A new method calculates intrinsic effective sample size for manifold-valued data.
problem Challenges in choosing effective sample size for manifold-valued data.
method Proposes an intrinsic effective sample size based on kernel discrepancy.
result Establishes an exact finite-sample risk interpretation and consistency of the estimator.
We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension D of the conditioning variable is larger than the sample size n, estimation and inference is feasible as long as the distribution of the conditioning variable has small intrinsic…
Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
New summary measures reveal geometric structure in weighted measures on manifolds.
problem Lack of geometric information in standard weight-only summaries.
method Heat-kernel entropy profiles, tracking nonuniformity across scales.
result Geometric effective sample size discounts nearby or duplicate particles.
New theory shows deep networks adapt to data's intrinsic dimensionality even when data isn't on a low-dimensional manifold.
problem Existing theories on deep nonparametric regression assume data lie on a low-dimensional manifold, which is often not the case in real-world applications.
method Introduces effective Minkowski dimension to characterize the intrinsic dimension of data subsets and proves sample complexity depends on this new complexity notation.
result Deep neural networks can adapt to the effective Minkowski dimension of data, circumventing the curse of dimensionality for moderate sample sizes.
Bagging reduces variance in LID estimation by preserving local distribution of NN distances.
problem High estimation variance from limited data in small neighborhoods.
method Subbagging to preserve local distribution of NN distances, combined with ensemble size.
result Bagging significantly reduces variance and MSE in LID estimation.
Study provides bounds for estimating intrinsic dimension using Gaussian kernels.
problem Estimating intrinsic dimension from data.
method Finite-sample concentration and anti-concentration bounds for Gaussian kernel sums.
result Explicit dependence on sample size, bandwidth, and geometric parameters.
New method adapts DLMs to intrinsic data dependence without prior knowledge.
problem Understanding how unmasking schedules affect DLM generation quality.
method Adapts unmasking schedule to target data distribution's dependence structure.
result Sampling convergence guarantees improve for low-complexity distributions.
Generative Adversarial Networks (GANs) are an elegant mechanism for data generation. However, a key challenge when using GANs is how to best measure their ability to generate realistic data. In this paper, we demonstrate that an intrinsic dimensional characterization of the data space learned by a GAN model leads to an…
Generates counterfactuals in target domain from source domain observations.
problem Cross-domain learning with domain shifts and lack of parallel datasets.
method Unsupervised, Neural Causal Models, Joint Causal Graphs, Effect-Intrinsic vs Domain-Intrinsic Variables.
result Framework generates counterfactuals that closely match ground truth.
This paper deals with a new filter algorithm for selecting the smallest subset of features carrying all the information content of a data set (i.e. for removing redundant features). It is an advanced version of the fractal dimension reduction technique, and it relies on the recently introduced Morisita estimator of Int…
New estimators for intrinsic dimension and Wasserstein distance improve OT accuracy.
problem Intrinsic dimension estimation and Wasserstein distance estimation in large-scale OT.
method Introduces novel estimators for intrinsic dimension and Wasserstein distance.
result Simple, tuning-free estimator of OT and fast intrinsic dimension estimator.
Study improves denoising score matching under relaxed manifold assumptions.
problem Improving denoising score matching under relaxed manifold assumptions.
method Model density with nonparametric Gaussian mixtures, relax manifold assumption, derive non-asymptotic bounds.
result Non-asymptotic bounds on approximation and generalization errors, rates of convergence determined by intrinsic dimension.
The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood est…
We consider the roughness properties of NYSE (New York Stock Exchange) stock-price fluctuations. The statistical properties of the data are relatively homogeneous within the same day but the large jumps between different days prevent the extension of the analysis to large times. This leads to intrinsic finite size effe…
New method tightens sub-Gaussian concentration inequalities.
problem Estimating variance-type parameters of sub-Gaussian distributions.
method Using sub-Gaussian intrinsic moment norm to maximize normalized moments.
result Provides tighter sub-Gaussian concentration inequalities.
