A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Improved mistake bound for group linear separable cases in online multiclass linear classification.
Paper develops robust methods for panel data with latent groups, improving inference under group separation violations.
Singing voice separation attempts to separate the vocal and instrumental parts of a music recording, which is a fundamental problem in music information retrieval. Recent work on singing voice separation has shown that the low-rank representation and informed separation approaches are both able to improve separation qu…
The paper proves vanishing bounded cohomology for various groups.
The study quantifies how many objects can be linearly classified under all views.
Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in the fundamental group of M, and that the double cosets for crossing surfaces are also separable. We deduce that if there is a "sufficient" collection of surfaces in M, then the fundamental group of M is…
New statistical measures assess group separability in low-dimensional geometrical spaces.
Equations of motion for linear Hamiltonians in the real Jacobi group
Adaptive clustering and personalization algorithms minimize regret in multi-agent stochastic linear bandits.
In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential. It turns out that the subgroup distortion of a subgroup of a 3-manifold group is …
This paper presents a new ensemble learning method for classification problems called projection pursuit random forest (PPF). PPF uses the PPtree algorithm introduced in Lee et al. (2013). In PPF, trees are constructed by splitting on linear combinations of randomly chosen variables. Projection pursuit is used to choos…
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
The paper examines subgroup separability for surface and virtual braid groups.
The study shows subgroup separability conditions for specific groups.
Criterion for subgroup separability in outer automorphism groups.
A random walk on a separable, geodesic hyperbolic metric space converges to the boundary with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when …
Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and classify using Bayes theorem. With LDA, we estimate a single, pooled covariance m…
Study on hyperbolic groups, focusing on separability and splittings.
We use the theory of group actions on profinite trees to prove that the fundamental group of a finite, 1-acylindrical graph of free groups with finitely generated edge groups is conjugacy separable. This has several applications: we prove that positive, one-relator groups are conjugacy separable; we provide a…
This paper investigates how data augmentation improves linear separation of manifold data.
We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups are separable. A consequence is that closed hyperbolic 3-manifolds have finite-sheeted Haken covers, which resolves the virtual Haken …
New examples show some convex-cocompact subgroups are separable.
Proposes Fair Archetypal Analysis to reduce fairness concerns in data representation.
New algorithms improve blind source separation for linear-quadratic mixtures.
Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric sp…
Let G be a countable group which acts by isometries on a separable, but not necessarily proper, Gromov hyperbolic space X. We say the action of G is weakly hyperbolic if G contains two independent hyperbolic isometries. We show that a random walk on such G converges to the Gromov boundary almost surely. We apply the co…
In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an…
Probabilistic proof shows separability in free groups.
Elementarily free groups are the finitely generated groups with the same elementary theory as free groups. We prove that elementarily free groups are subgroup separable, answering a question of Zlil Sela.
Adam optimizes linear classifiers with separable data.
The paper extends optimal transport for linear separability of sheared distributions in supervised learning.
Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane. For complex data with multimodal distributions this transformation is difficult t…
We study the problem of efficient online multiclass linear classification with bandit feedback, where all examples belong to one of classes and lie in the -dimensional Euclidean space. Previous works have left open the challenge of designing efficient algorithms with finite mistake bounds when the data is linear…
Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separab…
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski to…
Spectral analysis shows neural networks separate from linear methods in approximating functions.
A new algorithm finds a separating hyperplane with fewer updates.
New PCstar algorithm discovers causal structure of max-linear Bayesian networks.
Unified method for CNNs to approximate equivariant maps across various groups.
Generalizes underlap coefficient for multivariate group separation.
Let M be a hyperbolizable, nontrivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of the fundamental group of M into PSL(2,C) are separable-stable. The set of separable-stable representations forms a domain of discontinuity for the ac…
New models improve machine learning accuracy and transparency in finance.
Sharp conditions link separators to R-trees for space transformations.
Generalizes underlap coefficient for multivariate group separation.
New complex connects graph separability to group properties.
Shallow nonlinear networks can separate classes linearly with polynomially scaling width.
We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.