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.
The paper improves ranking by integrating covariates and sparse intrinsic scores.
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and non-uniformly smooth spatial boundaries. A Gaussian process regression using a non-stat…
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
Develops intrinsic Gaussian process regression for manifold-valued data.
In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies have actively investigated the theoretical properties of DNNs to understand thei…
New approach to Lagrangian systems using intrinsic geometry.
In this contribution we present an intrinsic description of time-variant Port Hamiltonian systems as they appear in modeling and control theory. This formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives, which guarantees that the structure of the equations is invari…
Proofs Fisher-Rao distance on Gaussian covariance manifold.
In this paper we propose and explore the k-Nearest Neighbour UCB algorithm for multi-armed bandits with covariates. We focus on a setting where the covariates are supported on a metric space of low intrinsic dimension, such as a manifold embedded within a high dimensional ambient feature space. The algorithm is concept…
Paper extends Bayesian Cramér-Rao bound with geometric considerations.
Intrinsic formulation of noncommutative geometry for quantum gravity.
We give in this paper which is the fifth in a series of eight a theory of covariant derivatives of multivector and extensor fields based on the geometric calculus of an arbitrary smooth manifold M, and the notion of a connection extensor field defining a parallelism structure on M. Also we give a novel and intrinsic pr…
New method for estimating covariance with robustness to outliers.
A new Riemannian framework for robust covariance estimation.
This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random initial condition. There is a single observation consisting of a nonlinear function o…
We consider a regular distribution in a Riemannian manifold . The Levi-Civita connection on together with the orthogonal projection allow to endow the space of sections of with a natural covariant derivative, the intrinsic connection. Hence we have two different covariant deri…
In this paper we study the extent to which conformally compact asymptotically hyperbolic metrics may be characterized intrinsically. Building on the work of the first author, we prove that decay of sectional curvature to -1 and decay of covariant derivatives of curvature outside an appropriate compact set yield Hölder …
We study the classification of special almost hermitian manifolds in Gray and Hervella's type classes. We prove that the exterior derivatives of the symplectic form and the complex volume form contain all the information about the intrinsic torsion of the $\SUn(n)$-structure. Furthermore, we apply the obtained results …
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding map covariant derivatives and a careful application of the DeTurck…
We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension of the conditioning variable is larger than the sample size , estimation and inference is feasible as long as the distribution of the conditioning variable has small intrinsic…
The paper refines classical covariance asymptotics using geometric information geometry.
Differential privacy of Gaussian process posterior sampling
We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without the exterior covariant derivative. This approach allows both structure equations and the Bianchi identities to be expressed in terms of forms…
Improved Kalman filtering with hierarchical variational approach.
Kernel -Greedy optimizes multi-armed bandits with covariates for sub-linear regret.
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, in-GPs can accommodate spatial domains arising…
New method for private linear regression under privacy constraints, achieving optimal rates.
Principal Component Analysis can be performed over small domains of an embedded Riemannian manifold in order to relate the covariance analysis of the underlying point set with the local extrinsic and intrinsic curvature. We show that the volume of domains on a submanifold of general codimension, determined by the inter…
A new method classifies almost contact metric manifolds using intrinsic endomorphisms.
Generates counterfactuals in target domain from source domain observations.
A novel method for feature selection using a reparameterized logitNormal distribution.
Rollings of reductive homogeneous spaces are studied using intrinsic curves.
This paper improves causal inference using deep neural networks for low-dimensional covariates.
We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U of M, based on the geometric and extensor calculus on an arbitrary smooth manifold M. This is done by introducing the notion of a connection ext…
FVNNs use graph convolutions on fair covariance estimates to improve fairness in machine learning.
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data distributions focus on global data properties such as mean and covariance; in that se…
New method models covariates and responses without parametric assumptions using manifold learning.
Paper solves a key problem in learning from high-dimensional covariance matrices.
New GL-GP models learn covariance respecting domain geometry.
We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξand its covariant derivative \widetilde\nablaξand determine r…
Invariant description of SU(2)-structures on 5-manifolds developed.
Bayesian method uses data spectra to estimate non-sparse high-dimensional models.
New method generates synthetic time series paths with more flexibility.
The Fisher-Rao geometry is applied to elliptical distributions for optimization and classification.
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the…
Proposes ICC method for dynamic portfolio optimization.
Unified geometric framework for Brownian motion on various manifolds.
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, …