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.
New concentration inequalities for tensors with heavy-tailed coefficients.
We prove that an approximated version of the Brunn--Minkowski inequality with volume distortion coefficient implies a Gaussian concentration-of-measure phenomenon. Our main theorem is applicable to discrete spaces.
New insights on offline RL with state aggregation and trajectory data.
Paper tackles offline preference-based RL with human feedback.
In the celebrated book entitled Metric Structures for Riemannian and Non-Riemannian Spaces, so-called Green Book, Gromov presented a problem regarding a metric measure space. Gromov posed the question Bound the expansion coefficient from below in terms of the observable diameter. The overall aim of the current study is…
Paper tackles robust offline RL for non-Markovian processes, improving efficiency and applicability.
The paper analyzes sparse high-dimensional linear regression with random design and unknown error variance, providing adaptiveness and concentration rates.
Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to …
Study improves robustness and sparsity in linear regression with adversarial outliers and heavy-tailed noise.
The Fokker-Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For special cases of such a Fokker-Planck equation we describe a construction of exact …
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…
To gain insights into the problem of regional inequality, we proposed new regional asset exchange models based on existing kinetic income-exchange models in economic physics. We did this by setting the spatial exchange range and adding bias to asset fraction probability in equivalent exchanges. Simulations of asset dis…
Improved concentration inequalities for sub-Weibull variables enhance statistical and machine learning applications.
New Gini indices capture more nuanced income inequality.
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…
This paper proposes a new methodology to compute Value at Risk (VaR) for quantifying losses in credit portfolios. We approximate the cumulative distribution of the loss function by a finite combination of Haar wavelets basis functions and calculate the coefficients of the approximation by inverting its Laplace transfor…
Study on Fox's trapezoidal conjecture for specific alternating links.
Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of these operators are concentrated near the level sets of these trace functions, an…
Paper tackles offline CMDP problems with near-optimal algorithm and sample complexity bound.
Recently the interest of researchers has shifted from the analysis of synchronous relationships of financial instruments to the analysis of more meaningful asynchronous relationships. Both of those analyses are concentrated only on Pearson's correlation coefficient and thus intraday lead-lag relationships associated wi…
SCOPE estimator improves covariance and precision matrix estimation.
The paper develops bounds for predictive values in binary classification.
In recent work, Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy -- complete concentration of wealth by a single …
Unified hybrid RL algorithm improves online RL performance with offline data.
X in R^D has mean zero and finite second moments. We show that there is a precise sense in which almost all linear projections of X into R^d (for d < D) look like a scale-mixture of spherical Gaussians -- specifically, a mixture of distributions N(0, sigma^2 I_d) where the weight of the particular sigma component is P …
Proposes HDBEN for heteroscedastic regression with improved sparsity and variance modeling.
We consider linear models where potential causes are correlated with one target quantity and propose a method to infer whether the association is causal or whether it is an artifact caused by overfitting or hidden common causes. We employ the idea that in the former case the vector of regression c…
Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view to explore various aspects of smooth kernels related to their inferential proper…
Study on hemisphere threshold for Escobar functional on Riemannian manifolds, revealing mass and boundary invariant behaviors.
We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information ab…
This paper analyzes SHAP values using Fourier expansions for model interpretability.
This note examines financial distributions to competing teams at the end of the most famous multiple stage professional (male) bicyclist race, TOUR DE FRANCE. A rank-size law (RSL) is calculated for the team financial gains. The RSL is found to be hyperbolic with a surprisingly simple decay exponent (about equal to -1)…
The paper improves count data regression models for overdispersed data.
Automatically differentiable estimation for BLP model reduces bias in demand estimation.
Subspace recovery from corrupted and missing data is crucial for various applications in signal processing and information theory. To complete missing values and detect column corruptions, existing robust Matrix Completion (MC) methods mostly concentrate on recovering a low-rank matrix from few corrupted coefficients w…
A new inference method using regression and batched discrepancies.
Theory for algebraic data on categories via concentration structures.
The paper introduces a new method for tail bounds of random vectors and matrices.
We investigate second order quasilinear equations of the form f_{ij} u_{x_ix_j}=0 where u is a function of n independent variables x_1, ..., x_n, and the coefficients f_{ij} are functions of the first order derivatives p^1=u_{x_1}, >..., p^n=u_{x_n} only. We demonstrate that the natural equivalence group of the problem…
This study assesses the reproducibility of 1H-MRS scans across different vendors and sessions.
Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.
Study Finsler metric measure manifolds' concentration properties.
New method improves missing mass concentration bounds.
Surfaces in 3-manifolds concentrate at curvature critical points.
Sharp concentration bounds for i.i.d. variables.
We survey recent results related to the concentration of eigenfunctions. We also prove some new results concerning ball-concentration, as well as showing that eigenfunctions saturating lower bounds for -norms must also, in a measure theoretical sense, have extreme concentration near a geodesic.
SLT reveals how grokking occurs via basin selection in training.