Long signal change-point detection

The detection of change-points in a spatially or time ordered data sequence is an important problem in many fields such as genetics and finance. We derive the asymptotic distribution of a statistic recently suggested for detecting change-points. Simulation of its estimated limit distribution leads to a new and computationally efficient change-point detection algorithm, which can be used on very long signals. We assess the algorithm via simulations and on previously benchmarked real-world data sets

High-Dimensional p-Norms

Abstract Let X = (X1,...,Xd) be a R d-valued random vector with i.i.d. components, and let ‖X‖p = ( ∑ d j=1 |Xj | p) 1/p be its p-norm, for p> 0. The impact of letting d go to infinity on ‖X‖p has surprising consequences, which may dramatically affect high-dimensional data processing. This effect is usually referred to as the distance concentration phenomenon in the computational learning literature. Despite a growing interest in this important question, previous work has essentially characterized the problem in terms of numerical experiments and incomplete mathematical statements. In the present paper, we solidify some of the arguments which previously appeared in the literature and offer new insights into the phenomenon.

Robert Merle d’Aubigné, 1900–1989

This biographical sketch of R. Merle d’Aubigné corresponds to the historic text, The Classic: Functional Results of Hip Arthroplasty with Acrylic Prosthesis, available at DOI 10.1007/s11999-008-0572-1

Asymptotic Normality in Density Support Estimation

http://www.math.washington.edu/~ejpecp/index.phpInternational audienceLet $X_1,\dots,X_n$ be $n$ independent observations drawn from a multivariate probability density $f$ with compact support $S_f$. This paper is devoted to the study of the estimator $\hat{S}_n$ of $S_f$ defined as unions of balls centered at the $X_i$ and of common radius $r_n$. Using tools from Riemannian geometry, and under mild assumptions on $f$ and the sequence $(r_n)$, we prove a central limit theorem for $\lambda (S_n \Delta S_f)$, where $\lambda$ denotes the Lebesgue measure on $\mathbb R^d$ and $\Delta$ the symmetric difference operatio

A Weighted k-Nearest Neighbor Density Estimate for Geometric Inference

Motivated by a broad range of potential applications in topological and geometric inference, we introduce a weighted version of the k-nearest neighbor density estimate. Various pointwise consistency results of this estimate are established. We present a general central limit theorem under the lightest possible conditions. In addition, a strong approximation result is obtained and the choice of the optimal set of weights is discussed. In particular, the classical k-nearest neighbor estimate is not optimal in a sense described in the manuscript. The proposed method has been implemented to recover level sets in both simulated and real-life data.Motivés par des problématiques d'inférence topologique et géométrique, cet article introduit une version pondérée de l'estimateur de densité basé sur les k-emes plus proches voisins. On établit plusieurs résultat de consistance ponctuelle. On présente un théorème de la limite centrale sous des hypothèses minimales. De plus un résultat d'approximation forte est démontré et le choix optimal des poids est discuté. En particulier, l'estimateur basé sur les k-emes plus proches voisins n'est pas optimal dans un sens précisé dans l'article. La méthode proposée a été implémentée pour retrouver les lignes de niveaux de la densité à partir de données synthétiques et réelles

Axial Skeletal Location Predicts Poor Outcome in Ewing's Sarcoma: A Single Institution Experience

Introduction. Ewing's sarcomas (EWSs) of bone and soft tissue are neuroectodermal tumors that affect both axial and appendicular locations. We hypothesized that axial location predicted poor outcome in EWS patients. Materials and Methods. Sixty-seven patients (57 with bone EWS and 10 with soft tissue EWS) were identified from our database. Thirty-four (51%) had axial EWS and 33 (49%) had appendicular EWS. Statistical analyses identified predictors of poor outcome. Results and Discussion. Axial location, large size, metastases at presentation, lack of definitive treatment, and positive surgical margins all correlated with poor outcome in univariate analysis. In multivariate analysis, axial location still predicted poor outcome when adjusted for pretreatment variables. Axial location was not statistically predictive of poor outcome when adjusted for treatment variables. Conclusions. Anatomic location has a negative effect on outcome in EWS that cannot be completely explained by pretreatment or treatment factors. Additional studies are required to determine if there is a biologic difference between axial and appendicular EWS