The performance of a machine learning system is usually evaluated by using i.i.d.\ observations with true labels. However, acquiring ground truth labels is expensive, while obtaining unlabeled samples may be cheaper. Stratified sampling can be beneficial in such settings and can reduce the number of true labels require…
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48 results for “stratified populations”
A/B testing improves marketing decisions by selecting effective stratification variables.
problem Improving the sensitivity of A/B testing through stratified sampling.
method Designing an algorithm to select a subset of stratification variables for variance reduction.
result The subset selection method outperforms other variance reduction techniques in A/B testing.
Optimal strategy for A/B/n testing with control in stratified populations.
problem Discovering which arms have higher weighted expectation than the control in stratified populations.
method Sequentially choosing one arm per time step based on weighted subpopulation means.
result The strategy is asymptotically optimal, ensuring correct answers with high probability.
StratPPI improves prediction-powered inference with stratified sampling.
problem Improving statistical estimates with limited human-labeled data.
method Combining small human-labeled data with large automatic-labeled data, stratifying data for tighter confidence intervals.
result StratPPI provides substantially tighter confidence intervals than unstratified approaches.
Italy's daily COVID-19 cases stratified by age groups.
problem Analyzing the spread and impact of COVID-19 across different age groups.
method Stratified daily data of COVID-19 cases by age classes.
result Detailed insights into how age affects COVID-19 outcomes.
By considering homotopies that preserve the stratification, one obtains a natural notion of homotopy for stratified spaces. In this short note, we introduce invariants of stratified homotopy, the stratified homotopy groups. We show that they satisify a stratified version of Whitehead's theorem. As an example, we introd…
Distributional Random Forests for Complex Survey Designs on Reproducing Kernel Hilbert Spacesstat.ME
SDRF estimates complex survey designs for conditional distributions.
problem Estimating conditional distributions under complex survey designs.
method Survey-calibrated distributional random forest (SDRF) with pseudo-population bootstrap and MMD split criterion.
result Established design consistency and model consistency for survey designs.
Paper introduces stratified vector bundles and their properties.
problem Understanding singular spaces and their vector bundles.
method Characterization via monoid actions and examples from various fields.
result Functorial properties extended to the stratified case.
Eigen-stratified models reduce model size and improve performance.
problem Large model size in Laplacian-regularized stratified models.
method Formulate eigen-stratified models with linear combinations of bottom eigenvectors of the graph Laplacian.
result Significant reduction in model size with eigen-stratified models.
Extends h-principle to stratified spaces using sheaf and jet theories.
problem Applying h-principle to stratified spaces.
method Developed new sheaf and bundle theories for stratified spaces, and proved the h-principle.
result Stratified continuous sheaves and homotopy fiber sheaves lead to the parametric h-principle.
We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include regular neighborhoods in PL stratified spaces.
Symplectic embedding extended to stratified spaces.
problem Symplectic embedding theorem for stratified spaces.
method Defined symplectic structure on stratified spaces, demonstrated embedding in complex projective space.
result Symplectic embedding theorem extended to stratified spaces.
Study examines APOE's impact on AD progression using a novel DEBM approach.
problem Understanding APOE's role in AD progression and developing targeted clinical trials.
method Developed a discriminative event-based model (DEBM) and proposed a stratified approach to improve model accuracy.
result Identified APOE carriers' impact on AD progression timeline, aiding clinical trial selection.
Proposes SSL method for non-randomly sampled data.
problem Evaluation of prediction rules under non-random sampling.
method Two-step procedure with imputation and augmentation.
result Proposed method outperforms supervised methods in efficiency.
Paper proves Whitney stratified spaces can be given a conically smooth structure.
problem Proving Whitney stratified spaces can be given a conically smooth structure.
method Introduced conically smooth structure by Ayala, Francis, and Tanaka. Proved conjecture that any Whitney stratified space admits a canonical conically smooth structure.
result Established a connection between Whitney stratified spaces and conically smooth spaces.
