This concept has been investigated extensively, but only through a worst-case lens. Instead, we study the expected distortion of voting rules with respect to an underlying distribution over voter utilities.

This article addresses the obstacle avoidance problem for setpoint stabilization and path-following tasks in complex dynamic 2D environments that go beyond conventional scenes with isolated convex obstacles. A combined motion planner and controller is proposed for setpoint stabilization that integrates the favorable convergence characteristics of closed-form motion planning techniques with the intuitive representation of system constraints through Model Predictive Control (MPC). The method is analytically proven to accomplish collision avoidance and convergence under certain conditions, and it is extended to path-following control. Various simulation scenarios using a non-holonomic unicycle robot are provided to showcase the efficacy of the control scheme and its improved convergence results compared to standard path-following MPC approaches with obstacle avoidance.

In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but only through a worst-case lens. Instead, we study the expected distortion of voting rules with respect to an underlying distribution over voter utilities. Our main contribution is the design and analysis of a novel and intuitive rule, binomial voting, which provides strong distribution-independent guarantees for both expected distortion and expected welfare.

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties -- with respect to the distribution of slices, beyond the uniform measure, is scarce. To bring new contributions to this line of research, we leverage the PAC-Bayesian theory and a central observation that SW may be interpreted as an average risk, the quantity PAC-Bayesian bounds have been designed to characterize. We provide three types of results: i) PAC-Bayesian generalization bounds that hold on what we refer as adaptive Sliced-Wasserstein distances, i.e. SW defined with respect to arbitrary distributions of slices (among which data-dependent distributions), ii) a principled procedure to learn the distribution of slices that yields maximally discriminative SW, by optimizing our theoretical bounds, and iii) empirical illustrations of our theoretical findings.

It's almost admission season and I've couple of friends who are in panic mode waiting for a call from the universities they've applied at. This made me think -- How can we predict whether a student will get an admit or not? What are the parameters for selection? Can it be mathematically expressed? All of these questions started popping up, so I decided to work out this problem and help my friend calm his nerves.