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.
Transformers can interpolate between arbitrary measures.
The paper extends inequalities for projection bodies to arbitrary measures.
This paper studies rectifiability in Carnot groups and proves geometric area formulas.
We establish an area-type formula for the intrinsic spherical Hausdorff measure of every regular curve embedded in an arbitrary graded group.
New metric reduces arbitrariness in fair binary classification predictions.
We will study metric measure spaces beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci bounds BE for which we prove the equivalence with sharp gradient estimates, the class of which will be preserved under…
Paper finds inequalities for eigenvalues of buckling problems on special metric spaces.
New method converts and optimizes sampling schedules for generative models.
It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this shor…
Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance of existing algorithms is highly sensitive in the presence of outliers that may …
Proves sufficiency of countable test plans for BV functions on metric spaces.
We consider the robust phase retrieval problem of recovering the unknown signal from the magnitude-only measurements, where the measurements can be contaminated by both sparse arbitrary corruption and bounded random noise. We propose a new nonconvex algorithm for robust phase retrieval, namely Robust Wirtinger Flow to …
Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.
New theorem proves convex bodies with specific curvature measures are rescaled Wulff shapes.
Given an arbitrary closed set A of , we establish the relation between the eigenvalues of the approximate differential of the spherical image map of A and the principal curvatures of A introduced by Hug-Last-Weil, thus extending a well known relation for sets of positive reach by Federer and Zaehle. The…
Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their risk-aversion functions. To date there has been very little guidance on the choice of risk-aversion functions underlying spectral risk measures. This paper addresses this issue by examining two popular …
New Fourier analysis method for non-uniform Boolean hypercube.
Paper presents a new algorithm to approximate Wasserstein-2 barycenters without bias.
We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel , which translates naturally into kernels between histograms or clouds of points. We first cover the case where $\Xcal$ is Euclidian, and focus on kernels which take into account th…
New formulations for comparing metric measure spaces with arbitrary positive measures.
Extends earthquake and horocycle flows to new measures.
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the main results is the representation of resulting risk measures from the properti…
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of cutting a nonorientable closed manifold or mod-2 cycle in into ori…
Paper approximates risk measures using SGD with Langevin dynamics.
We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).
We generalise the average asymptotic linking number of a pair of divergence-free vector fields on homology three-spheres by considering the linking of a divergence-free vector field on a manifold of arbitrary dimension with a codimension two foliation endowed with an invariant transverse measure. We prove that the aver…
This paper studies non-asymptotic model selection for the general case of arbitrary design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence---termed as the wor…
We develope a new and general notion of parametric measure models and statistical models on an arbitrary sample space which does not assume that all measures of the model have the same null sets. This is given by a diffferentiable map from the parameter manifold into the set of finite measures or probability me…
New curvature measures characterize non-convex Wulff shapes in normed spaces.
Background: The problem of predicting whether a drug combination of arbitrary orders is likely to induce adverse drug reactions is considered in this manuscript. Methods: Novel kernels over drug combinations of arbitrary orders are developed within support vector machines for the prediction. Graph matching methods are …
New method for triclustering with reduced arbitrariness.
This dissertation tackles challenges in reliable machine learning measurement.
Paper investigates conditions for independence of weak gradients on metric spaces.
New activation functions achieve arbitrary-accuracy Sobolev approximation by fixed-size neural networks.
Trivial links are unique up to number of link components, but they can be hard to recognize from arbitrary diagrams. We define a new measure of the complexity of a link embedding, the crumple, and show how this may be used to measure progress toward a trivial embedding. In conjunction with a modified form of arc presen…
The principle of peer review is central to the evaluation of research, by ensuring that only high-quality items are funded or published. But peer review has also received criticism, as the selection of reviewers may introduce biases in the system. In 2014, the organizers of the ``Neural Information Processing Systems\r…
New surfaces with special geodesic and horocycle behaviors discovered.
We show how the discovery of robust scalable numerical solvers for arbitrary bounded linear operators can be automated as a Game Theory problem by reformulating the process of computing with partial information and limited resources as that of playing underlying hierarchies of adversarial information games. When the so…
New bounds on NTK's smallest eigenvalue for arbitrary data without distributional assumptions.
We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to approximate the principal subspace to arbitrary precision, provided that the nu…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy a…
In an earlier paper of the authors it was shown that the sheaf theoretically based recently developed abstract differential geometry of the first author can in an easy and natural manner incorporate singularities on arbitrary closed nowhere dense sets in Euclidean spaces, singularities which therefore can have arbitrar…
Uniform measures have played a fundamental role in geometric measure theory since they naturally appear as tangent objects. For instance, they were essential in the groundbreaking work of Preiss on the rectifiability of Radon measures. However, relatively little is understood about the structure of general uniform meas…
Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
Formula for integrating random variables on hyperbolic surfaces.
The Gauss curvature measure of a pointed Euclidean convex body is a measure on the unit sphere which extends the notion of Gauss curvature to non-smooth bodies. Alexandrov's problem consists in finding a convex body with given curvature measure. In Euclidean space, A.D. Alexandrov gave a necessary and sufficient condit…
A flag area measure on an -dimensional euclidean vector space is a continuous translation-invariant valuation with values in the space of signed measures on the flag manifold consisting of a unit vector and a -dimensional linear subspace containing with . Using local parallel sets, …
Classifies measures for Anosov subgroups in higher ranks.