arXiv subjects

Yuexuan Wu

Publications and source records attributed to Yuexuan Wu.

3 recordsLinked to original sources

arXiv2026

Principal Nested Cones

In many applications, the data lie on a type of cone, where there is a distinction between an overall scale variable and the remaining scale-free structure. For example, the joint size and shape of objects are points on a cone, where size represents scale, and shape is the scale-free structure. Dimension reduction is central in such applications, as shape data are often high-dimensional. Interactions between shape and size are widespread and of significant interest in real-world applications. However, most existing methods either lack a single notion of size or focus solely on shape, effectively removing size information. We propose Principal Nested Cones (PNC), a nonlinear dimension reduction framework that preserves both shape and size. PNC represents data through a sequence of nested hypercones and progressively projects observations onto lower-dimensional cone spaces. The resulting PNC scores provide low-dimensional representations that jointly capture size-shape variation in an interpretable manner. To enable scalable computation in ultra-high-dimensional settings, we develop a fast approximation combining PCA-based transformation with standard PNC. Simulation studies and real data applications demonstrate that PNC captures nonlinear size-shape structure, improves representation and reconstruction, and yields interpretable insights across morphometric, developmental, and molecular datasets.

stat.ME↗

arXiv2026

"Game, Set, Match": Double Delight Watching a Grand Slam Tennis Match

Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the match, and where outcomes of points played are independent of each other, is assumed. Probabilities of winning a game tie-breaker, a game, a set tie-breaker, a set, and the match are obtained. Since tennis scoring systems are unique, probability calculations require decomposing big and complicated problems into smaller and simpler constituent problems, solving these sub-problems, then combining to obtain the solution to the big problem. The problems that arise from tennis scoring systems offer excellent pedagogical venues for teaching probability, in particular, the use of the Theorem of Total Probability and the Iterated Rules for Mean, Variance, and Covariance. There are also many interesting questions in tennis, foremost of which is whether a tennis match under this assumption will actually end with probability one; or whether when two players of `equal abilities' play a match, the first server possesses an advantage. These questions are addressed in this work. Tennis scoring systems are technically statistical decision systems to determine the better player. Since such a decision system is based on a finite number of points played, erroneous decisions could arise, such as the inferior player winning the match. We compare different systems in terms of the probability of the better player winning, as well as the duration of the match in terms of the number of points played.

math.PR↗

arXiv2021

Elastic Shape Analysis of Brain Structures for Predictive Modeling of PTSD

There is increasing evidence on the importance of brain morphology in predicting and classifying mental disorders. However, the vast majority of current shape approaches rely heavily on vertex-wise analysis that may not successfully capture complexities of subcortical structures. Additionally, the past works do not include interactions between these structures and exposure factors. Predictive modeling with such interactions is of paramount interest in heterogeneous mental disorders such as PTSD, where trauma exposure interacts with brain shape changes to influence behavior. We propose a comprehensive framework that overcomes these limitations by representing brain substructures as continuous parameterized surfaces and quantifying their shape differences using elastic shape metrics. Using the elastic shape metric, we compute shape summaries of subcortical data and represent individual shapes by their principal scores. These representations allow visualization tools that help localize changes when these PCs are varied. Subsequently, these PCs, the auxiliary exposure variables, and their interactions are used for regression modeling. We apply our method to data from the Grady Trauma Project, where the goal is to predict clinical measures of PTSD using shapes of brain substructures. Our analysis revealed considerably greater predictive power under the elastic shape analysis than widely used approaches such as vertex-wise shape analysis and even volumetric analysis. It helped identify local deformations in brain shapes related to change in PTSD severity. To our knowledge, this is one of the first brain shape analysis approaches that can seamlessly integrate the pre-processing steps under one umbrella for improved accuracy and are naturally able to account for interactions between brain shape and additional covariates to yield superior predictive performance when modeling clinical outcomes.

cs.CV↗