aggregation MIA-GRGN that combines graph structure, node characteristics and label joint distribution. Experiments on benchmark graph classification datasets show that MIA-GRGN achieves better classification results compared with the benchmark models and mainstream models, especially for datasets with less dense edge relationships between nodes.

Unsupervised Imputation of Non-Ignorably Missing Data Using Importance-Weighted Autoencoders

Deep Learning (DL) methods have dramatically increased in popularity in recent years. While its initial success was demonstrated in the classification and manipulation of image data, there has been significant growth in the application of DL methods to problems in the biomedical sciences. However, the greater prevalence and complexity of missing data in biomedical datasets present significant challenges for DL methods. Here, we provide a formal treatment of missing data in the context of Variational Autoencoders (VAEs), a popular unsupervised DL architecture commonly used for dimension reduction, imputation, and learning latent representations of complex data. We propose a new VAE architecture, NIMIWAE, that is one of the first to flexibly account for both ignorable and non-ignorable patterns of missingness in input features at training time. Following training, samples can be drawn from the approximate posterior distribution of the missing data can be used for multiple imputation, facilitating downstream analyses on high dimensional incomplete datasets. We demonstrate through statistical simulation that our method outperforms existing approaches for unsupervised learning tasks and imputation accuracy. We conclude with a case study of an EHR dataset pertaining to 12,000 ICU patients containing a large number of diagnostic measurements and clinical outcomes, where many features are only partially observed.

A hierarchical Bayesian model to monitor pelagic larvae in response to environmental changes

AbstractEuropean anchovies and round sardinella play a crucial role, both ecological and commercial, in the Mediterranean Sea. In this paper, we investigate the distribution of their larval stages by analyzing a dataset collected over time (1998–2016) and spaced along the area of the Strait of Sicily. Environmental factors are also integrated. We employ a hierarchical spatio-temporal Bayesian model and approximate the spatial field by a Gaussian Markov Random Field to reduce the computation effort using the Stochastic Partial Differential Equation method. Furthermore, the Integrated Nested Laplace Approximation is used for the posterior distributions of model parameters. Moreover, we propose an index that enables the temporal evaluation of species abundance by using an abundance aggregation within a spatially confined area. This index is derived through Monte Carlo sampling from the approximate posterior distribution of the fitted models. Model results suggest a strong relationship between sea currents’ directions and the distribution of larval European anchovies. For round sardinella, the analysis indicates increased sensitivity to warmer ocean conditions. The index suggests no clear overall trend over the years.

Bayesian modeling of quantiles of body mass index among under-five children in Ethiopia

BackgroundBody Mass Index (BMI) is a measurement of nutritional status, which is a vital pre-condition for good health. The prevalence of childhood malnutrition and the potential long-term health risks associated with obesity in Ethiopia have recently increased globally. The main objective of this study was to investigate the factors associated with the quantiles of under-five children’s BMI in Ethiopia.MethodsData on 5,323 children, aged between 0-59 months from March 21, 2019, to June 28, 2019, were obtained from the Ethiopian Mini Demographic Health Survey (EMDHS, 2019), based on the standards set by the World Health Organization. The study used a Bayesian quantile regression model to investigate the association of factors with the quantiles of under-five children’s body mass index. Markov Chain Monte Carlo (MCMC) with Gibbs sampling was used to estimate the country-specific marginal posterior distribution estimates of model parameters, using the Brq R package.ResultsOut of a total of 5323 children included in this study, 5.09% were underweight (less than 12.92 BMI), 10.05% were overweight (BMI: 17.06 – 18.27), and 5.02% were obese (greater than or equal to 18.27 BMI) children’s. The result of the Bayesian quantile regression model, including marginal posterior credible intervals (CIs), showed that for the prediction of the 0.05 quantile of BMI, the current age of children [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}= -0.007, 95% CI :(-0.01, -0.004)], the region Afar [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = - 0.32, 95% CI: (-0.57, -0.08)] and Somalia[β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = -0.72, 95% CI: (-0.96, -0.49)] were negatively associated with body mass index while maternal age [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.01, 95% CI: (0.005, 0.02)], mothers primary education [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document}= 0.19, 95% CI: (0.08, 0.29)], secondary and above [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.44, 95% CI: (0.29, 0.58)], and family follows protestant [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.22, 95% CI: (0.07, 0.37)] were positively associated with body mass index. In the prediction of the 0.95 (or 0.85?) quantile of BMI, in the upper quantile, still breastfeeding [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = -0.25, 95% CI: (-0.41, -0.10)], being female [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = -0.13, 95% CI: (-0.23, -0.03)] were negatively related while wealth index [β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta$$\\end{document} = 0.436, 95% CI: (0.25, 0.62)] was positively associated with under-five children’s BMI.ConclusionsIn conclusion, the research findings indicate that the percentage of lower and higher BMI for under-five children in Ethiopia is high. Factors such as the current age of children, sex of children, maternal age, religion of the family, region and wealth index were found to have a significant impact on the BMI of under-five children both at lower and upper quantile levels. Thus, these findings highlight the need for administrators and policymakers to devise and implement strategies aimed at enhancing the normal or healthy weight status among under-five children in Ethiopia.