We study bordism groups and bordism homology theories based on pseudomanifolds and stratified pseudomanifolds. The main seam of the paper demonstrates that when we uses classes of spaces determined by local link properties, the stratified and unstratified bordism theories are identical; this includes the known examples…
The paper proves symplectic neighbourhood theorems for stratified subspaces.
problem Finding symplectic neighbourhoods of stratified subspaces.
method Analogy with Weinstein's neighbourhood theorem, strong version of Moser's trick, and tubular neighbourhood theorem.
result Generalization of existing constructions for exotic Lagrangians.
In this paper we introduce the notion of a smooth structure on a stratified space, the notion of a Poisson smooth structure and the notion of a weakly symplectic smooth structure on a stratified symplectic space, refining the concept of a stratified symplectic Poisson algebra introduced by Sjamaar and Lerman. We show t…
Skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations (under dimension and compactness assumptions). In general, the stratified approximate fibrations cannot be replaced by bundles, and the teardrops cannot be replaced by ma…
Jet spaces on Carnot groupsmath.DG
Jet spaces on Carnot groups have a canonical Lie group structure.
problem Understanding jet spaces on Carnot groups.
method Constructing jet spaces over stratified Lie groups and showing they are stratified Lie groups.
result Every stratified Lie group of step can be embedded in a jet space over a stratified Lie group of step .
Paper proves collapsing result for orbifolds without curvature bounds.
problem Proving collapsing result for orbifolds without curvature bounds.
method Introduces weak submersions and stratified Riemannian metrics.
result Allows Gromov-Hausdorff limits of orbifolds with strictly lower dimension.
We show that conically smooth stratified spaces embed fully faithfully into -categories. This articulates a stratified generalization of the homotopy hypothesis proposed by Grothendieck. As such, each -category defines a stack on conically smooth stratified spaces, and we identify the descent conditions…
We develop a theory of tubular neighborhoods for the lower strata in manifold stratified spaces with two strata. In these topologically stratified spaces, manifold approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include the cla…
Hypergenerated Carnot groupsmath.MG
Characterizes hypergenerated stratified groups with flat boundaries.
problem Characterizing stratified groups with flat boundaries.
method Algebraic characterization and embedding analysis.
result Hypergenerated groups have locally bi-Lipschitz embeddings of non-characteristic hypersurfaces.
Studied invariants on stratified spaces, proving their stability.
problem Stability of invariants on stratified spaces.
method Defined and analyzed -Betti numbers and Novikov-Shubin invariants for compact smoothly stratified pseudo-manifolds with a wedge metric, extending results to these pseudo-manifolds.
result Invariance of -Betti numbers and Novikov-Shubin invariants under smoothly stratified, strongly stratum preserving homotopy equivalence.
Our objective is to develop a stratified Morse theory with tangential conditions. We define a continuous strata-wise smooth Morse function on an abstract stratified space by using control conditions and radiality assumptions on the gradient vector field. For critical points of a Morse function one can show that the loc…
A new method boosts survival analysis by stratifying patients and removing noise covariates.
problem Weak detection of treatment differences in randomized clinical trials due to patient heterogeneity.
method 5-Step Stratified Testing and Amalgamation Routine (5-STAR) using elastic net Cox regression and conditional inference trees.
result The 5-STAR routine significantly improves power in detecting treatment effects compared to traditional methods.
Classification of locally standard -pseudomanifolds over topological stratified pseudomanifoldsmath.GT
Paper classifies pseudomanifolds over stratified spaces.
problem Classifying pseudomanifolds over stratified spaces.
method Introducing locally standard -pseudomanifolds and using characteristic data.
result Locally standard -pseudomanifolds over topological stratified pseudomanifolds are classified by their characteristic data.
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are us…
Stratified fibre bundlesmath.GT
A stratified bundle is a fibered space in which strata are classical bundles and in which attachment of strata is controlled by a structure category of fibers. Well known results on fibre bundles are shown to be true for stratified bundles; namely the pull back theorem, the bundle theorem and the principal bundle theor…
Proves Verdier duality for sheaves on stratified spaces.
problem Verdier duality for constructible sheaves on stratified spaces.
method Uses conically smooth stratified spaces and Lurie's Verdier duality.
result Shows equivalence between constructible sheaves and cosheaves.
