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.
Unified approach to totally ramified values in various surface theories.
New method uses extreme value theory to estimate neural network errors.
The hidden tail of empirical distributions is analyzed using extreme value theory.
We introduce equivariant Liouville forms and Duistermaat-Heckman distributions for Hamiltonian group actions with group valued moment maps. The theory is illustrated by applications to moduli spaces of flat connections on 2-manifolds.
The paper tackles catastrophic risk in reinforcement learning using extreme value theory.
This paper extends Nevanlinna's unicity theorems to complete Kahler manifolds.
In this paper, we explore various statistical techniques for anomaly detection in conjunction with the popular Long Short-Term Memory (LSTM) deep learning model for transportation networks. We obtain the prediction errors from an LSTM model, and then apply three statistical models based on (i) the Gaussian distribution…
Paper introduces SPADE method to protect classifiers from OOD and adversarial samples.
Paper analyzes singular subspace estimation in noisy matrix models.
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory. The results are useful to certain phenomena that are fitted by the Pareto distribu…
Extreme value theory enhances statistical learning extrapolation for rare events.
Several well-established benchmark predictors exist for Value-at-Risk (VaR), a major instrument for financial risk management. Hybrid methods combining AR-GARCH filtering with skewed- residuals and the extreme value theory-based approach are particularly recommended. This study introduces yet another VaR predictor, …
New neural network models extreme value distributions with preserved shape constraints.
Proposes a method to model financial returns with extreme shocks using flexible tail transformations.
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other …
For spherically symmetric distributions, efficient quantisation can be achieved with moderate sample sizes.
We present in this article a survey of recent results in value distribution theory for the Gauss maps of several classes of immersed surfaces in space forms, for example, minimal surfaces in Euclidean -space (=3 or 4), improper affine spheres in the affine 3-space and flat surfaces in hyperbolic 3-space. In parti…
Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its foundational role, a key limitation of the data Shapley framework is that it only…
In a wide variety of sequential decision making problems, it can be important to estimate the impact of rare events in order to minimize risk exposure. A popular risk measure is the conditional value-at-risk (CVaR), which is commonly estimated by averaging observations that occur beyond a quantile at a given confidence…
This work analyzes self-attention matrices using random matrix theory.
The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the deviation of the stock price from the consensus value. We find an analytical expressi…
Efficient methods estimate bid and value distributions in auctions.
Paper generalizes Bloch-Ros principle to various surface classes.
Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.
The paper proves a distribution claim for neural network Jacobians.
The argument that the alarming level of Gini coefficient is 0.4 is very popular, especially in the media industry, all around the world for a long time. Although the 0.4 standard is widely accepted, the derivation of the value lacks rigid theoretical foundations. In fact, to the best of our knowledge, it is not based o…
Develops a dynamic mean field theory for reinforcement learning.
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a random variable with an elliptical distribution and the notion of portfolio risk is d…
New method attributes feature uncertainty in ML models using cooperative game theory.
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a hea…
It is well known that the initialization of weights in deep neural networks can have a dramatic impact on learning speed. For example, ensuring the mean squared singular value of a network's input-output Jacobian is is essential for avoiding the exponential vanishing or explosion of gradients. The stronger condi…
Random matrix analysis reveals that neural network weights are mostly random, with some indicating learned information.
The thesis evaluates and compares extreme mixture models in finance and insurance.
Unified framework for feature-based explanations using ANOVA and game theory.
Simpler one-step distributional RL framework for control.
"How much is my data worth?" is an increasingly common question posed by organizations and individuals alike. An answer to this question could allow, for instance, fairly distributing profits among multiple data contributors and determining prospective compensation when data breaches happen. In this paper, we study the…
We present a comprehensive theory of homogeneous volatility (and variance) estimators of arbitrary stochastic processes that fully exploit the OHLC (open, high, low, close) prices. For this, we develop the theory of most efficient point-wise homogeneous OHLC volatility estimators, valid for any price processes. We intr…
We present a method for constructing the log-optimal portfolio using the well-calibrated forecasts of market values. Dawid's notion of calibration and the Blackwell approachability theorem are used for computing well-calibrated forecasts. We select a portfolio using this "artificial" probability distribution of market …
New theory of sensitivity for unbiased estimators using Wasserstein geometry.
Study a market with uncertain informed traders, finding price impact depends on both asset value and informed trader count distribution.
The article models financial asset returns using Gaussian mixtures and EVT-based copulas to price equity options.
This paper develops DRO estimators for EVT statistics using point processes.
This paper uses ML and EVT to analyze tree ring data, improving accuracy of predictions.
This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calcula…
Establishes Poincaré's lemma for formal manifolds.
The geometry of graded principal bundles is discussed in the framework of graded manifold theory of Kostant-Berezin-Leites. In particular, we prove that a graded principal bundle is globally trivial if and only if it admits a global graded section and, further, that the sheaf of vertical derivations on such a bundle co…
Logistic regression for brain imaging without p-values.
Motivated by control-affine systems in optimal control theory, we introduce the notion of a point-affine distribution on a manifold X - i.e., an affine distribution F together with a distinguished vector field contained in F. We compute local invariants for point-affine distributions of constant type when dim(X)=n, ran…