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.
Estimates means in metric spaces using quantization.
We introduce the new class of submanifolds of co-Banach type in tame Fréchet manifolds and construct tame Fréchet submanifolds as inverse images of regular values of certain tame maps. Our method furnishes an easy way to construct tame Fréchet manifolds. The results presented are key ingredients in the construction of …
Paper studies weighted Fermat-Frechet problem for simplex edge lengths.
The study finds the minimum number of critical points for functionals on Frechet spaces and Finsler manifolds.
Study shows zero probability of cut locus for Fréchet mean on Riemannian manifolds.
Differentiates Fréchet mean for hyperbolic space applications.
Paper introduces a medoid-based approach for efficient Fréchet regression.
Study on Frechet distance properties for paths and graphs.
Deep single-index Fréchet regression for metric space-valued outputs
Global implicit function theorem for Fréchet spaces, solving derivative loss problems.
Some recent work in Frechet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Frechet manifolds that could be represented as projective limits of Banach manifolds. This led to …
We give sufficient conditions for a -local diffeomorphism between Fréchet spaces to be a global one. We extend the Clarke's theory of generalized gradients to the more general setting of Fréchet spaces. As a consequence, we define the Chang Palais-Smale condition for Lipschitz functions and show that a functio…
The consistency of Fréchet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fréchet medians are estimated. It…
Proposes a new random forest weighted local Fréchet regression method.
The paper develops predictors for functional data on manifolds.
A method for reducing dimensions in Fréchet regression models.
We study geometrical aspects of the space of fibrations between two given manifolds M and B, from the point of view of Frechet geometry. As a first result, we show that any connected component of this space is the base space of a Frechet-smooth principal bundle with the identity component of the group of diffeomorphism…
In this paper we prove a variation of the theorem in title, for equations with periodic coefficients, in Frechet spaces. The main result gives equivalent conditions ensuring the reduction of such an equation to one with constant coefficient. In the particular case of , we obtain the exact analogue of the cl…
Study shows moduli space of fibrations has specific homotopy types.
We compute an approximate Fréchet mean for sets of sparse graphs.
Paper develops methods for semi-supervised Fréchet regression.
We prove that each non-separable completely metrizable convex subset of a Frechet space is homeomorphic to a Hilbert space. This resolves an old (more than 30 years) problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowoslki and Torunczyk, th…
The abstract discusses the linear and smooth structures of mapping spaces.
We provide sufficient conditions for the existence of a global diffeomorphism between tame Fréchet spaces. We prove a version of the Mountain Pass Theorem which is a key ingredient in the proof of the main theorem.
Improved Fréchet regression tackles noise and multicollinearity.
This paper explores the impact of metric choice on Fréchet regression.
DFNNs predict non-Euclidean responses from Euclidean predictors.
The paper computes an approximation to the sample Frechet mean of graph sets using spectral information.
This work achieves exponential concentration in heavy-tailed data over CAT(κ) spaces using the Fréchet median.
Given a principal bundle on an orientable closed surface with compact connected structure group, we endow the space of based gauge equivalence classes of smooth connections relative to smooth based gauge transformations with the structure of a Fréchet manifold. Using Wilson loop holonomies and a certain characteristic …
We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fréchet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.
This work analyzes Fréchet regression using comparison geometry, providing theoretical and practical insights.
DFR models dynamic distributional data with weighted Fréchet means.
We extend the Palais-Smale condition to Keller's -functionals on Fréchet spaces. Using this condition together with Ekeland's variational principle, we obtain some results regarding the existence of minima. In this setting, we prove that the Palais-Smale condition for functionals bounded below implies the coerci…
A new algorithm solves signed Fréchet regression on manifolds with bounded curvature.
It is proved that the moduli space of all connected compact orientable embedded minimal affine Lagrangian submanifolds of a complex equiaffine space constitutes an infinite dimensional Frechet manifold (if it is not the empty set). The moduli space of all connected compact orientable metric Lagrangian embedded surfaces…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional data. However, current random forest approaches are not flexible enough to handle he…
We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between …
A new mechanism for differentially private Fréchet mean on SPD matrices.
Decentralized optimization on dynamic manifolds with improved regret bound.
We define Lie and Courant algebroids on Fréchet manifolds. Moreover, we construct a Dirac structure on the generalized tangent bundle of a Fréchet manifold and show that it inherits a Fréchet Lie algebroid structure. We show that the Lie algebroid cohomology of the $\bb$-cotangent bundle Lie algebroid of a weakly sympl…
FGBoost boosts gradient boosting for complex data.
Efficiently clusters data on manifolds using Fréchet maps.
GEORCE-FM algorithm optimizes Fréchet means and distances efficiently.
For a compact, smooth C^r orbifold (without boundary), we show that the topological structure of the orbifold diffeomorphism group is a Banach manifold for finite r \ge 1 and a Frechet manifold if r=infty. In each case, the local model is the separable Banach (Frechet) space of C^r (C^infty, resp.) orbisections of the …
Improves risk and variability measures continuity and consistency.
A general slice theorem for the action of a Fréchet Lie group on a Fréchet manifolds is established. The Nash-Moser theorem provides the fundamental tool to generalize the result of Palais to this infinite-dimensional setting. The presented slice theorem is illustrated by its application to gauge theories: the action o…
EpiMer merges models by solving Fréchet mean on a Riemannian manifold.