Enricherator: A Bayesian Method for Inferring Regularized Genome-wide Enrichments from Sequencing Count Data

A pervasive question in biological research studying gene regulation, chromatin structure, or genomics is where, and to what extent, does a signal of interest arise genome-wide? This question is addressed using a variety of methods relying on high-throughput sequencing data as their final output, including ChIP-seq for protein-DNA interactions,1 GapR-seq for measuring supercoiling,2 and HBD-seq or DRIP-seq for R-loop positioning.3,4 Current computational methods to calculate genome-wide enrichment of the signal of interest usually do not properly handle the count-based nature of sequencing data, they often do not make use of the local correlation structure of sequencing data, and they do not apply any regularization of enrichment estimates. This can result in unrealistic estimates of the true underlying biological enrichment of interest, unrealistically low estimates of confidence in point estimates of enrichment (or no estimates of confidence at all), unrealistic gyrations in enrichment estimates at very close (<10 bp) genomic loci due to noise inherent in sequencing data, and in a multiple-hypothesis testing problem during interpretation of genome-wide enrichment estimates. We developed a tool called Enricherator to infer genome-wide enrichments from sequencing count data. Enricherator uses the variational Bayes algorithm to fit a generalized linear model to sequencing count data and to sample from the approximate posterior distribution of enrichment estimates (https://github.com/jwschroeder3/enricherator). Enrichments inferred by Enricherator more precisely identify known binding sites in cases where low coverage between binding sites leads to false-positive peak calls in these noisy regions of the genome; these benefits extend to published datasets.

Bayesian deep learning for cosmic volumes with modified gravity

Context. The new generation of galaxy surveys will provide unprecedented data that will allow us to test gravity deviations at cosmological scales at a much higher precision than could be achieved previously. A robust cosmological analysis of the large-scale structure demands exploiting the nonlinear information encoded in the cosmic web. Machine-learning techniques provide these tools, but no a priori assessment of the uncertainties. Aims. We extract cosmological parameters from modified gravity (MG) simulations through deep neural networks that include uncertainty estimations. Methods. We implemented Bayesian neural networks (BNNs) with an enriched approximate posterior distribution considering two cases: the first case with a single Bayesian last layer (BLL), and the other case with Bayesian layers at all levels (FullB). We trained both BNNs with real-space density fields and power spectra from a suite of 2000 dark matter-only particle-mesh N-body simulations including MG models relying on MG-PICOLA, covering 256 h−1 Mpc side cubical volumes with 1283 particles. Results. BNNs excel in accurately predicting parameters for Ωm and σ8 and their respective correlation with the MG parameter. Furthermore, we find that BNNs yield well-calibrated uncertainty estimates that overcome the over- and under-estimation issues in traditional neural networks. The MG parameter leads to a significant degeneracy, and σ8 might be one possible explanation of the poor MG predictions. Ignoring MG, we obtain a deviation of the relative errors in Ωm and σ8 by 30% at least. Moreover, we report consistent results from the density field and power spectrum analysis and comparable results between BLL and FullB experiments. This halved the computing time. This work contributes to preparing the path for extracting cosmological parameters from complete small cosmic volumes towards the highly nonlinear regime.

PECJ: Stream Window Join on Disorder Data Streams with Proactive Error Compensation

Stream Window Join (SWJ), a vital operation in stream analytics, struggles with achieving a balance between accuracy and latency due to out-of-order data arrivals. Existing methods predominantly rely on adaptive buffering, but often fall short in performance, thereby constraining practical applications. We introduce PECJ, a solution that proactively incorporates unobserved data to enhance accuracy while reducing latency, thus requiring robust predictive modeling of stream oscillation. At the heart of PECJ lies a mathematical formulation of the posterior distribution approximation (PDA) problem using variational inference (VI). This approach circumvents error propagation while meeting the low-latency demands of SWJ. We detail the implementation of PECJ, striking a balance between complexity and generality, and discuss both analytical and learning-based approaches. Experimental evaluations reveal PECJ's superior performance. The successful integration of PECJ into a multi-threaded SWJ benchmark testbed further establishes its practical value, demonstrating promising advancements in enhancing data stream processing capabilities amidst out-of-order data.