In a previous article the author extended the Witten deformation to singular spaces with cone-like singularities and to a class of Morse functions called admissible Morse functions. The method applies in particular to complex cones and stratified Morse functions in the sense of the theory developed by Goresky and MacPh…
The study lists low-dimensional stratified groups and their properties.
problem Understanding the algebraic structure of stratified groups.
method Explicitly provided a list of low-dimensional stratified groups and their properties.
result All stratified groups in dimensions up to 7 and some free-nilpotent groups in dimensions up to 14 were studied.
We introduce the notions of a differentiable groupoid and a differentiable stratified groupoid, generalizations of Lie groupoids in which the spaces of objects and arrows have the structures of differentiable spaces, respectively differentiable stratified spaces, compatible with the groupoid structure. After studying b…
For a stratified group , we construct a class of polarised Lie groups, which we call modifications of , that are locally contactomorphic to it. Vice versa, we show that if a polarised group is locally contactomorphic to a stratified group , whose Lie algebra has finite Tanaka prolongation, then it must be a mo…
The main result of this paper is a sufficient condition in order to have a compact Thom-Mather stratified pseudomanifold endowed with a -iterated edge metric on its regular part -parabolic. Moreover, besides stratified pseudomanifolds, the -parabolicity of other classes of singular spaces, such as compac…
Develops deep generative models for stratified learning.
problem Challenges in learning distributions on stratified spaces with varying dimensions and singularities.
method Two generative frameworks: sieve maximum likelihood and diffusion-based.
result Establishes convergence rates and consistency for estimating intrinsic dimensions and number of strata.
Study minimax estimation of stratified structure from i.i.d. samples.
problem Estimating stratified structure from i.i.d. samples of stratified mixtures of immersed manifolds.
method Ascending hierarchical co-detection of points belonging to different layers, identifying number of layers and their dimensions, assigning points to layers accurately, estimating tangent spaces optimally.
result Achieves optimal estimation of mixture components at their optimal dimension-specific rates adaptively.
Stratify unifies and improves multi-step forecasting strategies.
problem Lack of unified frameworks for multi-step forecasting strategies.
method Proposes Stratify, a parameterized framework for multi-step forecasting.
result Novel strategies in Stratify outperform existing ones in over 84% of experiments.
Stratified models are models that depend in an arbitrary way on a set of selected categorical features, and depend linearly on the other features. In a basic and traditional formulation a separate model is fit for each value of the categorical feature, using only the data that has the specific categorical value. To thi…
This article is a survey of recent work of the author, together with Markus Banagl, Eric Leichtnam, Rafe Mazzeo, and Paolo Piazza, on the Hodge theory of stratified spaces. We discuss how to resolve a Thom-Mather stratified space to a manifold with corners with an iterated fibration structure and the generalization of …
The paper studies cohomology on incomplete manifolds and stratified spaces.
problem Analyzing cohomology groups on incomplete Riemannian manifolds and stratified spaces.
method Proves injective/surjective maps between and cohomology groups under certain conditions.
result Injective/surjective maps between and cohomology groups are established.
A stratified Lie system is a nonautonomous system of first-order ordinary differential equations on a manifold described by a -dependent vector field , where are vector fields on spanning an -dimensional Lie algebra that are tangent to the strata of a stratification …
In this article we prove that stratified spaces and other geometric subfamilies satisfy categorical Fraïssé properties, a matter that might be of interest for both geometers and logicians. As a motivation we show a new example of a stratified pseudomanifold that satisfies the finite oscillation property with respect to…
This paper surveys the significant progress over the past couple of decades in the theory of stratified spaces through the application of controlled methods as well as through the application of intersection homology.
We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the fields. They provide the most general setting to establish Gauss-Green formulas for vector fields of low regul…
For each submanifold of a stratified group, we find a number and a measure only depending on its tangent bundle, the grading and the fixed Riemannian metric. In two step stratified groups, we show that such number and measure coincide with the Hausdorff dimension and with the spherical Hausdorff measure of the submanif…
The paper characterizes and examines nilpotent complex structures on stratified Lie algebras.
problem Characterizing and understanding nilpotent complex structures on stratified Lie algebras.
method Introduced a new descending series to prove a new characterization of nilpotent complex structures and examined whether these structures preserve the strata.
result Found that there exists a -invariant stratification on a step 2 nilpotent Lie algebra with a complex structure.