Distributionally Robust Skeleton Learning of Discrete Bayesian Networks

We consider the problem of learning the exact skeleton of general discrete Bayesian networks from potentially corrupted data. Building on distributionally robust optimization and a regression approach, we propose to optimize the most adverse risk over a family of distributions within bounded Wasserstein distance or KL divergence to the empirical distribution. The worst-case risk accounts for the effect of outliers. The proposed approach applies for general categorical random variables without assuming faithfulness, an ordinal relationship or a specific form of conditional distribution. We present efficient algorithms and show the proposed methods are closely related to the standard regularized regression approach. Under mild assumptions, we derive non-asymptotic guarantees for successful structure learning with logarithmic sample complexities for bounded-degree graphs. Numerical study on synthetic and real datasets validates the effectiveness of our method. Code is available at https://github.com/DanielLeee/drslbn.Comment: NeurIPS 2O23 Spotlight. More empirical results adde

A shadow function model based on perspective projection and atmospheric effect for satellites in eclipse

Accurate Solar Radiation Pressure (SRP) modelling is critical for correctly describing the dynamics of satellites. A shadow function is a unitless quantity varying between 0 and 1 to scale the solar radiation flux at a satellite’s location during eclipses. Errors in modelling shadow function lead to inaccuracy in SRP that degrades the orbit quality. Shadow function modelling requires solutions to a geometrical problem (Earth’s oblateness) and a physical problem (atmospheric effects). This study presents a new shadow function model (PPM_atm) which uses a perspective projection based approach to solve the geometrical problem rigorously and a linear function to describe the reduction of solar radiation flux due to atmospheric effects. GRACE (Gravity Recovery And Climate Experiment) satellites carry accelerometers that record variations of non-conservative forces, which reveal the variations of shadow function during eclipses. In this study, the PPM_atm is validated using accelerometer observations of the GRACE-A satellite. Test results show that the PPM_atm is closer to the variations in accelerometer observations than the widely used SECM (Spherical Earth Conical Model). Taking the accelerometer observations derived shadow function as the “truth”, the relative error in PPM_atm is −0.79% while the SECM 11.07%. The influence of the PPM_atm is also shown in orbit prediction for Galileo satellites. Compared with the SECM, the PPM_atm can reduce the radial orbit error RMS by 5.6 cm over a 7-day prediction. The impacts of the errors in shadow function modelling on the orbit remain to be systematic and should be mitigated in long-term orbit prediction

When Humans Aren't Optimal: Robots that Collaborate with Risk-Aware Humans

In order to collaborate safely and efficiently, robots need to anticipate how their human partners will behave. Some of today's robots model humans as if they were also robots, and assume users are always optimal. Other robots account for human limitations, and relax this assumption so that the human is noisily rational. Both of these models make sense when the human receives deterministic rewards: i.e., gaining either $100 or$130 with certainty. But in real world scenarios, rewards are rarely deterministic. Instead, we must make choices subject to risk and uncertainty--and in these settings, humans exhibit a cognitive bias towards suboptimal behavior. For example, when deciding between gaining $100 with certainty or$130 only 80% of the time, people tend to make the risk-averse choice--even though it leads to a lower expected gain! In this paper, we adopt a well-known Risk-Aware human model from behavioral economics called Cumulative Prospect Theory and enable robots to leverage this model during human-robot interaction (HRI). In our user studies, we offer supporting evidence that the Risk-Aware model more accurately predicts suboptimal human behavior. We find that this increased modeling accuracy results in safer and more efficient human-robot collaboration. Overall, we extend existing rational human models so that collaborative robots can anticipate and plan around suboptimal human behavior during HRI.Comment: ACM/IEEE International Conference on Human-Robot Interactio