Most real world applications require dealing with stochasticity like sensor noise or predictive uncertainty, where formal specifications of desired behavior are inherently probabilistic. Despite the promise of formal verification in ensuring the reliability of neural networks, progress in the direction of probabilistic specifications has been limited.

Classical bilevel optimization is referred to as the case where there is no consensus constraint but with only two levels of the minimization subproblems, i.e.,

A recent line of research investigates how strategic agents may respond to such scoring tools to receive favorable assessments. While prior work has focused on the short-term strategic interactions between a decision-making institution (modeled as a principal) and individual decision-subjects (modeled as agents), we investigate interactions spanning multiple time-steps . In particular, we consider settings in which the agent's effort investment

We use three cameras and three screens to capture our dataset; please see Table 1 for the specifications. The following algorithms (Procedure 1 and Procedure 2) show the joint optimization method and the baseline alternating optimization method compared in the ablation study in Section 5.1 of the main paper. Procedure 1 The joint optimization algorithm.Input: Focused image M with moiré patterns and defocused blur image B without moiré patterns; Output: Estimated moiré-free image C; Procedure 2 The alternating optimization algorithm.Input: Focused image M with moiré patterns and defocused blur image B without moiré patterns; Output: Estimated moiré-free image C; We also test our model on a smartphone HUA WEI P30 PRO. To test on the real world examples, we do some preprocessing, e.g., alignment. Figure 1: Examples captured from natural scenes.

"one-shot" formulation of the Knowledge Gradient, enabled by a combination of

Efficient approximation and sampling methods of intractable distributions plays a key role in probabilistic machine learning, especially Bayesian inference.