arXiv Machine Learning
Jul 13
Terminal Dimension Reduction for Time Series with Applications
arXiv:2607. 09490v1 Announce Type: cross Abstract: Terminal embeddings have emerged as a powerful tool for dimension reduction.
Dimension Reduction for Curves: Simplified and Generalized
arXiv:2607. 03112v1 Announce Type: cross Abstract: We revisit random projections for reducing the dimension of high-dimensional polygonal curves.
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arXiv Machine Learning
Jun 18
Fisher Width: A Geometric Measure of Complexity on Statistical Manifolds
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
arXiv Machine Learning
Jul 28
Distance-Matrix Wasserstein Statistics for Scalable Gromov--Wasserstein Learning
arXiv:2605. 14981v2 Announce Type: replace Abstract: Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system.
arXiv Machine Learning
Jul 9
Fast determinantal sampling on general spaces and diffusion geometry
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
arXiv AI
Aug 12
Riemann GeoResolver: A Non-Euclidean Attention Framework from Euclidean Resolver to Hyperbolic-Spherical Geometry
arXiv:2608. 10416v1 Announce Type: cross Abstract: We present a theoretical foundation for inverse-distance attention, from its Euclidean prototype (Resolver) to its non-Euclidean realization (Riemann GeoResolver).
arXiv Machine Learning
1d ago
The Observable Wasserstein Distance
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
arXiv Machine Learning
Jun 17
Approximating Gaussian Whittle-Matern Fields over Well-Centered Triangulations of Riemannian Manifolds
arXiv:2606. 13827v2 Announce Type: replace-cross Abstract: Markovian Whittle-Mat\'ern fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, \[ (\kappa^2 - \Delta)^{\alpha/2} u = \mathcal{W}, \;\; \kappa \in \mathbb{R}, \; \alpha \in \mathbb{N}.
arXiv Machine Learning
Jun 15
Approximating Whittle-Matern Fields over Discretized Manifolds
arXiv:2606. 13827v1 Announce Type: cross Abstract: Markovian Whittle-Mat\'ern fields have been convergently approximated by discrete Gauss Markov Random Fields (GMRFs) with sparse precision matrices using a Finite Element approximation of the two-parameter family, \[ (\kappa^2 - \Delta)^{\alpha/2} u = \mathcal{W}, \;\; \kappa \in \mathbb{R}, \; \alpha \in \mathbb{N}.
arXiv Machine Learning
Jul 14
The VC dimension of partial concept classes via Radon's theorem
arXiv:2607. 10751v1 Announce Type: new Abstract: Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concepts partition the ground set into black ($f^{-1}(1)$), grey ($f^{-1}(\ast)$), and white parts ($f^{-1}(0)$).
arXiv Machine Learning
2d ago
Active Regression via Linear-Sample Sparsification
arXiv:1711. 10051v4 Announce Type: replace Abstract: We present an approach that improves the sample complexity for a variety of curve fitting problems, including active learning for linear regression, polynomial regression, and continuous sparse Fourier transforms.
arXiv Machine Learning
Jun 24
Exact Schur-Sylvester Dimensionality Reductions for Non-Smooth Stochastic Complexity and Manifold Sampling
arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
arXiv Machine Learning
2d ago
High-dimensional nonparametric changepoint detection via low-rank degree-two density projection
arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.