arXiv subjects

Israela Solomon

Publications and source records attributed to Israela Solomon.

3 recordsLinked to original sources

arXiv2026

Selecting Informative Conformal Prediction Sets with an Optimized FCR-Controlled Approach

Conformal methods provide prediction sets for outcomes with confidence guarantees. We study their use in a selective inference setting, where inference is performed only when the prediction set is informative. The analyst may consider as informative, for example, cases with prediction sets that are sufficiently small, exclude null values, or satisfy other appropriate monotone constraints. Because inference is typically restricted to informative cases in practical applications, accounting for the resulting selection bias is crucial to maintaining false coverage rate (FCR) control. A general framework for constructing such informative conformal prediction sets while controlling the FCR on the selected sample was suggested in Gazin et al. (2025). In this work we focus on oracle-guided procedures. We derive the optimal decision policy under a suitable power objective in the oracle setting where the probability of belonging to each prediction set can be computed. In practice, of course, only estimated probabilities are available. We therefore introduce a calibration procedure that adjusts the oracle policy to maintain finite sample FCR control. We show that this approach can achieve substantially higher power than available alternatives. We demonstrate the effectiveness of our new methods for classification outcomes on both real and simulated data.

stat.ME↗

arXiv2018

Motion Planning for Multiple Unit-Ball Robots in $\mathbb{R}^d$

We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and target positions: Revolving areas are regions where robots can maneuver in order to give way to another moving robot. Given that this assumption is fulfilled, the algorithm is complete, namely it is guaranteed to find a solution or report that none exists. A key goal in our design is to make the revolving areas as economical as possible and in particular to allow different revolving areas to overlap. This makes the analysis rather involved but in return makes the algorithm conceptually fairly simple. We show that for the case of $m$ unit-discs moving among polygonal obstacles of total complexity $n$ in $\mathbb{R}^2$, the algorithm can be executed in $O(n^2m + m(m+n)\log(m+n))$ time. We implemented the algorithm for this case and tested it on several scenarios, for which we show experimental results for up to $1000$ robots. Finally, we address the problem of choosing the order of execution of the paths in decoupled algorithms that locally solve interferences and show that finding the optimal order of execution is NP-hard. This motivated us to develop a heuristic for choosing the order; we describe the heuristic and demonstrate its effectiveness in certain scenarios.

cs.CG↗

arXiv2016

A Note on Testing Intersection of Convex Sets in Sublinear Time

We present a simple sublinear time algorithm for testing the following geometric property. Let $P_1, ..., P_n$ be $n$ convex sets in $\mathbb{R}^d$ ($n \gg d$), such as polytopes, balls, etc. We assume that the complexity of each set depends only on $d$ (and not on the number of sets $n$). We test the property that there exists a common point in all sets, i.e. that their intersection is nonempty. Our goal is to distinguish between the case where the intersection is nonempty, and the case where even after removing many of the sets the intersection is empty. In particular, our algorithm returns PASS if all of the $n$ sets intersect, and returns FAIL with probability at least $1-\epsilon$ if no point belongs to $\frac{\alpha}{d+1} n$ sets, for any given $0 < \alpha, \epsilon < 1$.

cs.DS↗