Decision making under uncertain conditions has been well studied when uncertainty can only be considered at the associative level of information. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rationally making choices using associative information. We provide here a previous result from Pearl and show that it can be considered as a causal version of the von Neumann-Morgenstern Theorem; furthermore, we consider the case when the true causal mechanism that controls the environment is unknown to the decision maker and propose a causal version of the Savage Theorem. As applications, we argue how previous optimal action learning methods for causal environments fit within the Causal Savage Theorem we present thus showing the utility of our result in the justification and design of learning algorithms; furthermore, we define a Causal Nash Equilibria for a strategic game in a causal environment in terms of the preferences induced by our Causal Decision Making Theorem.

Bayesian synthetic likelihood (BSL) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chosen summary statistic of the data via model simulation and density estimation. Compared to alternative methods such as approximate Bayesian computation (ABC), BSL requires little tuning and requires less model simulations than ABC when the chosen summary statistic is high-dimensional. The original synthetic likelihood relies on a multivariate normal approximation of the intractable likelihood, where the mean and covariance are estimated by simulation. An extension of BSL considers replacing the sample covariance with a penalised covariance estimator to reduce the number of required model simulations. Further, a semi-parametric approach has been developed to relax the normality assumption. In this paper, we present an R package called BSL that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software. The R package also includes several examples to illustrate how to use the package and demonstrate the utility of the methods.

Numerous engineering problems of interest to the industry are often characterized by expensive black-box objective experiments or computer simulations. Obtaining insight into the problem or performing subsequent optimizations requires hundreds of thousands of evaluations of the objective function which is most often a practically unachievable task. Gaussian Process (GP) surrogate modeling replaces the expensive function with a cheap-to-evaluate data-driven probabilistic model. While the GP does not assume a functional form of the problem, it is defined by a set of parameters, called hyperparameters. The hyperparameters define the characteristics of the objective function, such as smoothness, magnitude, periodicity, etc. Accurately estimating these hyperparameters is a key ingredient in developing a reliable and generalizable surrogate model. Markov chain Monte Carlo (MCMC) is a ubiquitously used Bayesian method to estimate these hyperparameters. At the GE Global Research Center, a customized industry-strength Bayesian hybrid modeling framework utilizing the GP, called GEBHM, has been employed and validated over many years. GEBHM is very effective on problems of small and medium size, typically less than 1000 training points. However, the GP does not scale well in time with a growing dataset and problem dimensionality which can be a major impediment in such problems. In this work, we extend and implement in GEBHM an Adaptive Sequential Monte Carlo (ASMC) methodology for training the GP enabling the modeling of large-scale industry problems. This implementation saves computational time (especially for large-scale problems) while not sacrificing predictability over the current MCMC implementation. We demonstrate the effectiveness and accuracy of GEBHM with ASMC on four mathematical problems and on two challenging industry applications of varying complexity.

We develop a stochastic whole-brain and body simulator of the nematode roundworm Caenorhabditis elegans (C. elegans) and show that it is sufficiently regularizing to allow imputation of latent membrane potentials from partial calcium fluorescence imaging observations. This is the first attempt we know of to "complete the circle," where an anatomically grounded whole-connectome simulator is used to impute a time-varying "brain" state at single-cell fidelity from covariates that are measurable in practice. The sequential Monte Carlo (SMC) method we employ not only enables imputation of said latent states but also presents a strategy for learning simulator parameters via variational optimization of the noisy model evidence approximation provided by SMC. Our imputation and parameter estimation experiments were conducted on distributed systems using novel implementations of the aforementioned techniques applied to synthetic data of dimension and type representative of that which are measured in laboratories currently.

Matrix Factorization (MF) is a common method for generating recommendations, where the proximity of entities like users or items in the embedded space indicates their similarity to one another. Though almost all applications implicitly use a Euclidean embedding space to represent two entity types, recent work has suggested that a hyperbolic Poincar\'e ball may be more well suited to representing multiple entity types, and in particular, hierarchies. We describe a novel method to embed a hierarchy of related music entities in hyperbolic space. We also describe how a parametric empirical Bayes approach can be used to estimate link reliability between entities in the hierarchy. Applying these methods together to build personalized playlists for users in a digital music service yielded a large and statistically significant increase in performance during an A/B test, as compared to the Euclidean model.

