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 algorithms reduce regret in online MDPs by adapting to data and variance.
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the positive orthant of the unit sphere. This measure gathers information on the localizat…
This paper proposes a new method to improve domain adaptation by distinguishing between marginal and dependence structure differences.
The paper examines how small positive dependence can lead to correlated tail risks.
We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory a…
Develops a new model for measuring extremal dependence in financial markets.
Study online learning in RKHS with dependent processes, focusing on \(β\)- and \(φ\)-mixing.
Study shows observability from a measurable set for Gevrey functions.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying space as a super Ricci flow as previously introduced by the second author. Our ma…
This study explores star-shaped regularizers learned from critic-based losses.
Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual information can fail even in simplistic situations. We then propose two conditions for r…
The paper improves SVM and localized SVM stability under triple perturbations.
Fairness-aware learning is a novel framework for classification tasks. Like regular empirical risk minimization (ERM), it aims to learn a classifier with a low error rate, and at the same time, for the predictions of the classifier to be independent of sensitive features, such as gender, religion, race, and ethnicity. …
Paper estimates EOT maps for non-compactly supported measures with subGaussian target.
We conduct an axiomatic study of the problem of estimating the strength of a known causal relationship between a pair of variables. We propose that an estimate of causal strength should be based on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause), and study d…
Current adoption of machine learning in industrial, societal and economical activities has raised concerns about the fairness, equity and ethics of automated decisions. Predictive models are often developed using biased datasets and thus retain or even exacerbate biases in their decisions and recommendations. Removing …
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regressi…
In the paper, we use and investigate copulas models to represent multivariate dependence in financial time series. We propose the algorithm of risk measure computation using copula models. Using the optimal mean- portfolio we compute portfolio's Profit and Loss series and corresponded risk measures curves. Value-…
New measure captures differences across entire distributions of counterfactual outcomes.
Paper introduces ENZ to measure significant coefficients in sparse recovery, improving over classical methods.
Proposes RM-CVaR for better portfolio optimization using multiple β-CVaR.
Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few hyperparameters or the kernel is even data dependent in a much more complicated manner. …
For each submanifold of a stratified group, we find a number and a measure only depending on its tangent bundle, the grading and the fixed Riemannian metric. In two step stratified groups, we show that such number and measure coincide with the Hausdorff dimension and with the spherical Hausdorff measure of the submanif…
Sleep-based regularization stabilizes STDP in recurrent neural networks.
Dynamic risk measures follow law invariance principles over time.
In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift problem, we derive high probability confidence bounds for the kernel mean matching (…
In the paper, the martingales and super-martingales relative to a regular set of measures are systematically studied. The notion of local regular super-martingale relative to a set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are fou…
We introduce a notion of "effective dimension" of a statistical model based on the number of cubes of size needed to cover the model space when endowed with the Fisher Information Matrix as metric, being the number of observations. The number of observations fixes a natural scale or resolution. The eff…
It is a well-known fact that adding noise to the input data often improves network performance. While the dropout technique may be a cause of memory loss, when it is applied to recurrent connections, Tikhonov regularization, which can be regarded as the training with additive noise, avoids this issue naturally, though …
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…
The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric model, hence avoiding linear or additive models. The key idea is to measure the …
Training a source model optimally for its own task is suboptimal for downstream transfer.
Study identifies unique minimizers for interaction kernels in particle systems.
The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned ke…
For a risk vector , whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the componen…
This paper introduces intrinsic time, a new measure of time for complex systems.
Anosov groups limit sets are Ahlfors regular, with applications in Teichmüller spaces.
Develops a new exponential map for time-varying vector fields.
New method synthesizes and analyzes probability measures using entropy-regularized optimal transport.
Entropy asymmetry affects regularization in ERM, leading to biased solutions.
Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.
Investigates regularity of solutions to complex Hessian equation.
SGD reduces test error by decorrelating updates.
Sparse RSP routing improves graph exploration and classification.