We propose a simple yet powerful framework for modeling integer-valued data, such as counts, scores, and rounded data. The data-generating process is defined by Simultaneously Transforming and Rounding (STAR) a continuous-valued process, which produces a flexible family of integer-valued distributions capable of modeli…
On-device research index
arXiv research
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.
168,742 papers · 148 categories
Trend · papers per month
48 results for “STAR transformation”
Semiparametric STAR model improves mental health data analysis.
problem Overdispersed, zero-inflated, bounded count data in self-reported mental health surveys.
method STAR transformation and rounding of latent Gaussian model, nonparametric transformation estimation, EM algorithm for maximum likelihood.
result Substantial improvements in goodness-of-fit compared to existing models.
We derive a closed formula for a star-product on complex projective space and on the domain using a completely elementary construction: Starting from the standard star-product of Wick type on and performing a quantum analogue of Marsden-Weinstein reduction, we ca…
The spherical Radon transform on the unit sphere can be regarded as a member of the analytic family of suitably normalized generalized cosine transforms. We derive new formulas for these transforms and apply them to study classes of intersections bodies in convex geometry.
STAR improves equivariant and invariant representation learning by routing projection heads.
problem Redundant feature learning in equivariant and invariant representation learning.
method Soft Task-Aware Routing (STAR) for projection heads specialization.
result Lower canonical correlations between invariant and equivariant embeddings.
The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is integrable if the local differential invariants of a solution to the curve flow evolve according to a soliton equation. In this paper, we sho…
Researchers create a star product on a Grassmannian with separation of variables.
problem Constructing a star product with separation of variables on .
method Solving recurrence relations using creation and annihilation operators on a Fock space.
result Explicit formula for a star product with separation of variables on .
New lower bound shows bandit convex optimization is harder than linear bandits.
problem Establishing a lower bound for stochastic bandit convex optimization.
method Constructing a hard class of convex functions and analyzing posterior spread of Fisher information matrices.
result A lower bound on minimax expected regret.
New lower bound shows bandit convex optimization is harder than previously thought.
problem Establishing a lower bound on the minimax expected regret for bandit convex optimization.
method Constructing a hard class of convex functions and analyzing the posterior spread of Fisher information matrices.
result A lower bound on the minimax expected regret.
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation of the sum of an approximately) low rank matrix with a second matrix endowed with a complementary …
Neural networks can achieve optimal sample complexity for learning single-index models.
problem Achieving optimal computational-statistical tradeoff in learning Gaussian single-index models.
method Unified gradient-based algorithm for training a two-layer neural network, adaptable to various loss and activation functions.
result Sample complexity of matches the SQ lower bound up to a polylogarithmic factor.
This paper connects geometric diagrams to spherical T-duality.
problem Establishing equivalence between geometric and string-theory frameworks.
method Introducing -diagrams and proving their equivalence to spherical T-dual pairs.
result Concrete geometric realization of spherical T-duality.
Sparse Max-Affine Regressionstat.ML
Paper proposes Sp-GD for sparse max-affine regression with theoretical guarantees.
problem Sparse max-affine regression model selection and estimation.
method Sparse Gradient Descent (Sp-GD) initialization using sparse PCA and covering search.
result Sp-GD provides ε-accurate estimates with optimal number of observations.
Study shows computational and statistical gaps in Gaussian Single-Index Models.
problem Statistical and computational trade-offs in high-dimensional regression problems.
method Analysis of SQ and LDP frameworks, partial-trace algorithm.
result Computational algorithms require significantly more samples than information-theoretic limits.
Star-Shaped deviationsq-fin.RM
Introduces Star-Shaped deviation measures for risk analysis.
problem Risk measurement and analysis in finance.
method Characterizes Star-Shaped deviation measures through acceptance sets and convex deviation measures.
result Exposes the relationship between Star-Shaped risk measures and deviation measures.
