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.
A framework for disentangling class-related and class-independent factors in data.
Extends L2-norm LDA to 2D inputs using Bhattacharyya bound.
Paper connects rejection learning to Bhattacharyya divergence.
Study reconstructs hidden perfect matchings in random graphs with specific edge weights.
Study on error probability for classification of heavy-tailed renewal processes.
In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which are measured by the weighted pairwise distances of class means and meanwhile mini…
Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.
New CRB derived for curved models using extrinsic geometry.
Article provides Bernstein gradient estimates for heat equations with potential terms.
In many machine learning problems, labeled training data is limited but unlabeled data is ample. Some of these problems have instances that can be factored into multiple views, each of which is nearly sufficent in determining the correct labels. In this paper we present a new algorithm for probabilistic multi-view lear…
We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling e…
Develops geometric framework for uncertainty-aware multi-class classification.
We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then demonstrate that the Kernel Score includes the Maximum Mean Discrepancy as a special …
We quantify forgetting in post-training models, distinguishing mass and drift.
Efficiently learns polytrees with known skeleton in polynomial time and sample complexity.
Algorithm learns latent simplex from perturbed points in input-sparsity time.
The clustering algorithms that view each object data as a single sample drawn from a certain distribution, Gaussian distribution, for example, has been a hot topic for decades. Many clustering algorithms: such as k-means and spectral clustering are proposed based on the single sample assumption. However, in real life, …
We develop a novel methodology based on the marriage between the Bhattacharyya distance, a measure of similarity across distributions of random variables, and the Johnson-Lindenstrauss Lemma, a technique for dimension reduction. The resulting technique is a simple yet powerful tool that allows comparisons between data-…
Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better genera…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure…
There has been a growing interest in mutual information measures due to their wide range of applications in Machine Learning and Computer Vision. In this paper, we present a generalized structured regression framework based on Shama-Mittal divergence, a relative entropy measure, which is introduced to the Machine Learn…
Hybrid clustering combines partitional and hierarchical clustering for computational effectiveness and versatility in cluster shape. In such clustering, a dissimilarity measure plays a crucial role in the hierarchical merging. The dissimilarity measure has great impact on the final clustering, and data-independent prop…
Images obtained with coherent illumination, as is the case of sonar, ultrasound-B, laser and Synthetic Aperture Radar -- SAR, are affected by speckle noise which reduces the ability to extract information from the data. Specialized techniques are required to deal with such imagery, which has been modeled by the G0 dist…
Deep Gaussian processes (DGP) have appealing Bayesian properties, can handle variable-sized data, and learn deep features. Their limitation is that they do not scale well with the size of the data. Existing approaches address this using a deep random feature (DRF) expansion model, which makes inference tractable by app…
In the field of statistics, many kind of divergence functions have been studied as an amount which measures the discrepancy between two probability distributions. In the differential geometrical approach in statistics (information geometry), dually flat spaces play a key role. In a dually flat space, there exist dual a…
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of squ…
In this short report, we investigate the ability of the DCCA coefficient to measure correlation level between non-stationary series. Based on a wide Monte Carlo simulation study, we show that the DCCA coefficient can estimate the correlation coefficient accurately regardless the strength of non-stationarity (measured b…
Formula connects linking coefficients to Kontsevich integral coefficients.
Mixture distributions arise in many parametric and non-parametric settings -- for example, in Gaussian mixture models and in non-parametric estimation. It is often necessary to compute the entropy of a mixture, but, in most cases, this quantity has no closed-form expression, making some form of approximation necessary.…
Computed distortion coefficients for the α-Grushin plane.
Machine learning predicts Kronecker coefficients with high accuracy.
Abstract: Determines thermoelastic coefficients from boundary data.
New filling functions for groups with coefficients show different asymptotic behavior.
Abstract: Determines Lamé coefficients from boundary measurements.
Defines and proves properties of weighted renormalized volume coefficients.
Improved 3D LiDAR data classification using product coefficients.
High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between…
We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose ele…
Paper calculates third coefficient in Kaehler-Einstein metric expansion.
Develops local elliptic regularity for geometrically-natural operators with low regularity coefficients.
The paper uses Floer homology to study twist coefficients and their behavior after capping off.
Extends A-type coefficient polynomials to B-type setting, introducing new invariants.
We simplify complex regression coefficients using linearization and feature comparison.
Bounding twist number of surface links using polynomial coefficients.
Characterizes differential forms and vector fields with constant coefficients on manifolds.
Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.
In this paper we use wavelet concepts to show that correlation coefficient between two financial data's is not constant but varies with scale from high correlation value to strongly anti-correlation value This studies is important because correlation coefficient is used to quantify degree of independence between two va…