Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.
The use of deep learning approaches for image reconstruction is of contemporary interest in radiology, especially for approaches that solve inverse problems associated with imaging. In deployment, these models may be exposed to input distributions that are widely shifted from training data, due in part to data biases or drifts. We propose a metric based on local Lipschitz determined from a single trained model that can be used to estimate the model uncertainty for image reconstructions. We demonstrate a monotonic relationship between the local Lipschitz value and Mean Absolute Error and show that this method can be used to provide a threshold that determines whether a given DL reconstruction approach was well suited to the task. Our uncertainty estimation method can be used to identify out-of-distribution test samples, relate information regarding epistemic uncertainties, and guide proper data augmentation. Quantifying uncertainty of learned reconstruction approaches is especially pertinent to the medical domain where reconstructed images must remain diagnostically accurate.
Deep reinforcement learning (DRL) has emerged as a promising approach for developing more intelligent autonomous vehicles (AVs). A typical DRL application on AVs is to train a neural network-based driving policy. However, the black-box nature of neural networks can result in unpredictable decision failures, making such AVs unreliable. To this end, this work proposes a method to identify and protect unreliable decisions of a DRL driving policy. The basic idea is to estimate and constrain the policy's performance uncertainty, which quantifies potential performance drop due to insufficient training data or network fitting errors. By constraining the uncertainty, the DRL model's performance is always greater than that of a baseline policy. The uncertainty caused by insufficient data is estimated by the bootstrapped method. Then, the uncertainty caused by the network fitting error is estimated using an ensemble network. Finally, a baseline policy is added as the performance lower bound to avoid potential decision failures. The overall framework is called uncertainty-bound reinforcement learning (UBRL). The proposed UBRL is evaluated on DRL policies with different amounts of training data, taking an unprotected left-turn driving case as an example. The result shows that the UBRL method can identify potentially unreliable decisions of DRL policy. The UBRL guarantees to outperform baseline policy even when the DRL policy is not well-trained and has high uncertainty. Meanwhile, the performance of UBRL improves with more training data. Such a method is valuable for the DRL application on real-road driving and provides a metric to evaluate a DRL policy.
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution. Developing efficient and accurate solution strategies that account for errors on the space, time and parameter domains simultaneously is highly challenging. Indeed, it is well known that standard polynomial-based approximations on the parameter domain can incur errors that grow in time. In this work, we focus on advection-diffusion problems with parameter-dependent wind fields. A novel adaptive solution strategy is proposed that allows users to combine stochastic collocation on the parameter domain with off-the-shelf adaptive timestepping algorithms with local error control. This is a non-intrusive strategy that builds a polynomial-based surrogate that is adapted sequentially in time. The algorithm is driven by a so-called hierarchical estimator for the parametric error and balances this against an estimate for the global timestepping error which is derived from a scaling argument.
We develop the first active learning method in the predict-then-optimize framework. Specifically, we develop a learning method that sequentially decides whether to request the "labels" of feature samples from an unlabeled data stream, where the labels correspond to the parameters of an optimization model for decision-making. Our active learning method is the first to be directly informed by the decision error induced by the predicted parameters, which is referred to as the Smart Predict-then-Optimize (SPO) loss. Motivated by the structure of the SPO loss, our algorithm adopts a margin-based criterion utilizing the concept of distance to degeneracy and minimizes a tractable surrogate of the SPO loss on the collected data. In particular, we develop an efficient active learning algorithm with both hard and soft rejection variants, each with theoretical excess risk (i.e., generalization) guarantees. We further derive bounds on the label complexity, which refers to the number of samples whose labels are acquired to achieve a desired small level of SPO risk. Under some natural low-noise conditions, we show that these bounds can be better than the naive supervised learning approach that labels all samples. Furthermore, when using the SPO+ loss function, a specialized surrogate of the SPO loss, we derive a significantly smaller label complexity under separability conditions. We also present numerical evidence showing the practical value of our proposed algorithms in the settings of personalized pricing and the shortest path problem.
Wildfire propagation is a highly stochastic process where small changes in environmental conditions (such as wind speed and direction) can lead to large changes in observed behaviour. A traditional approach to quantify uncertainty in fire-front progression is to generate probability maps via ensembles of simulations. However, use of ensembles is typically computationally expensive, which can limit the scope of uncertainty analysis. To address this, we explore the use of a spatio-temporal neural-based modelling approach to directly estimate the likelihood of fire propagation given uncertainty in input parameters. The uncertainty is represented by deliberately perturbing the input weather forecast during model training. The computational load is concentrated in the model training process, which allows larger probability spaces to be explored during deployment. Empirical evaluations indicate that the proposed model achieves comparable fire boundaries to those produced by the traditional SPARK simulation platform, with an overall Jaccard index (similarity score) of 67.4% on a set of 35 simulated fires. When compared to a related neural model (emulator) which was employed to generate probability maps via ensembles of emulated fires, the proposed approach produces competitive Jaccard similarity scores while being approximately an order of magnitude faster.
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a measure of uncertainty is necessary when change point methods are deployed in sensitive applications, for example, when one is interested in determining whether an organ is viable for transplant. The key of our proposal is framing the problem as a product of multiple single changes in the scale parameter. We fit the model through an iterative procedure similar to what is done for additive models. The novelty is that each iteration returns a probability distribution on time instances, which captures the uncertainty in the change point location. Leveraging a recent result in the literature, we can show that our proposal is a variational approximation of the exact model posterior distribution. We study the algorithm's convergence and the change point localization rate. Extensive experiments in simulation studies illustrate the performance of our method and the possibility of generalizing it to more complex data-generating mechanisms. We apply the new model to an experiment involving a novel technique to assess the viability of a liver and oceanographic data.
We present CEMA: Causal Explanations for Multi-Agent decision-making; a system to generate causal explanations for agents' decisions in stochastic sequential multi-agent environments. The core of CEMA is a novel causal selection method which, unlike prior work that assumes a specific causal structure, is applicable whenever a probabilistic model for predicting future states of the environment is available. We sample counterfactual worlds with this model which are used to identify and rank the salient causes behind decisions. We also designed CEMA to meet the requirements of social explainable AI. It can generate contrastive explanations based on selected causes and it works as an interaction loop with users to assure relevance and intelligibility for them. We implement CEMA for motion planning for autonomous driving and test it in four diverse simulated scenarios. We show that CEMA correctly and robustly identifies the relevant causes behind decisions and delivers relevant explanations to users' queries.
Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.
An in-depth understanding of uncertainty is the first step to making effective decisions under uncertainty. Deep/machine learning (ML/DL) has been hugely leveraged to solve complex problems involved with processing high-dimensional data. However, reasoning and quantifying different types of uncertainties to achieve effective decision-making have been much less explored in ML/DL than in other Artificial Intelligence (AI) domains. In particular, belief/evidence theories have been studied in KRR since the 1960s to reason and measure uncertainties to enhance decision-making effectiveness. We found that only a few studies have leveraged the mature uncertainty research in belief/evidence theories in ML/DL to tackle complex problems under different types of uncertainty. In this survey paper, we discuss several popular belief theories and their core ideas dealing with uncertainty causes and types and quantifying them, along with the discussions of their applicability in ML/DL. In addition, we discuss three main approaches that leverage belief theories in Deep Neural Networks (DNNs), including Evidential DNNs, Fuzzy DNNs, and Rough DNNs, in terms of their uncertainty causes, types, and quantification methods along with their applicability in diverse problem domains. Based on our in-depth survey, we discuss insights, lessons learned, limitations of the current state-of-the-art bridging belief theories and ML/DL, and finally, future research directions.
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.