This paper explores how effective sample size, dimensionality, and model performance are related in covariate shift adaptation.
problem Understanding the relationship between effective sample size, dimensionality, and generalization in covariate shift adaptation.
method Building a unified theory connecting effective sample size, data dimensionality, and generalization in the context of covariate shift adaptation.
result Dimensionality reduction or feature selection can increase effective sample size, supporting the practice of reducing dimensionality before covariate shift adaptation.
This paper classifies chiral graphs up to size 12.
problem Understanding the chirality of simple graphs to predict molecular behavior.
method Classifying minor minimal intrinsically chiral graphs among simple graphs of size up to 12.
result Complete set of minor minimal graphs for intrinsic properties of chiral molecules.
Study shows dataset properties impact adversarial machine learning robustness.
problem Vulnerability of DNNs to adversarial attacks.
method Examined five datasets, analyzed input size and contrast effects.
result Input size and contrast significantly influence adversarial success.
This paper analyzes deep federated learning for low-dimensional data, revealing intrinsic dimensionality's role in convergence rates.
problem Insufficient investigation of generalization error in heterogeneous federated learning, especially for low-dimensional data.
method Statistical analysis of deep federated regression in a two-stage sampling model.
result Intrinsic dimensionality, characterized by entropic dimension, determines convergence rates for deep learners.
Data acquisition, storage and management have been improved, while the key factors of many phenomena are not well known. Consequently, irrelevant and redundant features artificially increase the size of datasets, which complicates learning tasks, such as regression. To address this problem, feature selection methods ha…
A graph is intrinsically knotted if every embedding contains a knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, K7 and the 13 graphs obtained from K7 by ∇Y moves, are the only minor minimal intrinsically knotted graphs with 21 edges. This set incl…
The classification of multi-class microarray datasets is a hard task because of the small samples size in each class and the heavy overlaps among classes. To effectively solve these problems, we propose novel Error Correcting Output Code (ECOC) algorithm by Enhance Class Separability related Data Complexity measures du…
The paper explores properties of projections and gradient methods in hyperbolic space forms.
problem Optimization problems in hyperbolic space forms.
method Intrinsic κ-projection and gradient projection methods.
result Every accumulation point of the sequence generated by the gradient projection method is a stationary point.
This paper investigates the impact of pre-existing offline data on online learning, in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unkn…
Privacy affects how much data is needed for CVaR optimization.
problem Privacy constraints impact the effective sample size for CVaR optimization.
method Analyzes the privacy-relevant sample size and decomposes CVaR excess risk.
result The effective private tail sample size is εnτ, affecting CVaR learning rates.
Estimates intrinsic dimension of data for GANs.
problem Estimating intrinsic dimension of high-dimensional data.
method Uses Wasserstein distances for estimation.
result Provides sample complexity bounds for GANs.
DBPA assesses LLM perturbations using frequentist hypothesis testing.
problem Quantifying input perturbation impacts on LLM outputs.
method DBPA reformulates perturbation analysis as frequentist hypothesis testing, using Monte Carlo sampling for empirical null and alternative distributions.
result DBPA provides interpretable p-values and scalar effect sizes for LLM perturbations.
Scaling laws found for reinforcement learning performance with model size and compute.
problem Challenges in extending generative modeling scaling laws to reinforcement learning.
method Introduced intrinsic performance as a monotonic function of mean episode return.
result Intrinsic performance scales as a power law in model size and environment interactions.
Synthetic augmentation helps but not always in imbalanced learning.
problem Imbalanced learning causes poor performance on rare classes.
method Developed a statistical framework for synthetic augmentation in imbalanced learning.
result Synthetic augmentation is not always beneficial and depends on the imbalance regime.
Reduced sample complexity for group-invariant distributions.
problem Improving sample complexity for estimating divergences of group-invariant distributions.
method Quantified reduction in sample complexity for Wasserstein-1 metric and Lipschitz-regularized α-divergences under finite and infinite groups.
result Sample complexity reduction proportional to group size for finite groups, and convergence rate depends on intrinsic dimension for infinite groups.
