Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable. Approximate inference techniques trade off the ability to closely resemble the posterior distribution against speed of convergence and computational efficiency. We propose a novel Gaussian variational family that allows for retaining covariances between latent processes while achieving fast convergence by marginalising out all global latent variables. After providing a proof of how this marginalisation can be done for general covariances, we restrict them to the ones we empirically found to be most important in order to also achieve computational efficiency. We provide an efficient implementation of our new approach and apply it to several benchmark datasets. It yields excellent results and strikes a better balance between accuracy and calibrated uncertainty estimates than its state-of-the-art alternatives.
Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on methodically evaluating the predictive uncertainties of these models. In this work, we demonstrate that traditional training procedures for NLMs drastically underestimate uncertainty on out-of-distribution inputs, and that they therefore cannot be naively deployed in risk-sensitive applications. We identify the underlying reasons for this behavior and p…
The Broad Institute（博德研究所）；Cornell University（康奈尔大学）；University of Pennsylvania（宾夕法尼亚大学）
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially underestimated uncertainties. Notably, in the regression case the predictive variance is typically dominated by observation noise, yielding uncertainty estimates that make little use of the input-dependent function uncertainty that makes GP priors attractive. In this work we propose two simple methods for scalable GP regression that address this issue and thus …
Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused on formally evaluating the predictive uncertainties of these models. Furthermore, existing works point out the difficulties of encoding domain knowledge in models like NLMs, making them unsuitable for applications where interpretability is required. In this work, we show that traditional training procedures for NLMs can drastically underestimate uncertainty …
Identifying Drivers of Predictive Aleatoric Uncertainty
Hasso Plattner Institute（霍普夫纳研究所）；Digital Engineering Faculty（数字工程学院）；University of Potsdam（波茨坦大学）；Freie Universität Berlin（柏林自由大学）；Department of Mathematics and Computer Science（数学与计算机科学系）；Hasso Plattner Institute for Digital Health at Mount Sinai（辛克尔医学院霍普夫纳数字健康研究所）；Icahn School of Medicine at Mount Sinai（辛克尔医学院）
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to closed-loop performance deterioration and constraint violations. In this paper we introduce a new algorithm to explicitly consider time-invariant stochastic uncertainties in optimal control problems. The difficulty of propagating stochastic variables through nonlinear functions is dealt with by combining Gaussian processes with polynomial chaos expansions. The main no…
The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A rigorous Uncertainty Quantification (UQ) process should simultaneously consider multiple sources of quantifiable uncertainties: (1) parameter uncertainty due to randomness or lack of knowledge; (2) experimental uncertainty due to measurement noise; (3) model uncertainty caused by missing/incomplete physics and numerical approximation errors, and (4) code uncer…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Frederick National Laboratory for Cancer Research（弗雷德里克国家癌症研究实验室）
Neural Network (NN) models provide potential to speed up the drug discovery process and reduce its failure rates. The success of NN models require uncertainty quantification (UQ) as drug discovery explores chemical space beyond the training data distribution. Standard NN models do not provide uncertainty information. Methods that combine Bayesian models with NN models address this issue, but are difficult to implement and more expensive to train. Some methods require changing the NN architecture or training procedure, limiting the selection of NN models. Moreover, predictive uncertainty can co…
Databases are widespread, yet extracting relevant data can be difficult. Without substantial domain knowledge, multivariate search queries often return sparse or uninformative results. This paper introduces an approach for searching structured data based on probabilistic programming and nonparametric Bayes. Users specify queries in a probabilistic language that combines standard SQL database search operators with an information theoretic ranking function called predictive relevance. Predictive relevance can be calculated by a fast sparse matrix algorithm based on posterior samples from CrossCa…
Virginia Polytechnic Institute and State University（弗吉尼亚理工大学）；Georgia Institute of Technology（佐治亚理工学院）；The Boeing Company（波音公司）
In the machine learning domain, active learning is an iterative data selection algorithm for maximizing information acquisition and improving model performance with limited training samples. It is very useful, especially for the industrial applications where training samples are expensive, time-consuming, or difficult to obtain. Existing methods mainly focus on active learning for classification, and a few methods are designed for regression such as linear regression or Gaussian process. Uncertainties from measurement errors and intrinsic input noise inevitably exist in the experimental data, …
