The analysis is borrowed from the regression setting and aims to decompose the prediction error of a given classifier into the terms of B&V to evaluate their effects on the performance. Therefore, it can help answer questions such as "How can we compare the accuracy of two different types of classifiers?", "What is it that makes stronger classifiers perform well? Is it the reduction in the bias they bring about, or in variance, or both?". Other than being theoretically interesting, the answers to these questions are also meant to provide better classifier design strategies which bring about improved prediction performance. After the initial decomposition of the prediction error into the standard B&V terms in the regression setting by [1], different studies have attempted to carry over this analysis into the classification setting while preserving the meanings of the terms and the additive property of the decomposition.

Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov Chain Monte Carlo (MCMC) tend to be computationally intensive and inefficient for such high dimensional problems. To address this issue, several methods based on surrogate models have been proposed to speed up the inference process. More specifically, the calibration-emulation-sampling (CES) scheme has been proven to be successful in large dimensional UQ problems. In this work, we propose a novel CES approach for Bayesian inference based on deep neural network (DNN) models for the emulation phase. The resulting algorithm is not only computationally more efficient, but also less sensitive to the training set. Further, by using an Autoencoder (AE) for dimension reduction, we have been able to speed up our Bayesian inference method up to three orders of magnitude. Overall, our method, henceforth called \emph{Dimension-Reduced Emulative Autoencoder Monte Carlo (DREAM)} algorithm, is able to scale Bayesian UQ up to thousands of dimensions in physics-constrained inverse problems. Using two low-dimensional (linear and nonlinear) inverse problems we illustrate the validity this approach. Next, we apply our method to two high-dimensional numerical examples (elliptic and advection-diffussion) to demonstrate its computational advantage over existing algorithms.

The development and deployment of machine learning (ML) systems can be executed easily with modern tools, but the process is typically rushed and means-to-an-end. The lack of diligence can lead to technical debt, scope creep and misaligned objectives, model misuse and failures, and expensive consequences. Engineering systems, on the other hand, follow well-defined processes and testing standards to streamline development for high-quality, reliable results. The extreme is spacecraft systems, where mission critical measures and robustness are ingrained in the development process. Drawing on experience in both spacecraft engineering and ML (from research through product across domain areas), we have developed a proven systems engineering approach for machine learning development and deployment. Our "Machine Learning Technology Readiness Levels" (MLTRL) framework defines a principled process to ensure robust, reliable, and responsible systems while being streamlined for ML workflows, including key distinctions from traditional software engineering. Even more, MLTRL defines a lingua franca for people across teams and organizations to work collaboratively on artificial intelligence and machine learning technologies. Here we describe the framework and elucidate it with several real world use-cases of developing ML methods from basic research through productization and deployment, in areas such as medical diagnostics, consumer computer vision, satellite imagery, and particle physics.

In the biopharmaceutical manufacturing, fermentation process plays a critical role impacting on productivity and profit. Since biotherapeutics are manufactured in living cells whose biological mechanisms are complex and have highly variable outputs, in this paper, we introduce a model-based reinforcement learning framework accounting for model risk to support bioprocess online learning and guide the optimal and robust customized stopping policy for fermentation process. Specifically, built on the dynamic mechanisms of protein and impurity generation, we first construct a probabilistic model characterizing the impact of underlying bioprocess stochastic uncertainty on impurity and protein growth rates. Since biopharmaceutical manufacturing often has very limited data during the development and early stage of production, we derive the posterior distribution quantifying the process model risk, and further develop the Bayesian rule based knowledge update to support the online learning on underlying stochastic process. With the prediction risk accounting for both bioprocess stochastic uncertainty and model risk, the proposed reinforcement learning framework can proactively hedge all sources of uncertainties and support the optimal and robust customized decision making. We conduct the structural analysis of optimal policy and study the impact of model risk on the policy selection. We can show that it asymptotically converges to the optimal policy obtained under perfect information of underlying stochastic process. Our case studies demonstrate that the proposed framework can greatly improve the biomanufacturing industrial practice.

Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a preconditioning scheme involving a conditional normalizing flow (NF) capable of sampling from a low-fidelity posterior distribution directly. This conditional NF is used to speed up the training of the high-fidelity objective involving minimization of the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density for indirect measurements at hand. To minimize costs associated with the forward operator, we initialize the high-fidelity NF with the weights of the pretrained low-fidelity NF, which is trained beforehand on available model and data pairs. Our numerical experiments, including a 2D toy and a seismic compressed sensing example, demonstrate that thanks to the preconditioning considerable speed-ups are achievable compared to training NFs from scratch.

Theoretical and abstract approaches to information have made great advances, but human information processing is still unmatched in many areas, including information management, representation and understanding. Neurocognitive informatics is a new, emerging field that should help to improve the matching of artificial and natural systems, and inspire better computational algorithms to solve problems that are still beyond the reach of machines. In this position paper examples of neurocognitive inspirations and promising directions in this area are given.

Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to train conditional NPs. Moreover, we propose a new member to the Neural Process family called the Gaussian Neural Process (GNP), which models predictive correlations, incorporates translation equivariance, provides universal approximation guarantees, and demonstrates encouraging performance.

Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on the tractability of the normalizing constant, thus are more flexible to parameterize and can model a more expressive family of probability distributions. However, the unknown normalizing constant of EBMs makes training particularly difficult. Our goal is to provide a friendly introduction to modern approaches for EBM training. We start by explaining maximum likelihood training with Markov chain Monte Carlo (MCMC), and proceed to elaborate on MCMC-free approaches, including Score Matching (SM) and Noise Constrastive Estimation (NCE). We highlight theoretical connections among these three approaches, and end with a brief survey on alternative training methods, which are still under active research. Our tutorial is targeted at an audience with basic understanding of generative models who want to apply EBMs or start a research project in this direction.

It is desirable, and often a necessity, for machine learning models to be robust against adversarial attacks. This is particularly true for Bayesian models, as they are well-suited for safety-critical applications, in which adversarial attacks can have catastrophic outcomes. In this work, we take a deeper look at the adversarial robustness of Bayesian Neural Networks (BNNs). In particular, we consider whether the adversarial robustness of a BNN can be increased by model choices, particularly the Lipschitz continuity induced by the prior. Conducting in-depth analysis on the case of i.i.d., zero-mean Gaussian priors and posteriors approximated via mean-field variational inference, we find evidence that adversarial robustness is indeed sensitive to the prior variance.

We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has a particularly nice form, related to the well-known semidefinite program relaxation of the maxcut problem. Using the primal-dual optimality conditions, we bound the entries and rank of the primal and dual solutions. Furthermore, we bound the optimal objective value and prove asymptotic consistency of the probability estimates of a slightly modified model under mild technical assumptions. Our experiments on synthetic RDPGs not only recover natural clusters, but also reveal the underlying low-dimensional geometry of the original data. We also demonstrate that the method recovers latent structure in the Karate Club Graph and synthetic U.S. Senate vote graphs and is scalable to graphs with up to a few hundred nodes.