The paper addresses bias in stratified classification models and proposes a calibration method.
problem Stratified sampling introduces bias in classification models, affecting ranking performance.
method Developed an analytical solution to optimize ROC curve for stratified sampling bias.
result The proposed ranking algorithm effectively addresses stratified sampling bias in classification models.
Two algorithms reduce label complexity in machine learning using stratified sampling.
problem Reducing the number of true labels needed for machine learning evaluation.
method Proposes two algorithms that estimate strata properties and optimize evaluation accuracy.
result Demonstrates algorithms are rate optimal and reduce label complexity.
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.
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.
Paper finds efficient OPE estimator for multiple logging policies with minimum variance.
problem Finding optimal importance sampling weights for multiple logging policies with varying variances.
method Established efficiency bound under stratified sampling and proposed an estimator achieving this bound.
result Proposed estimator achieves minimum variance for any instance.
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.
Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks. In order to parallelize SGD, minibatch training is often employed. The standard approach is to uniformly sample a minibatch at each…
ABae efficiently computes subset means with expensive predicates using stratified sampling.
problem Computing subset means with expensive predicates efficiently.
method Stratified sampling and proxy models.
result Mean squared error of O(N−1) when N is split evenly between stages. 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.
Optimizes survey design for private mean estimation with reduced variance.
problem Minimizing variance in private mean estimation with privacy constraints.
method Formulates optimal survey design as an optimization problem, determining optimal subsampling sizes to minimize variance.
result Identifies the first privacy-aware stratified sampling scheme that minimizes variance under different privacy mechanisms.
A new method reduces data valuation variance for more trustworthy data trading.
problem Data valuation and trustworthy data trading in algorithmic prediction.
method Variance reduced Shapley value estimation using stratified sampling.
result VRDS method reduces estimation variance and improves data marketplace development.
MSTGD optimizes gradient descent with stratified sampling for faster convergence.
problem Fluctuation in gradient expectation and variance between iterations.
method Memory Stochastic Stratified Gradient Descent (MSTGD) with stratified sampling and variance reduction.
result MSTGD achieves an exponential convergence rate independent of dataset size and batch size.
Paper proposes SCott optimizer to reduce forecasting model training variance.
problem Large variance in gradient estimation for forecasting models.
method Stratified sampling and control variate to reduce gradient variance.
result SCott optimizer converges faster on time series forecasting problems.
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are wel…
Proposes a stratified sampling method for high-dimensional models using neural active manifolds.
problem Uncertainty propagation in computationally expensive models with many inputs.
method Neural active manifolds for nonlinear dimensionality reduction, followed by stratification in the reduced space.
result Effective variance reduction in high-dimensional models using stratified sampling.
SBSS uses similarity to split data for better classifier training.
problem Training better classifiers with realistic performance estimation.
method SBSS uses both input and output space information to split data using similarity functions.
result SBSS outperformed ordinary stratified 10-fold cross-validation in 75% of scenarios.
The paper introduces knot invariants using stratified homotopy groups.
problem Defining knot invariants in stratified spaces.
method Introducing stratified homotopy groups and proving their properties.
result Stratified Whitehead's theorem holds for these groups.
A new algorithm SSAG reduces gradient variance to achieve linear convergence in large-scale optimization.
problem Achieving linear convergence rate in large-scale optimization problems due to gradient variance.
method Introduces SSAG, a novel algorithm that combines stratified sampling and averaging over iterations to reduce gradient variance.
result SSAG achieves linear convergence rate of O((1-μ/(8CL))^k) with smaller storage and iterative costs, depending mainly on class variance.
New method estimates Wasserstein distances more efficiently.
problem Efficient estimation of Wasserstein distances.
method Orthogonal coupling in Monte Carlo estimation.
result Proposes a new variant of sliced Wasserstein distance.
New sampling strategy improves TR algorithms for stochastic optimization.
problem Derivative-free stochastic optimization with Monte Carlo estimates.
method Stratified adaptive sampling to optimize MC sample size.
result Reduced sample complexity and superior efficiency confirmed.
FedSTaS stratifies and samples clients for efficient FL.
problem Inefficient client sampling in federated learning.
method Stratifies clients based on compressed gradients, uses Neyman allocation for sampling, and samples local data uniformly.
result FedSTaS achieves higher accuracy than FedSTS in fixed training rounds.
New method accelerates large margin metric learning for nearest neighbor classification.
problem Efficiently learning metrics for nearest neighbor classification.
method Triplet mining and stratified sampling for large margin metric learning.
result Improved efficiency and scalability of optimization.
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 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.
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.
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 consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the problem of adapting to the function at the same time the number of samples into each stratum and the partition itself. More p…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully acknowledged through the posterior predictive distribution. Several such rules have b…
New groups contactomorphic to stratified ones found.
problem Understanding contactomorphic relationships between polarised and stratified Lie groups.
method Constructing modifications of stratified groups and proving contactomorphic relationships.
result Polarised groups are contactomorphic to stratified groups under specific conditions.
Study shows gradient variance increases during deep learning training, contrary to common belief.
problem Understanding and minimizing gradient variance in deep learning models.
method Gradient Clustering method using stratified sampling to minimize gradient variance.
result Gradient variance increases during training, and smaller learning rates coincide with higher variance.
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…
Sphere theorems extended to RCD spaces and improved for Einstein stratified spaces.
problem Generalizing sphere theorems to new types of spaces.
method Proved sphere theorems for RCD(n-1, n) spaces and Einstein stratified spaces.
result Extended sphere theorems to RCD spaces and improved results for Einstein stratified spaces.
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 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 s+1 can be embedded in a jet space over a stratified Lie group of step s. 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…
DM-SGD uses DPP to diversify mini-batches for SGD, improving model performance.
problem Improving mini-batch diversity in SGD to reduce variance and improve model interpretability.
method DM-SGD uses Determinantal Point Processes (DPP) to select mini-batches with diverse data points.
result DM-SGD outperforms regular SGD and stratified sampling in various setups.
Gauss-Green theorem proven for vector fields in stratified groups.
problem Establishing the Gauss-Green theorem for vector fields in noncommutative stratified Lie groups.
method Developed a new family of function spaces for divergence-measure fields and proved the Gauss-Green theorem.
result Gauss-Green theorem achieved for vector fields of low regularity on sets of finite perimeter in stratified groups.
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…
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.
Survey of Hodge theory on stratified spaces and related compactifications.
problem Analyzing Hodge theory on complex stratified spaces.
method Resolution of Thom-Mather stratified spaces to manifolds with corners, introduction of mezzoperversity, definition of Cheeger spaces.
result Novikov conjecture verified for Cheeger spaces.
Studied L2−invariants on stratified spaces, proving their stability.
problem Stability of L2−invariants on stratified spaces. method Defined and analyzed L2-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 L2-Betti numbers and Novikov-Shubin invariants under smoothly stratified, strongly stratum preserving homotopy equivalence. Analyzes solutions of stratified Lie systems and their geometric structures.
problem Nonautonomous systems of differential equations on manifolds.
method Analyzes particular solutions and properties of stratified Lie systems.
result Generalizes properties of Lie systems to stratified Lie systems.
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…