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.
Proposes a new model to maximize out-of-sample Sharpe ratios by forecasting tangency portfolios.
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy …
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance Unfolding (MVU) and Minimum Volume Embedding (MVE) use Semi-Definite Programming (SDP…
We study colorings of the hyperbolic plane, analogously to the Hadwiger-Nelson problem for the Euclidean plane. The idea is to color points using the minimum number of colors such that no two points at distance exactly are of the same color. The problem depends on and, following a strategy of Kloeckner, we show…
Graph regularized autoencoder improves anomaly detection performance.
Study entropic regularization of Gaussian measures and processes on Hilbert space.
Non-transitive subgroups of the orthogonal group play an important role in the non-Euclidean geometry. If is a closed subgroup in the orthogonal group such that the orbit of a single Euclidean unit vector does not cover the (Euclidean) unit sphere centered at the origin then there always exists a non-Euclidean Mink…
We calculate Euclidean distance degrees for common manifold optimization types.
Study of elastic models in non-Euclidean spaces via Γ-convergence.
Study infinite Euclidean distance discriminants of algebraic varieties.
The NL score optimizes speaker recognition tasks.
Private minimum Hellinger distance estimators maintain robustness and efficiency while ensuring privacy.
Mathematical framework for minimum enclosing ball problem.
Paper proposes a method to recover point configurations from noisy distance data.
We solve the vector embedding problem by minimizing total distortion under constraints.
We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in proportional to the minimum of the bridge distance and the bridge number of the knot. We also exhibit an infinite family of knots for which the minimum of the bridge distance and the bridge number is unb…
Matrix profile has been recently proposed as a promising technique to the problem of all-pairs-similarity search on time series. Efficient algorithms have been proposed for computing it, e.g., STAMP, STOMP and SCRIMP++. All these algorithms use the z-normalized Euclidean distance to measure the distance between subsequ…
The study compares Euclidean and cosine distances in medical drug prescription prediction.
New examples show flip distance and polyhedron triangulation numbers differ, with ratio close to 3/2.
We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerica…
The development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Markov clustering (MCL) is a renowned algorithm that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data, but it has n…
Revisits Isomap, showing it constructs Euclidean representations of geodesic structure.
We investigate a robust penalized logistic regression algorithm based on a minimum distance criterion. Influential outliers are often associated with the explosion of parameter vector estimates, but in the context of standard logistic regression, the bias due to outliers always causes the parameter vector to implode, t…
Extends manifold learning to non-Euclidean metrics.
In this article we study point configurations minimizing the discrete energy on a compact Riemannian manifold, where the energy kernel is taken to be the Green's function for the Laplacian. We show that every point in a minimizing configuration lies inside an open set called harmonic ball where no other point can enter…
Euclidean nets reveal properties of higher-dimensional manifolds.
New Sliced-Wasserstein distances for non-Euclidean data.
We address noisy Euclidean distances in high dimensions, estimating noise levels and correcting distances.
Smooth maps preserve distances on specific revolution surfaces.
Paper offers a method for finding the smallest sphere enclosing a set in d-dimensional space.
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distanc…
Unified proof of knot unknotting bounds using Ma-Qiu index.
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional noisy data. Our method, Minimum Distance Lasso (MD-Lasso), combines minimum distanc…
Paper tackles robust Euclidean distance estimation with sparse outliers.
Introduces Grassmann Distance Complexity to measure algebraic set nearest point problems.
Study rigidity by logarithmic capacity and related functions.
A new method compares unaligned datasets using log-Euclidean signatures of SPD matrices.
Paper proposes MWDE for estimating finite location-scale mixtures.
Region-based classification of PolSAR data can be effectively performed by seeking for the assignment that minimizes a distance between prototypes and segments. Silva et al (2013) used stochastic distances between complex multivariate Wishart models which, differently from other measures, are computationally tractable.…
The paper studies convexity of products of squared Euclidean distances.
Consider an orientable compact surface in three dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic curves, we show that any other isometric surface differs by at most a Euclidean motion…
Study robust distribution estimation with Wasserstein distance, achieving optimal risk.
Rigidity is the property of a structure that does not flex. It is well studied in discrete geometry and mechanics, and has applications in material science, engineering and biological sciences. A bar-and-joint framework is a pair of graph together with a map of the vertices of into the Euclidean pla…
We present a boundary version of a theorem about solenoidal unit vector fields with minimum energy on a spherical domain of an odd dimensional Euclidean sphere.
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also pres…
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow …
In this work, a novel solution to the speaker identification problem is proposed through minimization of statistical divergences between the probability distribution (g). of feature vectors from the test utterance and the probability distributions of the feature vector corresponding to the speaker classes. This approac…
Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize their training objective in a data-efficient way. In this spirit, we present an ar…