The prediction of financial markets is a challenging yet important task. In modern electronically-driven markets, traditional time-series econometric methods often appear incapable of capturing the true complexity of the multi-level interactions driving the price dynamics. While recent research has established the effectiveness of traditional machine learning (ML) models in financial applications, their intrinsic inability to deal with uncertainties, which is a great concern in econometrics research and real business applications, constitutes a major drawback. Bayesian methods naturally appear…
Many biochemical applications such as molecular property prediction require models to generalize beyond their training domains (environments). Moreover, natural environments in these tasks are structured, defined by complex descriptors such as molecular scaffolds or protein families. Therefore, most environments are either never seen during training, or contain only a single training example. To address these challenges, we propose a new regret minimization (RGM) algorithm and its extension for structured environments. RGM builds from invariant risk minimization (IRM) by recasting simultaneous…
Bayesian Generalized Network Autoregressive Model with Structured Shrinkage and Persistence Priors
Human-Centered Artificial Intelligence Research Institute, Ewha Womans University（梨花女子大学人类中心人工智能研究所）；Department of Statistics and Actuarial Science, Soongsil University（崇实大学统计与精算科学系）
Predictive uncertainties in classification tasks are often a consequence of model inadequacy or insufficient training data. In popular applications, such as image processing, we are often required to scrutinise these uncertainties by meaningfully attributing them to input features. This helps to improve interpretability assessments. However, there exist few effective frameworks for this purpose. Vanilla forms of popular methods for the provision of saliency masks, such as SHAP or integrated gradients, adapt poorly to target measures of uncertainty. Thus, state-of-the-art tools instead proceed …
The cost and scarcity of fully supervised labels in statistical machine learning encourage using partially labeled data for model validation as a cheaper and more accessible alternative. Effectively collecting and leveraging weakly supervised data for large-space structured prediction tasks thus becomes an important part of an end-to-end learning system. We propose a new computationally-friendly methodology to construct predictive sets using only partially labeled data on top of black-box predictive models. To do so, we introduce "probe" functions as a way to describe weakly supervised instanc…
Rutgers, The State University of New Jersey（罗格斯大学新泽西州立大学）；Michigan State University（密歇根州立大学）
We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a tree-structured Ising model distribution, whereas the observable variables are generated by a binary symmetric channel taking the hidden variables as its input (flipping each bit independently with some constant probability $q\in [0,1/2)$). In the absence of noise, predictive learning on Ising models was recently studied by Bresler and Karzand (2020); this paper quantifie…
Estimates of predictive uncertainty are important for accurate model-based planning and reinforcement learning. However, predictive uncertainties---especially ones derived from modern deep learning systems---can be inaccurate and impose a bottleneck on performance. This paper explores which uncertainties are needed for model-based reinforcement learning and argues that good uncertainties must be calibrated, i.e. their probabilities should match empirical frequencies of predicted events. We describe a simple way to augment any model-based reinforcement learning agent with a calibrated model and…
This paper aims to improve the reliability of optimal control using models constructed by machine learning methods. Optimal control problems based on such models are generally non-convex and difficult to solve online. In this paper, we propose a model that combines the Hammerstein-Wiener model with input convex neural networks, which have recently been proposed in the field of machine learning. An important feature of the proposed model is that resulting optimal control problems are effectively solvable exploiting their convexity and partial linearity while retaining flexible modeling ability.…
The expense of acquiring labels in large-scale statistical machine learning makes partially and weakly-labeled data attractive, though it is not always apparent how to leverage such data for model fitting or validation. We present a methodology to bridge the gap between partial supervision and validation, developing a conformal prediction framework to provide valid predictive confidence sets -- sets that cover a true label with a prescribed probability, independent of the underlying distribution -- using weakly labeled data. To do so, we introduce a (necessary) new notion of coverage and predi…