The legacy measurements of the LHC will require analyzing high-dimensional event data for subtle kinematic signatures, which is challenging for established analysis methods. Recently, a powerful family of multivariate inference techniques that leverage both matrix element information and machine learning has been developed. This approach neither requires the reduction of high-dimensional data to summary statistics nor any simplifications to the underlying physics or detector response. In this paper we introduce MadMiner, a Python module that streamlines the steps involved in this procedure. Wrapping around MadGraph5_aMC and Pythia 8, it supports almost any physics process and model. To aid phenomenological studies, the tool also wraps around Delphes 3, though it is extendable to a full Geant4-based detector simulation. We demonstrate the use of MadMiner in an example analysis of dimension-six operators in ttH production, finding that the new techniques substantially increase the sensitivity to new physics.

The importance weighted autoencoder (IWAE) (Burda et al., 2016) and reweighted wake-sleep (RWS) algorithm (Bornschein and Bengio, 2015) are popular approaches which employ multiple samples to achieve bias reductions compared to standard variational methods. However, their relationship has hitherto been unclear. We introduce a simple, unified framework for multi-sample variational inference termed adaptive importance sampling for learning (AISLE) and show that it admits IWAE and RWS as special cases. Through a principled application of a variance-reduction technique from Tucker et al. (2019), we also show that the sticking-the-landing (STL) gradient from Roeder et al. (2017), which previously lacked theoretical justification, can be recovered as a special case of RWS (and hence of AISLE). In particular, this indicates that the breakdown of RWS -- but not of STL -- observed in Tucker et al. (2019) may not be attributable to the lack of a joint objective for the generative-model and inference-network parameters as previously conjectured. Finally, we argue that our adaptive-importance-sampling interpretation of variational inference leads to more natural and principled extensions to sequential Monte Carlo methods than the IWAE-type multi-sample objective interpretation.

Learning robot controllers by minimizing a black-box objective cost using Bayesian optimization (BO) can be time-consuming and challenging. It is very often the case that some roll-outs result in failure behaviors, causing premature experiment detention. In such cases, the designer is forced to decide on heuristic cost penalties because the acquired data is often scarce, or not comparable with that of the stable policies. To overcome this, we propose a Bayesian model that captures exactly what we know about the cost of unstable controllers prior to data collection: Nothing, except that it should be a somewhat large number. The resulting Bayesian model, approximated with a Gaussian process, predicts high cost values in regions where failures are likely to occur. In this way, the model guides the BO exploration toward regions of stability. We demonstrate the benefits of the proposed model in several illustrative and statistical synthetic benchmarks, and also in experiments on a real robotic platform. In addition, we propose and experimentally validate a new BO method to account for unknown constraints. Such method is an extension of Max-Value Entropy Search, a recent information-theoretic method, to solve unconstrained global optimization problems.

Accurately predicting future behaviors of surrounding vehicles is an essential capability for autonomous vehicles in order to plan safe and feasible trajectories. The behaviors of others, however, are full of uncertainties. Both rational and irrational behaviors exist, and the autonomous vehicles need to be aware of this in their prediction module. The prediction module is also expected to generate reasonable results in the presence of unseen and corner scenarios. Two types of prediction models are typically used to solve the prediction problem: learning-based model and planning-based model. Learning-based model utilizes real driving data to model the human behaviors. Depending on the structure of the data, learning-based models can predict both rational and irrational behaviors. But the balance between them cannot be customized, which creates challenges in generalizing the prediction results. Planning-based model, on the other hand, usually assumes human as a rational agent, i.e., it anticipates only rational behavior of human drivers. In this paper, a generic prediction architecture is proposed to address various rationalities in human behavior. We leverage the advantages from both learning-based and planning-based prediction models. The proposed approach is able to predict continuous trajectories that well-reflect possible future situations of other drivers. Moreover, the prediction performance remains stable under various unseen driving scenarios. A case study under a real-world roundabout scenario is provided to demonstrate the performance and capability of the proposed prediction architecture.

Variational autoencoders (VAE) have quickly become a central tool in machine learning, applicable to a broad range of data types and latent variable models. By far the most common first step, taken by seminal papers and by core software libraries alike, is to model MNIST data using a deep network parameterizing a Bernoulli likelihood. This practice contains what appears to be and what is often set aside as a minor inconvenience: the pixel data is [0, 1] valued, not {0, 1} as supported by the Bernoulli likelihood. Here we show that, far from being a triviality or nuisance that is convenient to ignore, this error has profound importance to VAE, both qualitative and quantitative. We introduce and fully characterize a new [0, 1]-supported, single parameter distribution: the continuous Bernoulli, which patches this pervasive bug in VAE. This distribution is not nitpicking; it produces meaningful performance improvements across a range of metrics and datasets, including sharper image samples, and suggests a broader class of performant VAE.