Uncertainty-aware human-like driving policy learning with deep Bayesian inverse reinforcement learning

The application of deep reinforcement learning in driving policy learning for automated vehicles is limited by the difficulty of designing reward functions. Most existing inverse reinforcement learning (IRL) methods make a structure assumption on the reward function and omit the uncertainty of neural networks. In view of this, this paper proposes a novel deep Bayesian IRL method that addresses both the reward function designing and the uncertainty-measuring issues by learning an approximate posterior distribution over the reward function. Furthermore, we propose to train uncertainty-aware human-like driving policies by maximising the predicted reward and penalising its uncertainty. Finally, the proposed methods were validated in simulated highway driving scenarios. The results show that AVRL models uncertainty and learns reward functions significantly outperforming the existing IRL method applied in automated driving. It was also found that penalising the uncertainty of the reward function during policy training improves the success rate and human likeness of the learned policy.

Bayesian inference for nonprobability samples with nonignorable missingness

AbstractNonprobability samples, especially web survey data, have been available in many different fields. However, nonprobability samples suffer from selection bias, which will yield biased estimates. Moreover, missingness, especially nonignorable missingness, may also be encountered in nonprobability samples. Thus, it is a challenging task to make inference from nonprobability samples with nonignorable missingness. In this article, we propose a Bayesian approach to infer the population based on nonprobability samples with nonignorable missingness. In our method, different Logistic regression models are employed to estimate the selection probabilities and the response probabilities; the superpopulation model is used to explain the relationship between the study variable and covariates. Further, Bayesian and approximate Bayesian methods are proposed to estimate the response model parameters and the superpopulation model parameters, respectively. Specifically, the estimating functions for the response model parameters and superpopulation model parameters are utilized to derive the approximate posterior distribution in superpopulation model estimation. Simulation studies are conducted to investigate the finite sample performance of the proposed method. The data from the Pew Research Center and the Behavioral Risk Factor Surveillance System are used to show better performance of our proposed method over the other approaches.

Deep Variational Network for Blind Pansharpening.

Deep-learning-based methods play an important role in pansharpening that uses panchromatic images to enhance the spatial resolution of multispectral images while maintaining spectral features. However, most existing methods mainly consider only one fixed degradation in the training process. Therefore, their performance may drop significantly when the degradation of testing data is unknown (blind) and different from the training data, which is common in real-world applications. To address this issue, we proposed a deep variational network for blind pansharpening, named VBPN, which integrates degradation estimation and image fusion into a whole Bayesian framework. First, by taking the noise and blurring parameters of the multispectral image with the noise parameters of the panchromatic image as hidden variables, we parameterize the approximate posterior distribution for the fusion problem using neural networks. Since all parameters in this posterior distribution are explicitly modeled, the degradation parameters of the multispectral image and the panchromatic image are easily estimated. Furthermore, we designed VPBN composed of degradation estimation and image fusion subnetworks, which can optimize the fusion results guided by the variational inference according to the testing data. As a result, the blind pansharpening performance can be improved. In general, VPBN has good interpretability and generalization ability by combining the advantages of model-based and deep-learning-based approaches. Experiments on simulated and real datasets prove that VPBN can achieve state-of-the-art fusion results.

A dimension-reduced variational approach for solving physics-based inverse problems using generative adversarial network priors and normalizing flows

