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.
The resilience of low-degree Rademacher chaos is studied, providing probabilistic lower bounds.
The study reveals chaos in geometric objects embedded in higher dimensions.
The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain precise symmetry (Feigenbaum numbers) is even more surprising. As an illustration o…
New bound on Rademacher complexity for vector functions.
Extends inequality for Rademacher complexities using -stable variables.
A formula for Rademacher symbols in triangle groups is provided.
Study on spin random fields using chaos decomposition for cosmic microwave background modeling.
We develop a technique for deriving data-dependent error bounds for transductive learning algorithms based on transductive Rademacher complexity. Our technique is based on a novel general error bound for transduction in terms of transductive Rademacher complexity, together with a novel bounding technique for Rademacher…
In this paper we calibrate chaotic models for interest rates to market data using a polynomial-exponential parametrization for the chaos coefficients. We identify a subclass of one-variable models that allow us to introduce complexity from higher order chaos in a controlled way while retaining considerable analytic tra…
Improved generalization bounds for CNNs using Rademacher complexity.
New insights into neural network training efficiency.
Enhances polynomial chaos models with uncertainty intervals.
Study shows uniform-time chaos propagation in mean field Langevin dynamics.
Statistical learning theory connects to spin glass models via Rademacher complexity and replica theory.
The paper introduces invariants to describe period-doubling routes to chaos in dynamical systems.
The paper bounds the complexity of GCNs using Rademacher complexity.
Uniform-in-time analysis for Stein Variational Gradient Descent across various metrics.
Analyzes the complexity of linear hypothesis sets using Rademacher complexity.
The paper analyzes risk bounds and Rademacher complexity in batch RL.
Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.
Neural networks can model chaos efficiently by becoming geometrically chaotic.
Neural networks solve SPDEs using Wiener chaos expansion.
The contraction inequality for Rademacher averages is extended to Lipschitz functions with vector-valued domains, and it is also shown that in the bounding expression the Rademacher variables can be replaced by arbitrary iid symmetric and sub-gaussian variables. Example applications are given for multi-category learnin…
The paper models asset prices using Wiener chaos expansions for efficient calibration to implied volatility surfaces.
Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.
We show how to control the generalization error of time series models wherein past values of the outcome are used to predict future values. The results are based on a generalization of standard i.i.d. concentration inequalities to dependent data without the mixing assumptions common in the time series setting. Our proo…
The Financial Chaos Index models stock market volatility across three regimes based on mutual price fluctuations.
In this letter, as a proof of concept, we propose a deep learning-based approach to attack the chaos-based image encryption algorithm in \cite{guan2005chaos}. The proposed method first projects the chaos-based encrypted images into the low-dimensional feature space, where essential information of plain images has been …
The paper analyzes adversarial robustness for linear models and neural networks using Rademacher complexity.
The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs classifiers as linear operators. The goal of this paper is to extend thi…
Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.
A new neural network model uses polynomial chaos theory to improve neural signal processing.
Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorith…
Paper improves performance guarantees for Rademacher projections.
In this paper we study the price dynamics in a simple model of financial markets with heterogeneous agents. We concentrate on how increases in the total number of active traders influences fluctuations of asset prices. We find that a curious route to chaos is observed when the total number of [active traders] increases…
New findings show Rademacher complexities are not crucial for learning complexities.
Great successes of deep neural networks have been witnessed in various real applications. Many algorithmic and implementation techniques have been developed, however, theoretical understanding of many aspects of deep neural networks is far from clear. A particular interesting issue is the usefulness of dropout, which w…
Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum m…
For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a -heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional $…
Sparse Polynomial Chaos expansions improve accuracy and efficiency in simulations.
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of "2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization" by V. Koltchinskii [arXiv:0708.0083]
Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical norm. This result is convenient to apply in real applications and could yield re…
It has long been suggested that the biological brain operates at some critical point between two different phases, possibly order and chaos. Despite many indirect empirical evidence from the brain and analytical indication on simple neural networks, the foundation of this hypothesis on generic non-linear systems remain…