Unlike in the traditional statistical modeling for which a user typically hand-specify a prior, Neural Processes (NPs) implicitly define a broad class of stochastic processes with neural networks. Given a data stream, NP learns a stochastic process that best describes the data. While this "data-driven" way of learning stochastic processes has proven to handle various types of data, NPs still rely on an assumption that uncertainty in stochastic processes is modeled by a single latent variable, which potentially limits the flexibility. To this end, we propose the Boostrapping Neural Process (BNP), a novel extension of the NP family using the bootstrap. The bootstrap is a classical data-driven technique for estimating uncertainty, which allows BNP to learn the stochasticity in NPs without assuming a particular form. We demonstrate the efficacy of BNP on various types of data and its robustness in the presence of model-data mismatch.

Convolutional Neural Networks (CNNs) have proven to be state-of-the-art models for supervised computer vision tasks, such as image classification. However, large labeled data sets are generally needed for the training and validation of such models. In many domains, unlabeled data is available but labeling is expensive, for instance when specific expert knowledge is required. Active Learning (AL) is one approach to mitigate the problem of limited labeled data. Through selecting the most informative and representative data instances for labeling, AL can contribute to more efficient learning of the model. Recent AL methods for CNNs propose different solutions for the selection of instances to be labeled. However, they do not perform consistently well and are often computationally expensive. In this paper, we propose a novel AL algorithm that efficiently learns from unlabeled data by capturing high prediction uncertainty. By replacing the softmax standard output of a CNN with the parameters of a Dirichlet density, the model learns to identify data instances that contribute efficiently to improving model performance during training. We demonstrate in several experiments with publicly available data that our method consistently outperforms other state-of-the-art AL approaches. It can be easily implemented and does not require extensive computational resources for training. Additionally, we are able to show the benefits of the approach on a real-world medical use case in the field of automated detection of visual signals for pneumonia on chest radiographs.

One of the core assumptions in causal discovery is the faithfulness assumption---i.e. assuming that independencies found in the data are due to separations in the true causal graph. This assumption can, however, be violated in many ways, including xor connections, deterministic functions or cancelling paths. In this work, we propose a weaker assumption that we call 2-adjacency faithfulness. In contrast to adjacency faithfulness, which assumes that there is no conditional independence between each pair of variables that are connected in the causal graph, we only require no conditional independence between a node and a subset of its Markov blanket that can contain up to two nodes. Equivalently, we adapt orientation faithfulness to this setting. We further propose a sound orientation rule for causal discovery that applies under weaker assumptions. As a proof of concept, we derive a modified Grow and Shrink algorithm that recovers the Markov blanket of a target node and prove its correctness under strictly weaker assumptions than the standard faithfulness assumption.

We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a recursive partitioning of the sample space. It does not rely on gradients, nor require any problem-specific tuning, and is asymptotically exact for any density function with a bounded domain. The output is an approximation to the whole density function including the normalization constant, via partitions organized in efficient data structures. This allows for evidence estimation, as well as approximate posteriors that allow for fast sampling and fast evaluations of the density. It shows competitive performance to recent state-of-the-art methods on synthetic and real-world problem examples including parameter inference for gravitational-wave physics.

Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP) approximation of the integrand. As a result, BQ is inherently limited to cases where GP approximations can be done in an efficient manner, thus often prohibiting very high-dimensional or non-smooth target functions. This paper proposes to tackle this issue with a new Bayesian numerical integration algorithm based on Bayesian Additive Regression Trees (BART) priors, which we call BART-Int. BART priors are easy to tune and well-suited for discontinuous functions. We demonstrate that they also lend themselves naturally to a sequential design setting and that explicit convergence rates can be obtained in a variety of settings. The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.

Credit scoring is a rapidly expanding analytical technique used by banks and other financial institutions. Academic studies on credit scoring provide a range of classification techniques used to differentiate between good and bad borrowers. The main contribution of this paper is to introduce a new method for credit scoring based on Gaussian Mixture Models. Our algorithm classifies consumers into groups which are labeled as positive or negative. Labels are estimated according to the probability associated with each class. We apply our model with real world databases from Australia, Japan, and Germany. Numerical results show that not only our model's performance is comparable to others, but also its flexibility avoids over-fitting even in the absence of standard cross validation techniques. The framework developed by this paper can provide a computationally efficient and powerful tool for assessment of consumer default risk in related financial institutions.