We propose a novel modular inference approach combining two different generative models — generative adversarial networks (GAN) and normalizing flows — to approximate the posterior distribution of physics-based Bayesian inverse problems framed in high-dimensional ambient spaces. We dub the proposed framework GAN-Flow. The proposed method leverages the intrinsic dimension reduction and superior sample generation capabilities of GANs to define a low-dimensional data-driven prior distribution. Once a trained GAN-prior is available, the inverse problem is solved entirely in the latent space of the GAN using variational Bayesian inference with normalizing flow-based variational distribution, which approximates low-dimensional posterior distribution by transforming realizations from the low-dimensional latent prior (Gaussian) to corresponding realizations of a low-dimensional variational posterior distribution. The trained GAN generator then maps realizations from this approximate posterior distribution in the latent space back to the high-dimensional ambient space. We also propose a two-stage training strategy for GAN-Flow wherein we train the two generative models sequentially. Thereafter, GAN-Flow can estimate the statistics of posterior-predictive quantities of interest at virtually no additional computational cost. The synergy between the two types of generative models allows us to overcome many challenges associated with the application of Bayesian inference to large-scale inverse problems, chief among which are describing an informative prior and sampling from the high-dimensional posterior. GAN-Flow does not involve Markov chain Monte Carlo simulation, making it particularly suitable for solving large-scale inverse problems. We demonstrate the efficacy and flexibility of GAN-Flow on various physics-based inverse problems of varying ambient dimensionality and prior knowledge using different types of GANs and normalizing flows. Notably, one of the applications we consider involves a 65,536-dimensional inverse problem of phase retrieval wherein an object is reconstructed from sparse noisy measurements of the magnitude of its Fourier transform.

Variational Approximation for Adaptive Extended Target Tracking in Clutter With Random Matrix

As a computationally efficient framework, the random matrix approach can simultaneously estimate the kinematic state and extent of the extended target. For the extended target tracking in clutter, the measurement origin uncertainty, the unknown detection probability and measurement rate challenge the existing methods. In this paper, we propose the Beta Gamma Gaussian inverse Wishart filter based on the variational approximation. The proposed method takes the association event as an unknown parameter with a prior distribution. Following a more rigorous path, we derive an approximate posterior distribution of the unknowns using the analytical techniques of variational Bayesian inference. The joint estimations of the kinematic state, extent, detection probability, measurement rate and association events are obtained in this work. The simulation results illustrate the effectiveness and robustness of the proposed approach.

Laplace based Bayesian inference for ordinary differential equation models using regularized artificial neural networks

Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterised by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically intractable trajectories which result in likelihoods and posterior distributions that are similarly intractable. Bayesian inference for ODE systems via simulation methods require numerical approximations to produce inference with high accuracy at a cost of heavy computational power and slow convergence. At the same time, Artificial Neural Networks (ANN) offer tractability that can be utilized to construct an approximate but tractable likelihood and posterior distribution. In this paper we propose a hybrid approach, where Laplace-based Bayesian inference is combined with an ANN architecture for obtaining approximations to the ODE trajectories as a function of the unknown initial values and system parameters. Suitable choices of customized loss functions are proposed to fine tune the approximated ODE trajectories and the subsequent Laplace approximation procedure. The effectiveness of our proposed methods is demonstrated using an epidemiological system with non-analytical solutions—the Susceptible-Infectious-Removed (SIR) model for infectious diseases—based on simulated and real-life influenza datasets. The novelty and attractiveness of our proposed approach include (i) a new development of Bayesian inference using ANN architectures for ODE based dynamical systems, and (ii) a computationally fast posterior inference by avoiding convergence issues of benchmark Markov Chain Monte Carlo methods. These two features establish the developed approach as an accurate alternative to traditional Bayesian computational methods, with improved computational cost.

PyVBMC: Efficient Bayesian inference in Python

PyVBMC is a Python implementation of the Variational Bayesian Monte Carlo (VBMC) algorithm for posterior and model inference for black-box computational models (Acerbi, 2018, 2020). VBMC is an approximate inference method designed for efficient parameter estimation and model assessment when model evaluations are mildly-to-very expensive (e.g., a second or more) and/or noisy. Specifically, VBMC computes: - a flexible (non-Gaussian) approximate posterior distribution of the model parameters, from which statistics and posterior samples can be easily extracted; - an approximation of the model evidence or marginal likelihood, a metric used for Bayesian model selection. PyVBMC can be applied to any computational or statistical model with up to roughly 10-15 continuous parameters, with the only requirement that the user can provide a Python function that computes the target log likelihood of the model, or an approximation thereof (e.g., an estimate of the likelihood obtained via simulation or Monte Carlo methods). PyVBMC is particularly effective when the model takes more than about a second per evaluation, with dramatic speed-ups of 1-2 orders of magnitude when compared to traditional approximate inference methods. Extensive benchmarks on both artificial test problems and a large number of real models from the computational sciences, particularly computational and cognitive neuroscience, show that VBMC generally - and often vastly - outperforms alternative methods for sample-efficient Bayesian inference, and is applicable to both exact and simulator-based models (Acerbi, 2018, 2019, 2020). PyVBMC brings this state-of-the-art inference algorithm to Python, along with an easy-to-use Pythonic interface for running the algorithm and manipulating and visualizing its results.

