CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification

• URL: http://arxiv.org/abs/2607.03145v1
• Date: Fri, 03 Jul 2026 09:36:02 GMT
• Title: CuBAS: Information Geometric Curvature-Based Adaptive Sampling for Supervised Classification
• Abstract summary: CuBAS is an information-geometric framework for adaptive data selection in supervised classification.<n>A labeled dataset can be viewed as a statistical manifold, on which local curvature, estimated via the ratio of second to first-order observed Fisher information, faithfully encodes the geometric complexity of the data distribution.
• Score: 52.452902154360565
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution. We introduce CuBAS (Curvature-Based Adaptive Sampling), an information-geometric framework for adaptive data selection in supervised classification, grounded in the q-state Potts Markov random field (MRF) model. The central insight is that a labeled dataset can be viewed as a statistical manifold, on which local curvature, estimated via the ratio of second to first-order observed Fisher information, faithfully encodes the geometric complexity of the data distribution. We construct a k-nearest-neighbor graph over the labeled data and derive a closed-form curvature score at each vertex from the Potts sufficient statistics. This curvature signal partitions the graph into two complementary regimes: low-curvature regions, corresponding to smooth, homogeneous clusters, and high-curvature regions, concentrated around decision boundaries that are disproportionately informative for classification. By selecting nodes from both regimes, CuBAS constructs compact yet maximally informative training subsets. Empirical evaluation across more than 60 benchmark datasets demonstrates consistent and statistically significant improvements over random sampling and uncertainty-based baselines, across a wide range of labeling budgets and classifier architectures. CuBAS is computationally efficient (linear in the number of k-NN graph edges), theoretically grounded in the differential geometry of statistical manifolds, and interpretable in terms of the local shape operator of the data manifold.

Related papers

• Active Learning with Low-Rank Structure for Data Selection [85.43185363043362]
  We introduce a new data selection framework based on low-rank approximation and residual-based sampling.<n>We show that it is possible to select a weighted subset of $tildeOleft(k + frac1varepsilon2right)$ data points whose average loss approximates the average loss over the full dataset.
  arXiv  Detail & Related papers  (2026-06-14T22:29:59Z)
• SEED: Targeted Data Selection by Weighted Independent Set [76.68391670109433]
  We develop a robust and scalable data selection pipeline dubbed SEED.<n>SEED consistently outperforms state-of-the-art methods on instruction tuning, visual instruction tuning, and semantic segmentation.
  arXiv  Detail & Related papers  (2026-05-15T07:26:54Z)
• A Mean Curvature Approach to Boundary Detection: Geometric Insights for Unsupervised Learning [52.452902154360565]
  We introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning.<n>MCBP explicitly models the intrinsic curvature of the data manifold and computes pointwise mean curvature without requiring principled manifold parametrization.<n>Experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance.
  arXiv  Detail & Related papers  (2026-05-05T20:19:09Z)
• Curvature-Aware PCA with Geodesic Tangent Space Aggregation for Semi-Supervised Learning [52.452902154360565]
  GTSA-PCA is a geometric extension of Principal Component Analysis.<n>It integrates curvature awareness and geodesic consistency within a unified spectral framework.<n>Our results position GTSA-PCA as a principled bridge between statistical and geometric approaches to dimensionality reduction.
  arXiv  Detail & Related papers  (2026-04-20T20:36:36Z)
• GRIP: Geometric Refinement and Adaptive Information Potential for Data Efficiency [28.832806758251607]
  textbfGRIP (Geometric Refinement and Adaptive Information Potential) is a framework that unifies these dimensions by modeling the corpus as an information-dense geometric space.<n>Our work establishes a robust geometric foundation for adaptive data curation in large-scale pre-training.
  arXiv  Detail & Related papers  (2026-02-04T15:23:24Z)
• Optimizing Distributional Geometry Alignment with Optimal Transport for Generative Dataset Distillation [109.13471554184554]
  We reformulate dataset distillation as an Optimal Transport (OT) distance minimization problem.<n>OT offers a geometrically faithful framework for distribution matching.<n>Our method consistently outperforms state-of-the-art approaches in an efficient manner.
  arXiv  Detail & Related papers  (2025-11-29T04:04:05Z)
• EVINGCA: Adaptive Graph Clustering with Evolving Neighborhood Statistics [0.0]
  Clustering algorithms often rely on restrictive assumptions.<n>EVINGCA is a graph-based clustering algorithm that treats cluster formation as an adaptive non-linear graph evolving process.
  arXiv  Detail & Related papers  (2025-10-29T03:44:05Z)
• Metric Distribution to Vector: Constructing Data Representation via Broad-Scale Discrepancies [15.40538348604094]
  We present a novel embedding strategy named $mathbfMetricDistribution2vec$ to extract distribution characteristics into the vectorial representation for each data. We demonstrate the application and effectiveness of our representation method in the supervised prediction tasks on extensive real-world structural graph datasets.
  arXiv  Detail & Related papers  (2022-10-02T03:18:30Z)
• Learning non-Gaussian graphical models via Hessian scores and triangular transport [6.308539010172309]
  We propose an algorithm for learning the Markov structure of continuous and non-Gaussian distributions. Our algorithm SING estimates the density using a deterministic coupling, induced by a triangular transport map, and iteratively exploits sparse structure in the map to reveal sparsity in the graph.
  arXiv  Detail & Related papers  (2021-01-08T16:42:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.