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Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of the need to query expensive numerical solvers repeatedly. Projection-based reduced order models (ROMs), such as the Galerkin-reduced basis (RB) method, have been extensively developed in the last decades to overcome the computational complexity of high fidelity full order models (FOMs), providing remarkable speedups when addressing UQ tasks related with parameterized differential problems. Nonetheless, constructing a projection-based ROM that can be efficiently queried usually requires extensive modifications to the original code, a task which is non-trivial for nonlinear problems, or even not possible at all when proprietary software is used. Non-intrusive ROMs - which rely on the FOM as a black box - have been recently developed to overcome this issue. In this work, we consider ROMs exploiting proper orthogonal decomposition to construct a reduced basis from a set of FOM snapshots, and Gaussian process regression (GPR) to approximate the RB projection coefficients. Two different approaches, namely a global GPR and a tensor-decomposition-based GPR, are explored on a set of 3D time-dependent solid mechanics examples. Finally, the non-intrusive ROM is exploited to perform global sensitivity analysis (relying on both screening and variance-based methods) and parameter estimation (through Markov chain Monte Carlo methods), showing remarkable computational speedups and very good accuracy compared to high-fidelity FOMs.

Time-inconsistency is a characteristic of human behavior in which people plan for long-term benefits but take actions that differ from the plan due to conflicts with short-term benefits. Such time-inconsistent behavior is believed to be caused by present bias, a tendency to overestimate immediate rewards and underestimate future rewards. It is essential in behavioral economics to investigate the relationship between present bias and time-inconsistency. In this paper, we propose a model for analyzing agent behavior with present bias in tasks to make progress toward a goal over a specific period. Unlike previous models, the state sequence of the agent can be described analytically in our model. Based on this property, we analyze three crucial problems related to agents under present bias: task abandonment, optimal goal setting, and optimal reward scheduling. Extensive analysis reveals how present bias affects the condition under which task abandonment occurs and optimal intervention strategies. Our findings are meaningful for preventing task abandonment and intervening through incentives in the real world.

Deep learning-based grasp prediction models have become an industry standard for robotic bin-picking systems. To maximize pick success, production environments are often equipped with several end-effector tools that can be swapped on-the-fly, based on the target object. Tool-change, however, takes time. Choosing the order of grasps to perform, and corresponding tool-change actions, can improve system throughput; this is the topic of our work. The main challenge in planning tool change is uncertainty - we typically cannot see objects in the bin that are currently occluded. Inspired by queuing and admission control problems, we model the problem as a Markov Decision Process (MDP), where the goal is to maximize expected throughput, and we pursue an approximate solution based on model predictive control, where at each time step we plan based only on the currently visible objects. Special to our method is the idea of void zones, which are geometrical boundaries in which an unknown object will be present, and therefore cannot be accounted for during planning. Our planning problem can be solved using integer linear programming (ILP). However, we find that an approximate solution based on sparse tree search yields near optimal performance at a fraction of the time. Another question that we explore is how to measure the performance of tool-change planning: we find that throughput alone can fail to capture delicate and smooth behavior, and propose a principled alternative. Finally, we demonstrate our algorithms on both synthetic and real world bin picking tasks.

Deterministic methods for motion planning guarantee safety amidst uncertainty in obstacle locations by trying to restrict the robot from operating in any possible location that an obstacle could be in. Unfortunately, this can result in overly conservative behavior. Chance-constrained optimization can be applied to improve the performance of motion planning algorithms by allowing for a user-specified amount of bounded constraint violation. However, state-of-the-art methods rely either on moment-based inequalities, which can be overly conservative, or make it difficult to satisfy assumptions about the class of probability distributions used to model uncertainty. To address these challenges, this work proposes a real-time, risk-aware reachability based motion planning framework called RADIUS. The method first generates a reachable set of parameterized trajectories for the robot offline. At run time, RADIUS computes a closed-form over-approximation of the risk of a collision with an obstacle. This is done without restricting the probability distribution used to model uncertainty to a simple class (e.g., Gaussian). Then, RADIUS performs real-time optimization to construct a trajectory that can be followed by the robot in a manner that is certified to have a risk of collision that is less than or equal to a user-specified threshold. The proposed algorithm is compared to several state-of-the-art chance-constrained and deterministic methods in simulation, and is shown to consistently outperform them in a variety of driving scenarios. A demonstration of the proposed framework on hardware is also provided.

Deep regression is an important problem with numerous applications. These range from computer vision tasks such as age estimation from photographs, to medical tasks such as ejection fraction estimation from echocardiograms for disease tracking. Semi-supervised approaches for deep regression are notably under-explored compared to classification and segmentation tasks, however. Unlike classification tasks, which rely on thresholding functions for generating class pseudo-labels, regression tasks use real number target predictions directly as pseudo-labels, making them more sensitive to prediction quality. In this work, we propose a novel approach to semi-supervised regression, namely Uncertainty-Consistent Variational Model Ensembling (UCVME), which improves training by generating high-quality pseudo-labels and uncertainty estimates for heteroscedastic regression. Given that aleatoric uncertainty is only dependent on input data by definition and should be equal for the same inputs, we present a novel uncertainty consistency loss for co-trained models. Our consistency loss significantly improves uncertainty estimates and allows higher quality pseudo-labels to be assigned greater importance under heteroscedastic regression. Furthermore, we introduce a novel variational model ensembling approach to reduce prediction noise and generate more robust pseudo-labels. We analytically show our method generates higher quality targets for unlabeled data and further improves training. Experiments show that our method outperforms state-of-the-art alternatives on different tasks and can be competitive with supervised methods that use full labels. Our code is available at //github.com/xmed-lab/UCVME.

Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative'' labels, which occur when some classes are more likely to be labeled than others. In the missing data literature, such labels are called missing not at random. In this paper, we propose a novel approach to address this issue by estimating the missing-data mechanism and using inverse propensity weighting to debias any SSL algorithm, including those using data augmentation. We also propose a likelihood ratio test to assess whether or not labels are indeed informative. Finally, we demonstrate the performance of the proposed methods on different datasets, in particular on two medical datasets for which we design pseudo-realistic missing data scenarios.

The vast amount of health data has been continuously collected for each patient, providing opportunities to support diverse healthcare predictive tasks such as seizure detection and hospitalization prediction. Existing models are mostly trained on other patients data and evaluated on new patients. Many of them might suffer from poor generalizability. One key reason can be overfitting due to the unique information related to patient identities and their data collection environments, referred to as patient covariates in the paper. These patient covariates usually do not contribute to predicting the targets but are often difficult to remove. As a result, they can bias the model training process and impede generalization. In healthcare applications, most existing domain generalization methods assume a small number of domains. In this paper, considering the diversity of patient covariates, we propose a new setting by treating each patient as a separate domain (leading to many domains). We develop a new domain generalization method ManyDG, that can scale to such many-domain problems. Our method identifies the patient domain covariates by mutual reconstruction and removes them via an orthogonal projection step. Extensive experiments show that ManyDG can boost the generalization performance on multiple real-world healthcare tasks (e.g., 3.7% Jaccard improvements on MIMIC drug recommendation) and support realistic but challenging settings such as insufficient data and continuous learning.

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability measures rather than points in $\mathbb{R}^n$, and that finding low-dimensional descriptions of such datasets requires manifold learning algorithms in the Wasserstein space. Most available algorithms are based on computing the pairwise Wasserstein distance matrix, which can be computationally challenging for large datasets in high dimensions. Our algorithm leverages approximation schemes such as Sinkhorn distances and linearized optimal transport to speed-up computations, and in particular, avoids computing a pairwise distance matrix. We provide guarantees on the embedding quality under such approximations, including when explicit descriptions of the probability measures are not available and one must deal with finite samples instead. Experiments demonstrate that LOT Wassmap attains correct embeddings and that the quality improves with increased sample size. We also show how LOT Wassmap significantly reduces the computational cost when compared to algorithms that depend on pairwise distance computations.

Existing statistical methods can estimate a policy, or a mapping from covariates to decisions, which can then instruct decision makers (e.g., whether to administer hypotension treatment based on covariates blood pressure and heart rate). There is great interest in using such data-driven policies in healthcare. However, it is often important to explain to the healthcare provider, and to the patient, how a new policy differs from the current standard of care. This end is facilitated if one can pinpoint the aspects of the policy (i.e., the parameters for blood pressure and heart rate) that change when moving from the standard of care to the new, suggested policy. To this end, we adapt ideas from Trust Region Policy Optimization (TRPO). In our work, however, unlike in TRPO, the difference between the suggested policy and standard of care is required to be sparse, aiding with interpretability. This yields ``relative sparsity," where, as a function of a tuning parameter, $\lambda$, we can approximately control the number of parameters in our suggested policy that differ from their counterparts in the standard of care (e.g., heart rate only). We propose a criterion for selecting $\lambda$, perform simulations, and illustrate our method with a real, observational healthcare dataset, deriving a policy that is easy to explain in the context of the current standard of care. Our work promotes the adoption of data-driven decision aids, which have great potential to improve health outcomes.

Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation monitoring. However, there are also limitations; satellites are difficult to manufacture, expensive to maintain, and tricky to launch into orbit. Therefore, it is critical that satellites are employed efficiently. This poses a challenge known as the satellite mission planning problem, which could be computationally prohibitive to solve on large scales. However, close-to-optimal algorithms can often provide satisfactory resolutions, such as greedy reinforcement learning, and optimization algorithms. This paper introduces a set of quantum algorithms to solve the mission planning problem and demonstrate an advantage over the classical algorithms implemented thus far. The problem is formulated as maximizing the number of high-priority tasks completed on real datasets containing thousands of tasks and multiple satellites. This work demonstrates that through solution-chaining and clustering, optimization and machine learning algorithms offer the greatest potential for optimal solutions. Most notably, this paper illustrates that a hybridized quantum-enhanced reinforcement learning agent can achieve a completion percentage of 98.5% over high-priority tasks, which is a significant improvement over the baseline greedy methods with a completion rate of 63.6%. The results presented in this work pave the way to quantum-enabled solutions in the space industry and, more generally, future mission planning problems across industries.