Wireless Beacon Enabled Hybrid Sparse Channel Estimation for RIS-Aided mmWave Communications

The inability of reconfigurable intelligent surfaces (RISs) to signal processing has become a critical bottleneck in terms of the precise capture of cascaded channels. There exists a pair of critical issues: i) the high-dimensional cascaded channel to be estimated, which always entails substantial pilot overhead typically proportional to RIS elements, and ii) the high possibilities of false alarms and unfaithful angle detection during cascaded channel estimates, referred to as the angular distortion, particularly in the case of conventional fully-passive RIS systems. To circumvent these issues, we investigate in this paper a multi-user multiple-input multiple-output (MIMO) system assisted by a wireless beacon (WB) enabled RIS over millimeter wave (mmWave) frequency. Specifically, WB is a functionally independent hardware that attaches parasitically to the RIS using only one radio frequency chain for broadcasting pilots, allowing for the accurate acquisition of partial cascaded channel information, e.g., some of angles of arrival/departure (AoA/AoDs) and complex gains. This efficiently eliminates the angular distortion effect and thus facilitates high precision recovery of sparse cascaded mmWave channels. Then, a hybrid structured sparsity (HSS) model is presented to capture hybrid sparse priors and approximate exact posterior distributions associated with RIS-aided twin-hop channels. We conceive of channel estimation as a compressive sensing problem in contrast to its conventional copy due to the presence of an unknown sensing matrix. To tackle this problem, an expectation-maximization (EM)-based algorithm, i.e., HSS-EM, is developed in order to fully employ the sparse priors encapsulated by the proposed HSS model for a robust and accurate recovery of the cascaded channels. Numerical results validate our analytical claims and demonstrate the significant improvement in terms of the normalized mean square error (NMSE) performance over conventional designs.

Monte Carlo tree search algorithms for risk-aware and multi-objective reinforcement learning

In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from a single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For example, in a medical setting a patient may only have one opportunity to treat their illness. Making decisions using just the expected future returns–known in reinforcement learning as the value–cannot account for the potential range of adverse or positive outcomes a decision may have. Therefore, we should use the distribution over expected future returns differently to represent the critical information that the agent requires at decision time by taking both the future and accrued returns into consideration. In this paper, we propose two novel Monte Carlo tree search algorithms. Firstly, we present a Monte Carlo tree search algorithm that can compute policies for nonlinear utility functions (NLU-MCTS) by optimising the utility of the different possible returns attainable from individual policy executions, resulting in good policies for both risk-aware and multi-objective settings. Secondly, we propose a distributional Monte Carlo tree search algorithm (DMCTS) which extends NLU-MCTS. DMCTS computes an approximate posterior distribution over the utility of the returns, and utilises Thompson sampling during planning to compute policies in risk-aware and multi-objective settings. Both algorithms outperform the state-of-the-art in multi-objective reinforcement learning for the expected utility of the returns.

Visualization in 2D/3D registration matters for assuring technology-assisted image-guided surgery.

Image-guided navigation and surgical robotics are the next frontiers of minimally invasive surgery. Assuring safety in high-stakes clinical environments is critical for their deployment. 2D/3D registration is an essential, enabling algorithm for most of these systems, as it provides spatial alignment of preoperative data with intraoperative images. While these algorithms have been studied widely, there is a need for verification methods to enable human stakeholders to assess and either approve or reject registration results to ensure safe operation. To address the verification problem from the perspective of human perception, we develop novel visualization paradigms and use a sampling method based on approximate posterior distribution to simulate registration offsets. We then conduct a user study with 22 participants to investigate how different visualization paradigms (Neutral, Attention-Guiding, Correspondence-Suggesting) affect human performance in evaluating the simulated 2D/3D registration results using 12 pelvic fluoroscopy images. All three visualization paradigms allow users to perform better than random guessing to differentiate between offsets of varying magnitude. The novel paradigms show better performance than the neutral paradigm when using an absolute threshold to differentiate acceptable and unacceptable registrations (highest accuracy: Correspondence-Suggesting (65.1%), highest F1 score: Attention-Guiding (65.7%)), as well as when using a paradigm-specific threshold for the same discrimination (highest accuracy: Attention-Guiding (70.4%), highest F1 score: Corresponding-Suggesting (65.0%)). This study demonstrates that visualization paradigms do affect the human-based assessment of 2D/3D registration errors. However, further exploration is needed to understand this effect better and develop more effective methods to assure accuracy. This research serves as a crucial step toward enhanced surgical autonomy and safety assurance in technology-assisted image-guided surgery.