Estimating epistemic uncertainty of models used in low-latency applications and Out-Of-Distribution samples detection is a challenge due to the computationally demanding nature of uncertainty estimation techniques. Estimating model uncertainty using approximation techniques like Monte Carlo Dropout (MCD), DropConnect (MCDC) requires a large number of forward passes through the network, rendering them inapt for low-latency applications. We propose Select-DC which uses a subset of layers in a neural network to model epistemic uncertainty with MCDC. Through our experiments, we show a significant reduction in the GFLOPS required to model uncertainty, compared to Monte Carlo DropConnect, with marginal trade-off in performance. We perform a suite of experiments on CIFAR 10, CIFAR 100, and SVHN datasets with ResNet and VGG models. We further show how applying DropConnect to various layers in the network with different drop probabilities affects the networks performance and the entropy of the predictive distribution.

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural networks (DNNs) can serve as highly-accurate surrogate models, with the capacity to handle diverse datatypes, offering tremendous speed-ups for prediction and many other downstream tasks. An important use-case for these surrogates is the comparison between simulations and experiments; prediction uncertainty estimates are crucial for making such comparisons meaningful, yet standard DNNs do not provide them. In this work we define the fundamental requirements for a DNN to be useful for scientific applications, and demonstrate a general variational inference approach to equip predictions of scalar and image data from a DNN surrogate model trained on inertial confinement fusion simulations with calibrated Bayesian uncertainties. Critically, these uncertainties are interpretable, meaningful and preserve physics-correlations in the predicted quantities.

Models of discrete-valued outcomes are easily misspecified if the data exhibit zero-inflation, overdispersion or contamination. Without additional knowledge about the existence and nature of this misspecification, model inference and prediction are adversely affected. Here, we introduce a robust discrepancy-based Bayesian approach using the Total Variation Distance (TVD). In the process, we address and resolve two challenges: First, we study convergence and robustness properties of a computationally efficient estimator for the TVD between a parametric model and the data-generating mechanism. Second, we provide an efficient inference method adapted from Lyddon et al. (2019) which corresponds to formulating an uninformative nonparametric prior directly over the data-generating mechanism. Lastly, we empirically demonstrate that our approach is robust and significantly improves predictive performance on a range of simulated and real world data.

Purpose: Bayesian calibration is theoretically superior to standard direct-search algorithm because it can reveal the full joint posterior distribution of the calibrated parameters. However, to date, Bayesian calibration has not been used often in health decision sciences due to practical and computational burdens. In this paper we propose to use artificial neural networks (ANN) as one solution to these limitations. Methods: Bayesian Calibration using Artificial Neural Networks (BayCANN) involves (1) training an ANN metamodel on a sample of model inputs and outputs, and (2) then calibrating the trained ANN metamodel instead of the full model in a probabilistic programming language to obtain the posterior joint distribution of the calibrated parameters. We demonstrate BayCANN by calibrating a natural history model of colorectal cancer to adenoma prevalence and cancer incidence data. In addition, we compare the efficiency and accuracy of BayCANN against performing a Bayesian calibration directly on the simulation model using an incremental mixture importance sampling (IMIS) algorithm. Results: BayCANN was generally more accurate than IMIS in recovering the "true" parameter values. The ratio of the absolute ANN deviation from the truth compared to IMIS for eight out of the nine calibrated parameters were less than one indicating that BayCANN was more accurate than IMIS. In addition, BayCANN took about 15 minutes total compared to the IMIS method which took 80 minutes. Conclusions: In our case study, BayCANN was more accurate than IMIS and was five-folds faster. Because BayCANN does not depend on the structure of the simulation model, it can be adapted to models of various levels of complexity with minor changes to its structure. We provide BayCANN's open-source implementation in R.