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Variational Autoencoders (VAEs) have gained significant popularity among researchers as a powerful tool for understanding unknown distributions based on limited samples. This popularity stems partly from their impressive performance and…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
Conditional value-at-risk (CVaR) precisely characterizes the influence that rare, catastrophic events can exert over decisions. Such characterizations are important for both normal decision-making and for psychiatric conditions such as…
Treatment non-compliance, where individuals deviate from their assigned experimental conditions, frequently complicates the estimation of causal effects. To address this, we introduce a novel learning framework based on a mixture of experts…
We present a new uncertainty principle for risk-aware statistical estimation, effectively quantifying the inherent trade-off between mean squared error ($\mse$) and risk, the latter measured by the associated average predictive squared…
In the classical Reinforcement Learning (RL) setting, one aims to find a policy that maximizes its expected return. This objective may be inappropriate in safety-critical domains such as healthcare or autonomous driving, where intrinsic…
Ensemble Conditional Variance Estimation (ECVE) is a novel sufficient dimension reduction (SDR) method in regressions with continuous response and predictors. ECVE applies to general non-additive error regression models. It operates under…
Medical image segmentation is inherently an ambiguous task due to factors such as partial volumes and variations in anatomical definitions. While in most cases the segmentation uncertainty is around the border of structures of interest,…
We consider a discrete-time nonatomic routing game with variable demand and uncertain costs. Given a routing network with single origin and destination, the cost function of each edge depends on some uncertain persistent state parameter. At…
Risk management is very important for individual investors or companies. There are many ways to measure the risk of investment. Prices of risky assets vary rapidly and randomly due to the complexity of finance market. Random interval is a…
In this paper we focus on noncooperative games with uncertain constraints coupling the agents' decisions. We consider a setting where bounded deviations of agents' decisions from the equilibrium are possible, and uncertain constraints are…
Weighted average derivative effects (WADEs) are nonparametric estimands with uses in economics and causal inference. Debiased WADE estimators typically require learning the conditional mean outcome as well as a Riesz representer (RR) that…
The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed…
Safe navigation is a fundamental challenge in multi-robot systems due to the uncertainty surrounding the future trajectory of the robots that act as obstacles for each other. In this work, we propose a principled data-driven approach where…
We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the…
Balancing safety and efficiency when planning in crowded scenarios with uncertain dynamics is challenging where it is imperative to accomplish the robot's mission without incurring any safety violations. Typically, chance constraints are…
The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and…
We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a generative model of the data distribution. WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution,…
Modeling the decision-making behavior of vehicles presents unique challenges, particularly during unprotected left turns at intersections, where the uncertainty of human drivers is especially pronounced. In this context, connected…
This paper investigates the application of probabilistic prediction methodologies in route planning within a road network context. Specifically, we introduce the Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which…