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.
Proves a conjecture about manifolds and scalar curvature.
Paper introduces a modified Allen-Cahn equation for better energy equipartition.
Optimizes kernel discrepancies by selecting subsets efficiently.
New discrepancy function compares discrete probability measures considering space geometry.
This paper introduces localized discrepancy theories for unsupervised domain adaptation.
An invariant description of Bianchi Homogeneous (B.H.) 3-spaces is presented, by considering the action of the Automorphism Group on the configuration space of the real, symmetric, positive definite, matrices. Thus, the gauge degrees of freedom are removed and the remaining (gauge invariant) degrees, are th…
The article introduces practical estimators for kernel discrepancies.
MPMC generates low-discrepancy points using graph neural networks.
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…
Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary conditions. In order to show the existence of the limit, we apply the phase field me…
Study of elastic models in non-Euclidean spaces via Γ-convergence.
This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. As corollaries of the general technique we bound the discrepancy …
Semi-parametric framework for nonlinear system identification
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
The performance of standard learning procedures has been observed to differ widely across groups. Recent studies usually attribute this loss discrepancy to an information deficiency for one group (e.g., one group has less data). In this work, we point to a more subtle source of loss discrepancy---feature noise. Our mai…
New partition designs reduce star discrepancy in high-dimensional sampling.
A new method for density estimation using mixture discrepancy and moments.
Stochastic Stein Discrepancies improve inference efficiency.
Bayes-consistent disagreement discrepancy loss improves model robustness.
Maximum mean discrepancy (MMD) has been widely adopted in domain adaptation to measure the discrepancy between the source and target domain distributions. Many existing domain adaptation approaches are based on the joint MMD, which is computed as the (weighted) sum of the marginal distribution discrepancy and the condi…
Unsupervised domain adaptation is the problem setting where data generating distributions in the source and target domains are different, and labels in the target domain are unavailable. One important question in unsupervised domain adaptation is how to measure the difference between the source and target domains. A pr…
Appropriately evaluating the discrepancy between domains is essential for the success of unsupervised domain adaptation. In this paper, we first point out that existing discrepancy measures are less informative when complex models such as deep neural networks are used, in addition to the facts that they can be computat…
Framework identifies discrepancies in physics models, improving sensor accuracy.
The paper refines classical covariance asymptotics using geometric information geometry.
Study on discrepancy principle for learning algorithms in nonparametric regression.
Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a higher dimensional manifold of the next layer as a curved submanifold, provided t…
Stein discrepancy improves UDA performance in low-data scenarios.
Inequalities linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterise uncertainty in model inputs and how that propagates through to outputs or predictions. In this perspective piece we dr…
Active learning algorithms propose which unlabeled objects should be queried for their labels to improve a predictive model the most. We study active learners that minimize generalization bounds and uncover relationships between these bounds that lead to an improved approach to active learning. In particular we show th…
SRRM improves recursive transport surrogates in the small-discrepancy regime.
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case o…
New conditions ensure MMDs separate and converge to target distributions.
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
Study finds polynomial convergence rate for Farey sequences linked to Riemann hypothesis.
A new framework improves kernel Stein discrepancy tests for validating distributions.
First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured behavior. Even in mechanical systems, where the equations are assumed to be well-kn…
We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm , that is known to linearize the Wasserstein distance and plays a fundamental role in the dynamic formulation of…
Bayesian inference uses Stein discrepancy for robustness in intractable likelihoods.
Homological stability fails for 4-manifold moduli spaces, detected by new class.
Study discrete analog of zeta-determinant maximization on triangulated surfaces.
We propose a framework for synthesis of geological images based on an exemplar image. We synthesize new realizations such that the discrepancy in the patch distribution between the realizations and the exemplar image is minimized. Such discrepancy is quantified using a kernel method for two-sample test called maximum m…
Two methods using low-discrepancy points improve data compression for neural networks.
Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational co…
Study shows boundedness of klt singularities in 3D or with bounded Kollár components.
When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kerne…