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Humans effortlessly infer the 3D shape of objects. What computations underlie this ability? Although various computational models have been proposed, none of them capture the human ability to match object shape across viewpoints. Here, we ask whether and how this gap might be closed. We begin with a relatively novel class of computational models, 3D neural fields, which encapsulate the basic principles of classic analysis-by-synthesis in a deep neural network (DNN). First, we find that a 3D Light Field Network (3D-LFN) supports 3D matching judgments well aligned to humans for within-category comparisons, adversarially-defined comparisons that accentuate the 3D failure cases of standard DNN models, and adversarially-defined comparisons for algorithmically generated shapes with no category structure. We then investigate the source of the 3D-LFN's ability to achieve human-aligned performance through a series of computational experiments. Exposure to multiple viewpoints of objects during training and a multi-view learning objective are the primary factors behind model-human alignment; even conventional DNN architectures come much closer to human behavior when trained with multi-view objectives. Finally, we find that while the models trained with multi-view learning objectives are able to partially generalize to new object categories, they fall short of human alignment. This work provides a foundation for understanding human shape inferences within neurally mappable computational architectures.

StreamBed is a capacity planning system for stream processing.It predicts, ahead of any production deployment, the resources that a query will require to process an incoming data rate sustainably, and the appropriate configuration of these resources. StreamBed builds a capacity planning model by piloting a series of runs of the target query in a small-scale, controlled testbed. We implement StreamBed for the popular Flink DSP engine. Our evaluation with large-scale queries of the Nexmark benchmark demonstrates that StreamBed can effectively and accurately predict capacity requirements for jobs spanning more than 1,000 cores using a testbed of only 48 cores.

Counterfactual prediction methods are required when a model will be deployed in a setting where treatment policies differ from the setting where the model was developed, or when the prediction question is explicitly counterfactual. However, estimating and evaluating counterfactual prediction models is challenging because one does not observe the full set of potential outcomes for all individuals. Here, we discuss how to tailor a model to a counterfactual estimand, how to assess the model's performance, and how to perform model and tuning parameter selection. We also provide identifiability results for measures of performance for a potentially misspecified counterfactual prediction model based on training and test data from the same (factual) source population. Last, we illustrate the methods using simulation and apply them to the task of developing a statin-na\"{i}ve risk prediction model for cardiovascular disease.

Markov categories have recently turned out to be a powerful high-level framework for probability and statistics. They accommodate purely categorical definitions of notions like conditional probability and almost sure equality, as well as proofs of fundamental results such as the Hewitt-Savage 0/1 Law, the de Finetti Theorem and the Ergodic Decomposition Theorem. In this work, we develop additional relevant notions from probability theory in the setting of Markov categories. This comprises improved versions of previously introduced definitions of absolute continuity and supports, as well as a detailed study of idempotents and idempotent splitting in Markov categories. Our main result on idempotent splitting is that every idempotent measurable Markov kernel between standard Borel spaces splits through another standard Borel space, and we derive this as an instance of a general categorical criterion for idempotent splitting in Markov categories.

Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric regression models can provide a convenient alternative method for prediction. To this end, we consider an extension to the classical $k$--$NN$ regression, termed $\alpha$--$k$--$NN$ regression, that yields a highly flexible non-parametric regression model for compositional data through the use of the $\alpha$-transformation. Unlike many of the recommended regression models for compositional data, zeros values (which commonly occur in practice) are not problematic and they can be incorporated into the proposed models without modification. Extensive simulation studies and real-life data analyses highlight the advantage of using these non-parametric regressions for complex relationships between the compositional response data and Euclidean predictor variables. Both suggest that $\alpha$--$k$--$NN$ regression can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables. In addition, the $\alpha$--$k$--$NN$ regression, in contrast to current regression techniques, enjoys a high computational efficiency rendering it highly attractive for use with large scale, massive, or big data.

In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived. The proposed approach is highly flexible and suitable for studying the human cardiovascular system, which is composed of vessels with high morphological and mechanical variability. The resulting multiscale hyperbolic model of blood flow is solved using an asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method, which ensures the consistency of the numerical scheme with the different asymptotic limits of the mathematical model without affecting the choice of the time step by restrictions related to the smallness of the scaling parameters. Several numerical tests confirm the validity of the proposed methodology, including a case study investigating the hemodynamics of a thoracic aorta in the presence of a stent.

Correlation matrix visualization is essential for understanding the relationships between variables in a dataset, but missing data can pose a significant challenge in estimating correlation coefficients. In this paper, we compare the effects of various missing data methods on the correlation plot, focusing on two common missing patterns: random and monotone. We aim to provide practical strategies and recommendations for researchers and practitioners in creating and analyzing the correlation plot. Our experimental results suggest that while imputation is commonly used for missing data, using imputed data for plotting the correlation matrix may lead to a significantly misleading inference of the relation between the features. We recommend using DPER, a direct parameter estimation approach, for plotting the correlation matrix based on its performance in the experiments.

This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of the examined body in order to maximize the value of the resulting boundary deformations as data for the inverse problem of reconstructing the Lam\'e parameters inside the object. We resort to a linearized measurement model and adopt the framework of Bayesian experimental design, under the assumption that the prior and measurement noise distributions are mutually independent Gaussians. This enables the use of the standard Bayesian A-optimality criterion for deducing optimal positions for the pressure activations. The (second) derivatives of the boundary measurements with respect to the Lam\'e parameters and the positions of the boundary pressure activations are deduced to allow minimizing the corresponding objective function, i.e., the trace of the covariance matrix of the posterior distribution, by a gradient-based optimization algorithm. Two-dimensional numerical experiments are performed to demonstrate the functionality of our approach.

Binary regression models represent a popular model-based approach for binary classification. In the Bayesian framework, computational challenges in the form of the posterior distribution motivate still-ongoing fruitful research. Here, we focus on the computation of predictive probabilities in Bayesian probit models via expectation propagation (EP). Leveraging more general results in recent literature, we show that such predictive probabilities admit a closed-form expression. Improvements over state-of-the-art approaches are shown in a simulation study.

Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model that can draw global samples with the aim of approximating the posterior. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. We then present our adapted Metropolis-Hastings algorithm which combines local proposals with global proposals taken from a diffusion model that is regularly trained on the samples produced during the MCMC run. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the Bayesian posterior across several analytic functions, as well as for a physical example based on a global analysis of parton distribution functions. Our method is extensible to other MCMC techniques, and we briefly compare our method to similar approaches based on normalizing flows. A code implementation can be found at //github.com/NickHunt-Smith/MCMC-diffusion.