A new clustering method handles uncertain covariates efficiently.
problem Clustering with uncertain covariates in datasets.
method Greedy and optimistic clustering algorithm using non-linear transformation and empirical uncertainty sets.
result Improved performance in finding sibling stars.
Simplifies F-measure for better interpretability.
problem Lack of intuitive interpretation of F-measure.
method Introduces F* (F-star) transformation.
result F* provides an immediate practical interpretation.
Algorithm achieves optimal regret for unknown Lipschitz convex losses.
problem Online learning with unknown Lipschitz constant and target vector norm.
method Develops an online learning algorithm without knowledge of or .
result Matches optimal regret bound up to logarithmic factors.
New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
Paper proves conjecture about star-shaped curves evolving under GAPF, but not always preserves star shape.
problem What conditions guarantee global existence of Gage's area-preserving flow for nonconvex initial curves?
method Using Dittberner's singularity analysis theory, constructed a ``flying wing'' curve to show limitations.
result Gage's area-preserving flow does not always preserve star-shapedness of evolving curves.
In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric . It is proved that there exist no Hopf hypersurfaces in , with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on …
Classifies star products on Lie algebroid duals and extends to projectable quantizations.
problem Classifying and extending quantizations on Lie algebroid duals.
method Classification through second Lie algebroid cohomology, extension to projectable quantizations.
result Quantization commutes with reduction in the considered setting.
New set-valued star-shaped risk measures introduced for better risk assessment.
problem Improving risk assessment in financial contexts.
method Developed new set-valued star-shaped risk measures and proved their representation theorems.
result Set-valued star-shaped risk measures can be represented as unions of set-valued convex risk measures.
Flow turns star-shaped curves into circles.
problem Transforming star-shaped curves into circles.
method Gage's area-preserving flow.
result Curves evolve into circles over time.
Transformer with denoising diffusion improves probabilistic density estimation.
problem Estimating non-Gaussian and multimodal probability distributions for regression problems.
method Training a denoising diffusion head on top of a Transformer model.
result The model provides reasonable probability density estimation for high-dimensional inputs.
The paper studies dynamic star-shaped risk measures and their representation.
problem Representing dynamic star-shaped risk measures and their properties.
method Representation theorems for dynamic monetary and star-shaped risk measures.
result Dynamic star-shaped risk measures can be represented as the lower envelope of a family of dynamic convex risk measures.
Paper disproves symmetry of stars at infinity in a specific graph.
problem Symmetry of stars at infinity in a specific graph.
method Defined incidence geometry of stars at infinity; provided an example.
result Relation of one boundary point being included in a star of another is not symmetric.
Study star products on Poisson manifolds compatible with reduction.
problem Finding star products compatible with coisotropic reduction.
method Compute second constraint Hochschild cohomology of constraint algebra.
result Determine infinitesimal star products on Poisson manifolds.
The paper characterizes dynamic return and star-shaped risk measures via BSDEs.
problem Characterizing dynamic return and star-shaped risk measures.
method Characterization of star-shaped functionals and BSDEs.
result Existence of convex BSDEs with non-empty set of supersolutions.
Deform moment map on symplectic connections using star product algebras.
problem Understanding symplectic connections and their deformations.
method Study vector bundle of Fedosov star product algebras, formal connection, curvature, and star product trace.
result Showed star product trace as a formal symplectic form and moment map.
Paper analyzes Birkhoff relaxation for graph alignment, providing theoretical guarantees.
problem Finding vertex correspondence between two graphs to maximize edge overlap.
method Birkhoff relaxation as a convex relaxation of the quadratic assignment problem (QAP).
result Theoretical guarantees on the performance of Birkhoff relaxation under specific conditions.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
We compare the star surgery operations introduced in [KS] to the generalized rational blow-down. We show that star surgery shares the properties that make rational blow-down useful for constructions of small exotic symplectic 4-manifolds. Then we show that star surgery operations provide a strictly more general class o…
Estimates how many times a star appears due to gravitational lensing.
problem Estimating the number of times an observer sees a star due to gravitational lensing.
method Use affine linking numbers to estimate the number of times an observer sees a star.
result Estimates the number of times an observer sees a star due to gravitational lensing.
