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.
Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.
In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between empirical risk minimization and class probability estimation. Based on existing literat…
Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.
While defaults are rare events, losses can be substantial even for credit portfolios with a large number of contracts. Therefore, not only a good evaluation of the probability of default is crucial, but also the severity of losses needs to be estimated. The recovery rate is often modeled independently with regard to th…
Robust portfolio optimization considers uncertainty in market probabilities.
Aggregates probability models using Wasserstein space and variational approach.
Upper bound for max-sliced 2-Wasserstein distance between measures.
Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a new classifier that satisfies simultaneously the two following properties with …
In this paper, we present a simple analysis of {\bf fast rates} with {\it high probability} of {\bf empirical minimization} for {\it stochastic composite optimization} over a finite-dimensional bounded convex set with exponential concave loss functions and an arbitrary convex regularization. To the best of our knowledg…
This paper improves learning uncertain Bayesian networks from incomplete data.
Mitigates spurious correlations without bias labels.
New method approximates high-dimensional probability densities efficiently.
Bayesian method estimates coverage from sketching imperfect data.
The paper analyzes the performance of empirical risk minimization for -norm linear regression.
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization can cover Euclidean spaces with large dimensionality, with the optimal dependence…
We discuss the problem of risk estimation in the classification problem, with specific focus on finding distributions that maximize the confidence intervals of risk estimation. We derived simple analytic approximations for the maximum bias of empirical risk for histogram classifier. We carry out a detailed study on usi…
A new calibration metric bridges testability and actionability.
Based on empirical financial time-series, we show that the "silence-breaking" probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going low-variability period. Such a scaling law has been previously predicted theoretically [R. …
ECOD detects outliers without parameters, fast and simple.
The paper bounds the expectation of empirical processes indexed by Hölder classes.
We study the minimax optimal rate for estimating the Wasserstein- metric between two unknown probability measures based on i.i.d. empirical samples from them. We show that estimating the Wasserstein metric itself between probability measures, is not significantly easier than estimating the probability measures u…
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log…
The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.
New method for PU learning with instance-dependent propensity scores.
SURF simplifies distribution estimation with simple, robust, and fast algorithms.
A new method for matrix completion with model-free weights.
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability bounds on the estimated sparsity as well as on the excess misclassification ris…
Develops simple approximations for credit risk estimation.
Nonparametric adaptive robust control tackles model uncertainty in stochastic processes.
This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods, such as the principle of entropy maximization, to the probability distributions of …
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing e…
A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.
NNLMs optimize poorly for word probabilities due to embedding space structure.
Establishes upper bounds on generalization error in active learning.
Investigates financial and economic systems using statistical mechanics and information theory.
The paper proposes a new method for covariate balancing using IPM to improve causal inference.
This paper introduces AdaSDCA: an adaptive variant of stochastic dual coordinate ascent (SDCA) for solving the regularized empirical risk minimization problems. Our modification consists in allowing the method adaptively change the probability distribution over the dual variables throughout the iterative process. AdaSD…
New metrics avoid high-dimensional analysis challenges, proving convergence without 'curse of dimensionality'.
We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pd…
LinMED is a new linear bandit algorithm with near-optimal regret bound.
Efficient classifier error estimation without re-training.
We introduce a new discriminant analysis method (Empirical Discriminant Analysis or EDA) for binary classification in machine learning. Given a dataset of feature vectors, this method defines an empirical feature map transforming the training and test data into new data with components having Gaussian empirical distrib…
Boosted decision trees typically yield good accuracy, precision, and ROC area. However, because the outputs from boosting are not well calibrated posterior probabilities, boosting yields poor squared error and cross-entropy. We empirically demonstrate why AdaBoost predicts distorted probabilities and examine three cali…
We apply multiple testing procedures to the validation of estimated default probabilities in credit rating systems. The goal is to identify rating classes for which the probability of default is estimated inaccurately, while still maintaining a predefined level of committing type I errors as measured by the familywise …
While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approx…
Asset prices contain information about the probability distribution of future states and the stochastic discounting of those states as used by investors. To better understand the challenge in distinguishing investors' beliefs from risk-adjusted discounting, we use Perron-Frobenius Theory to isolate a positive martingal…
This study investigates self-supervised learning with Wasserstein distance on tree structures.
New probability path model improves flow matching forecasting performance.