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.
Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the model, the model error as well as the statistics of the model error. This method…
Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be need…
Lagrangian data assimilation is a complex problem in oceanic and atmospheric modeling. Tracking drifters in large-scale geophysical flows can involve uncertainty in drifter location, complex inertial effects, and other factors which make comparing them to simulated Lagrangian trajectories from numerical models extremel…
A new framework evaluates HTE estimators using relative error.
problem Lack of robust evaluation methods for HTE estimators.
method Proposes a relative error-based evaluation framework and neural network architecture to estimate nuisance parameters and robustly compare HTE estimators.
result Demonstrates reliable comparisons and improved HTE estimation through the proposed framework and learning algorithm.
In the regression setting, given a set of hyper-parameters, a model-estimation procedure constructs a model from training data. The optimal hyper-parameters that minimize generalization error of the model are usually unknown. In practice they are often estimated using split-sample validation. Up to now, there is an ope…
Random forests are among the most popular classification and regression methods used in industrial applications. To be effective, the parameters of random forests must be carefully tuned. This is usually done by choosing values that minimize the prediction error on a held out dataset. We argue that error reduction is o…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber M-estimator, for which theoretical results on estimation error have recently been proposed in high-dimensional statistics literature. However, t…
In this paper we study the consistency of an empirical minimum error entropy (MEE) algorithm in a regression setting. We introduce two types of consistency. The error entropy consistency, which requires the error entropy of the learned function to approximate the minimum error entropy, is shown to be always true if the…
Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space…
We consider assets for which price Xt and squared volatility Yt are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from N sub-sampled data (XnT,YnT), estimation errors do impact the classical option pricing PDEs. We estimate thes…
This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the time of parameter estimation. The paper provides explicit formulas for those err…
In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy near-optimal error bounds under assumptions on the rank, coherence, and spikiness of B…
The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify the output sensitivity to the parameters (i.e. their relevance to the network ou…
Enhances reinforcement learning uncertainty estimation with a generalized Gaussian error model.
problem Inaccurate error representations and compromised uncertainty estimation in conventional uncertainty-aware TD learning.
method Introduces a novel framework for generalized Gaussian error modeling in deep reinforcement learning, incorporating higher-order moments, particularly kurtosis, to improve uncertainty estimation and mitigation.
result Significant performance gains in policy gradient algorithms with the proposed framework.
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced. Typically the parameters are c…
The study analyzes robustness of estimators in linear models with adversarial errors.
problem Analyzing robustness of estimators in linear models with adversarial errors.
method Develops a general theory for minimum norm interpolating estimators and RERM in linear models without conditions on errors.
result Quantitative bound for the prediction error relating it to Rademacher complexity, norm of minimum norm interpolator of errors, and subdifferential size.