Consider a Markov decision process (MDP) that admits a set of state-action features, which can linearly express the process's probabilistic transition model. We propose a parametric Q-learning algorithm that finds an approximate-optimal policy using a sample size proportional to the feature dimension K and invariant …
Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a manifold whose Intrinsic Dimension (ID) is much lower than the crude large number of co…
Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
MRI image quality affects statistical and predictive analysis of brain morphology.
problem Impact of MRI image quality on statistical and predictive analysis of brain morphology.
method Systematic testing of image quality on univariate statistics and machine learning classification using three large datasets.
result Low-quality MRI data significantly affects detecting significant sex/gender differences in smaller samples, but not in larger ones.
This work improves sampling efficiency on complex spaces using determinantal processes.
problem Efficient sampling from large-scale datasets with general spaces.
method Determinantal point processes on general spaces and diffusion geometry.
result Improved sampling rates for determinantal processes on Riemannian manifolds and networks.
New confidence intervals improve treatment effect estimation in randomized experiments.
problem Improving confidence intervals for treatment effects in randomized experiments.
method Systematic exploitation of negative dependence or variance adaptivity.
result Achieved nonasymptotic confidence intervals with the same effective sample size as asymptotic ones.
Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points being located close to low-dimensional varieties or fine-grained lumping. We test a…
Study shows more data improves model explanations, aiding reliable knowledge extraction.
problem Challenges in deriving reliable knowledge from machine learning models due to the Rashōmon effect.
method Examined the influence of sample size on explanations from models in a Rashōmon set using SHAP.
result Explanations from <128 samples are highly variable, but agreement improves with more data.
Extends L2-norm LDA to 2D inputs using Bhattacharyya bound.
problem L2-norm LDA loses useful image information for 2D inputs.
method 2DBLDA maximizes matrix-based between-class distance and minimizes within-class distance, optimizing Bhattacharyya error bound.
result 2DBLDA improves image recognition and face reconstruction.
Neural networks' performance scales with data size, explained by data manifold dimensionality.
problem Understanding the scaling of neural network performance with the number of parameters.
method Explained by the intrinsic dimension of the data manifold, confirmed through teacher/student framework and various datasets.
result The scaling exponent α is approximately 4 divided by the intrinsic dimension d of the data manifold.
A new method compares unaligned datasets using log-Euclidean signatures of SPD matrices.
problem Efficiently comparing datasets with unknown alignment.
method Diffusion operators, Riemannian geometry, log-Euclidean metric.
result LES distance recovers meaningful structural differences, outperforming existing methods.
Analyzes error sources in global feature effect estimation methods.
problem Unexplored error sources in global feature effect estimation methods.
method Systematic, estimator-level analysis of bias and variance.
result Holdout data is theoretically cleanest, but estimation variance depends on sample size and model characteristics.
eDCF estimates intrinsic dimension using local connectivity.
problem Challenges in estimating intrinsic dimension due to scale dependence.
method eDCF: a novel, scalable, and parallelizable method based on Connectivity Factor (CF).
result eDCF consistently matches leading estimators with comparable MAE and higher exact intrinsic dimension match rates.
A new method monitors unstructured 3D shapes without registration.
problem Error-prone registration and mesh reconstruction steps in PCD monitoring.
method Intrinsic geometric properties of shapes, using Laplacian and geodesic distances.
result Effective monitoring of defects without registration and mesh reconstruction.
We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We conduct an extensive study of intrinsic scale for several networks, ranging fro…
Q*BERT learns to navigate text-based games by building a knowledge graph.
problem Text-based games have bottlenecks that standard RL agents struggle to overcome.
method Q*BERT learns a knowledge graph and uses intrinsic motivation to detect and overcome bottlenecks.
result Q*BERT outperforms state-of-the-art agents in text games, including Zork.
The paper analyzes ESS metrics and their connections to entropy families.
problem Improving the accuracy of effective sample size approximations.
method Examined Rényi and Tsallis entropy families and their relationship to ESS.
result Proved that ESS functions in the Huggins-Roy family meet theoretical conditions.