arXiv subjects

Jean-Eudes Dazard

Publications and source records attributed to Jean-Eudes Dazard.

6 recordsLinked to original sources

arXiv2022

High Dimensional Mode Hunting Using Pettiest Components Analysis

Principal components analysis has been used to reduce the dimensionality of datasets for a long time. In this paper, we will demonstrate that in mode detection the components of smallest variance, the pettiest components, are more important. We prove that for a multivariate normal or Laplace distribution, we obtain boxes of optimal volume by implementing "pettiest component analysis", in the sense that their volume is minimal over all possible boxes with the same number of dimensions and fixed probability. This reduction in volume produces an information gain that is measured using active information. We illustrate our results with a simulation and a search for modal patterns of digitized images of hand-written numbers using the famous MNIST database; in both cases pettiest components work better than their competitors. In fact, we show that modes obtained with pettiest components generate better written digits for MNIST than principal components.

stat.ME↗

arXiv2020

Mode hunting through active information

We propose a new method to find modes based on active information. We develop an algorithm that, when applied to the whole space, will say whether there are any modes present \textit{and} where they are; this algorithm will reduce the dimensionality without resorting to Principal Components; and more importantly, population-wise, will not detect modes when they are not present.

physics.data-an↗

arXiv2015

Cross-validation and Peeling Strategies for Survival Bump Hunting using Recursive Peeling Methods

We introduce a framework to build a survival/risk bump hunting model with a censored time-to-event response. Our Survival Bump Hunting (SBH) method is based on a recursive peeling procedure that uses a specific survival peeling criterion derived from non/semi-parametric statistics such as the hazards-ratio, the log-rank test or the Nelson-Aalen estimator. To optimize the tuning parameter of the model and validate it, we introduce an objective function based on survival or prediction-error statistics, such as the log-rank test and the concordance error rate. We also describe two alternative cross-validation techniques adapted to the joint task of decision-rule making by recursive peeling and survival estimation. Numerical analyses show the importance of replicated cross-validation and the differences between criteria and techniques in both low and high-dimensional settings. Although several non-parametric survival models exist, none addresses the problem of directly identifying local extrema. We show how SBH efficiently estimates extreme survival/risk subgroups unlike other models. This provides an insight into the behavior of commonly used models and suggests alternatives to be adopted in practice. Finally, our SBH framework was applied to a clinical dataset. In it, we identified subsets of patients characterized by clinical and demographic covariates with a distinct extreme survival outcome, for which tailored medical interventions could be made. An R package `PRIMsrc` is available on CRAN and GitHub.

stat.ME↗

arXiv2014

Unsupervised Bump Hunting Using Principal Components

Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used effectively within a response-predictor set relationship in the context of mode hunting. Specifically focusing on the Patient Rule Induction Method (PRIM), we first develop a fast version of this algorithm (fastPRIM) under normality which facilitates the theoretical studies to follow. Using basic geometrical arguments, we then demonstrate how the PC rotation of the predictor space alone can in fact generate improved mode estimators. Simulation results are used to illustrate our findings.

stat.ML↗

arXiv2014

On the explanatory power of principal components

We show that if we have an orthogonal base ($u_1,\ldots,u_p$) in a $p$-dimensional vector space, and select $p+1$ vectors $v_1,\ldots, v_p$ and $w$ such that the vectors traverse the origin, then the probability of $w$ being to closer to all the vectors in the base than to $v_1,\ldots, v_p$ is at least 1/2 and converges as $p$ increases to infinity to a normal distribution on the interval [-1,1]; i.e., $Φ(1)-Φ(-1)\approx0.6826$. This result has relevant consequences for Principal Components Analysis in the context of regression and other learning settings, if we take the orthogonal base as the direction of the principal components.

math.PR↗

arXiv2004

Design Principle of Gene Expression Used by Human Stem Cells; Implication for Pluripotency

Human embryonic stem cells (ESC) are undifferentiated and are endowed with the capacities of self renewal and pluripotential differentiation. Adult stem cells renew their own tissue, but whether they can trans-differentiate to other tissues is still controversial. To understand the genetic program that underlies the pluripotency of stem cells, we compared the transcription profile of ESC with that of progenitor/stem cells of human hematopoietic and keratinocytic origins, along with their mature cells to be viewed as snapshots along tissue differentiation. ESC gene profile show higher complexity with significantly more highly expressed genes than adult cells. We hypothesize that ESC use a strategy of expressing genes that represent various differentiation pathways and selection of only a few for continuous expression upon differentiation to a particular target. Such a strategy may be necessary for the pluripotency of ESC. The progenitors of either hematopoietic or keratinocytic cells also follow the same design principle. Using advanced clustering, we show that many of the ESC expressed genes are turned off in the progenitors/stem cells followed by a further downregulation in adult tissues. Concomitantly, genes specific to the target tissue are upregulated towards matured cells of skin or blood.

q-bio.QM↗