Open Access. Powered by Scholars. Published by Universities.®
Harmonic Analysis and Representation Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
- Keyword
-
- (Abstract Harmonic Analysis) Explicit machine computation and programs (not the theory of computation or programming) (1)
- 20C30 (1)
- 43-04 (1)
- 43A30 (1)
- AI Privacy (1)
-
- Adaptive Boundary Selection (1)
- Adversarial Robustness (1)
- Artificial Intelligence (1)
- Bayesian Hyperparameter Optimization (1)
- Biorthogonality (1)
- CDT-1D CNN (1)
- Chain-of-Thought (1)
- Economics (1)
- Energy preservation (1)
- Finite Element Methods (1)
- Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups (1)
- Heston Stochastic Volatility Model (1)
- High-Frequency Options Trading (1)
- Language Modeling (1)
- Learning Theory (1)
- Machine Learning (1)
- Membership Inference Attack (1)
- Multi-Task Learning (1)
- PAC-Bayes Theory (1)
- Property Testing (1)
- Quadrature mirror filterbank (1)
- Representations of finite symmetric groups (1)
- Simpson-Sobolev Regularization (1)
- Temporal Cross- Validation (1)
- Wavelets (1)
- Publication
- Publication Type
Articles 1 - 4 of 4
Full-Text Articles in Harmonic Analysis and Representation
Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender
Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender
Mathematics Theses and Dissertations
This dissertation presents a computational framework for high-frequency options trading that combines Cross-Data-Type 1-D Convolutional Neural Networks (CDT-1D CNN) with Simpson-Sobolev regularization for directional prediction, and finite element methods (FEM) for realistic option pricing during backtesting. The core innovation lies in developing a mathematically rigorous regularization approach that maintains the adaptability of modern deep learning while enabling accurate evaluation through stochastic volatility models. The primary contribution is the Simpson-Sobolev regularization scheme, which extends traditional Sobolev regularization by incorporating Simpson’s rule for numerical integration. This approach achieves higher-order accuracy in approximating the Sobolev norms that control function smoothness. Simpson’s rule attains …
Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac
Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac
Dartmouth College Ph.D Dissertations
In this dissertation, we take a step towards addressing the major problem of a lack of standardized and rigorous approaches to testing and evaluation of AI systems. Taking inspiration from both the fields of Property Testing and Property Based Testing (for programs), we develop a novel taxonomy of partially overlapping classes of properties of AI systems, including simple properties, compound properties, higher order properties, data relation properties, and architecture-utility properties. We argue that this taxonomy categorizes a diverse set of AI traits -- including accuracy, fairness, robustness, monotonicity, point-wise and global privacy properties, sensitivity, and more -- according to the …
Construction Of Energy Preserving Qmf, Jian-Ao Lian, Yonghui Wang
Construction Of Energy Preserving Qmf, Jian-Ao Lian, Yonghui Wang
Applications and Applied Mathematics: An International Journal (AAM)
Recently, a family of perfect reconstruction (PR) quadrature mirror filterbanks (QMF) with finite impulse response filters (FIR) from systems of biorthogonal refinable functions and wavelets were introduced and also applied to image processing. However, a detailed procedure was absent. The main objective of this paper is to present extensive examples that will provide a thorough process of construction of the new family of PR QMF with FIR filterbanks. These new filters are linearphase due to the symmetry property of their corresponding biorthogonal refinable functions and wavelets. In addition, these filters have odd lengths so that the symmetric extension can be …
Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott
Fast Algorithms For Analyzing Partially Ranked Data, Matthew Mcdermott
HMC Senior Theses
Imagine your local creamery administers a survey asking their patrons to choose their five favorite ice cream flavors. Any data collected by this survey would be an example of partially ranked data, as the set of all possible flavors is only ranked into subsets of the chosen flavors and the non-chosen flavors. If the creamery asks you to help analyze this data, what approaches could you take? One approach is to use the natural symmetries of the underlying data space to decompose any data set into smaller parts that can be more easily understood. In this work, I describe …