Improved SGD learning for single index models reduces sample complexity.
problem Learning a single index model with optimal sample complexity.
method Using smoothed loss in online SGD to reduce sample complexity.
result Online SGD with smoothed loss achieves optimal sample complexity of .
The paper finds at least four prime closed characteristics on star-shaped hypersurfaces in 8D space.
problem Finding prime closed characteristics on compact star-shaped hypersurfaces in 8D space.
method Proved existence of at least four prime closed characteristics for non-degenerate compact star-shaped hypersurfaces in without prime closed characteristics of Maslov-type index -1.
result Existence of at least four prime closed characteristics on compact star-shaped hypersurfaces in .
This paper connects monetary and star-shaped risk measures by showing their equivalence under certain conditions.
problem Understanding the relationship between monetary and star-shaped risk measures.
method Analyzing the acceptability of 0 and the normalization property.
result Monetary risk measures are only a translation away from star-shapedness under mild conditions.
Anisotropic weighted isoperimetric inequalities for star-shaped and -mean convex hypersurfacemath.DG
The paper proves inequalities for star-shaped and -mean convex hypersurfaces in .
problem Proving geometric inequalities for specific types of hypersurfaces.
method Using anisotropic -momentum, perimeter, and volume, the paper derives inequalities for star-shaped and -mean convex hypersurfaces.
result The Wulff shape of is the unique minimizer of the corresponding functionals among all star-shaped and -mean convex sets.
We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection introduced by the first author. We establish a necess…
Constructs non-unital monoidal category of contact manifolds and Legendrian correspondence calculus
problem Constructing a non-unital monoidal category of contact manifolds without contact forms
method Developing contact topology without contact forms and defining the star product
result Proving the associativity of the star product and the pentagon axiom
Sharp inequalities for star bodies in 2D space.
problem Understanding star bodies in 2D space.
method Sharp inequalities for star bodies in .
result New inequalities and proofs for star bodies.
The paper characterizes law-invariant star-shaped risk measures.
problem Understanding and characterizing law-invariant star-shaped risk measures.
method Developed characterizations for positively homogeneous and star-shaped functionals, derived Kusuoka-type representations, and offered representations of general law-invariant star-shaped functionals.
result Characterizations of law-invariant star-shaped functionals, including their connections to Value-at-Risk and Expected Shortfall.
The study counts geodesics on curved surfaces with specific intersections.
problem Counting geodesics with exact intersection numbers on curved surfaces.
method Introduced a dynamical scattering operator and used Pollicott-Ruelle resonances.
result Asymptotic growth of geodesics with prescribed intersections.
Introduces Star-Shaped DDPMs for non-Gaussian distributions.
problem Difficulties in defining DDPMs for non-Gaussian distributions.
method Star-shaped diffusion process, duality with specific Markovian diffusions, efficient algorithms.
result SS-DDPMs can model distributions like Beta, von Mises-Fisher, Dirichlet, Wishart.
Study tunnel numbers of cable knots and their companions, proving new bounds and constructing examples.
problem Understanding the relationship between the tunnel numbers of a knot and its cable.
method Combinatorial techniques and analysis of Heegaard splittings.
result Proves that for many cases, the tunnel number of a cable knot equals the original knot's tunnel number plus one.
The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.
problem Generalizing convex and star-shaped concepts to symplectic vector spaces.
method Study of variational problems for symplectically convex and star-shaped curves.
result Extremal points of the variational problem are rigid multiply traversed conics for a range of parameters.
We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective first-class constraint (gauge) system equivalent to the original second-class o…
Study quantization schemes on Kähler manifolds linking star products and BV quantizations.
problem Quantization of structures on Kähler manifolds.
method Construct Fedosov's star products and Batalin-Vilkovisky (BV) quantizations.
result One-loop exactness of BV quantizations, leading to a cochain level formula.