Bayesian Inference
Technology Readiness Levels for Machine Learning Systems
Lavin, Alexander, Gilligan-Lee, Ciarรกn M., Visnjic, Alessya, Ganju, Siddha, Newman, Dava, Ganguly, Sujoy, Lange, Danny, Baydin, Atฤฑlฤฑm Gรผneล, Sharma, Amit, Gibson, Adam, Gal, Yarin, Xing, Eric P., Mattmann, Chris, Parr, James
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.
Reinforcement Learning under Model Risk for Biomanufacturing Fermentation Control
Wang, Bo, Xie, Wei, Martagan, Tugce, Akcay, Alp
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.
Preconditioned training of normalizing flows for variational inference in inverse problems
Siahkoohi, Ali, Rizzuti, Gabrio, Louboutin, Mathias, Witte, Philipp A., Herrmann, Felix J.
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.
Neurocognitive Informatics Manifesto
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.
The Gaussian Neural Process
Bruinsma, Wessel P., Requeima, James, Foong, Andrew Y. K., Gordon, Jonathan, Turner, Richard E.
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.
How to Train Your Energy-Based Models
Song, Yang, Kingma, Diederik P.
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.
The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networks
Blaas, Arno, Roberts, Stephen J.
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.
Bayesian Inference of Random Dot Product Graphs via Conic Programming
Wu, David, Palmer, David R., Deford, Daryl R.
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.
Learning optimal Bayesian prior probabilities from data
Noninformative uniform priors are staples of Bayesian inference, especially in Bayesian machine learning. This study challenges the assumption that they are optimal and their use in Bayesian inference yields optimal outcomes. Instead of using arbitrary noninformative uniform priors, we propose a machine learning based alternative method, learning optimal priors from data by maximizing a target function of interest. Applying na\"ive Bayes text classification methodology and a search algorithm developed for this study, our system learned priors from data using the positive predictive value metric as the target function. The task was to find Wikipedia articles that had not (but should have) been categorized under certain Wikipedia categories. We conducted five sets of experiments using separate Wikipedia categories. While the baseline models used the popular Bayes-Laplace priors, the study models learned the optimal priors for each set of experiments separately before using them. The results showed that the study models consistently outperformed the baseline models with a wide margin of statistical significance (p < 0.001). The measured performance improvement of the study model over the baseline was as high as 443% with the mean value of 193% over five Wikipedia categories.
An Elo-like System for Massive Multiplayer Competitions
Rating systems play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating system for contests with many participants. It is widely applicable to competition formats with discrete ranked matches, such as online programming competitions, obstacle courses races, and some video games. The simplicity of our system allows us to prove theoretical bounds on robustness and runtime. In addition, we show that the system aligns incentives: that is, a player who seeks to maximize their rating will never want to underperform. Experimentally, the rating system rivals or surpasses existing systems in prediction accuracy, and computes faster than existing systems by up to an order of magnitude.