High Rank Path Development: an approach of learning the filtration of stochastic processes

• URL: http://arxiv.org/abs/2405.14913v1
• Date: Thu, 23 May 2024 13:20:47 GMT
• Title: High Rank Path Development: an approach of learning the filtration of stochastic processes
• Authors: Jiajie Tao, Hao Ni, Chong Liu,
• Abstract summary: We introduce a novel metric called High Rank PCF Distance (HRPCFD) for extended weak convergence. We then show that such HRPCFD admits many favourable analytic properties which allows us to design an efficient algorithm for training HRPCFD from data and construct the HRPCF-GAN. Our numerical experiments on both hypothesis testing and generative modelling validate the out-performance of our approach compared with several state-of-the-art methods.
• Score: 6.245824251614165
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Since the weak convergence for stochastic processes does not account for the growth of information over time which is represented by the underlying filtration, a slightly erroneous stochastic model in weak topology may cause huge loss in multi-periods decision making problems. To address such discontinuities Aldous introduced the extended weak convergence, which can fully characterise all essential properties, including the filtration, of stochastic processes; however was considered to be hard to find efficient numerical implementations. In this paper, we introduce a novel metric called High Rank PCF Distance (HRPCFD) for extended weak convergence based on the high rank path development method from rough path theory, which also defines the characteristic function for measure-valued processes. We then show that such HRPCFD admits many favourable analytic properties which allows us to design an efficient algorithm for training HRPCFD from data and construct the HRPCF-GAN by using HRPCFD as the discriminator for conditional time series generation. Our numerical experiments on both hypothesis testing and generative modelling validate the out-performance of our approach compared with several state-of-the-art methods, highlighting its potential in broad applications of synthetic time series generation and in addressing classic financial and economic challenges, such as optimal stopping or utility maximisation problems.

Related papers

• Preconditioned Inexact Stochastic ADMM for Deep Model [35.37705488695026]
  This paper develops an algorithm, PISA, which enables scalable parallel computing and supports various second-moment schemes. Grounded in rigorous theoretical guarantees, the algorithm converges under the sole assumption of Lipschitz of the gradient. Comprehensive experimental evaluations for or fine-tuning diverse FMs, including vision models, large language models, reinforcement learning models, generative adversarial networks, and recurrent neural networks, demonstrate its superior numerical performance compared to various state-of-the-art Directions.
  arXiv  Detail & Related papers  (2025-02-15T12:28:51Z)
• Efficient Training of Neural Stochastic Differential Equations by Matching Finite Dimensional Distributions [3.889230974713832]
  We develop a novel scoring rule for comparing continuous Markov processes. This scoring rule allows us to bypass the computational overhead associated with signature kernels. We demonstrate that FDM achieves superior performance, consistently outperforming existing methods in terms of both computational efficiency and generative quality.
  arXiv  Detail & Related papers  (2024-10-04T23:26:38Z)
• Stochastic Q-learning for Large Discrete Action Spaces [79.1700188160944]
  In complex environments with discrete action spaces, effective decision-making is critical in reinforcement learning (RL) We present value-based RL approaches which, as opposed to optimizing over the entire set of $n$ actions, only consider a variable set of actions, possibly as small as $mathcalO(log(n)$)$. The presented value-based RL methods include, among others, Q-learning, StochDQN, StochDDQN, all of which integrate this approach for both value-function updates and action selection.
  arXiv  Detail & Related papers  (2024-05-16T17:58:44Z)
• Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms [88.74308282658133]
  Reization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. Recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes. We propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls.
  arXiv  Detail & Related papers  (2023-10-30T18:43:21Z)
• Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation [26.520247496906492]
  In this work, we analyze if fully data-driven fluid solvers that utilize an autoregressive rollout based on conditional diffusion models are a viable option to address this challenge. To quantitatively and qualitatively benchmark the performance of various flow prediction approaches, three challenging 2D scenarios including incompressible and transonic flows, as well as isotropic turbulence are employed. We find that even simple diffusion-based approaches can outperform multiple established flow prediction methods in terms of accuracy and temporal stability, while being on par with state-of-the-art stabilization techniques like unrolling at training time.
  arXiv  Detail & Related papers  (2023-09-04T18:01:42Z)
• PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers [40.097474800631]
  Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Deep neural network based surrogates have gained increased interest.
  arXiv  Detail & Related papers  (2023-08-10T17:53:05Z)
• Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior [51.60683890503293]
  We propose a theoretical framework for studying behavior cloning of complex expert demonstrations using generative modeling. We show that pure supervised cloning can generate trajectories matching the per-time step distribution of arbitrary expert trajectories.
  arXiv  Detail & Related papers  (2023-07-27T04:27:26Z)
• Provably Efficient UCB-type Algorithms For Learning Predictive State Representations [55.00359893021461]
  The sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs) This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational tractability, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.
  arXiv  Detail & Related papers  (2023-07-01T18:35:21Z)
• Learning from time-dependent streaming data with online stochastic algorithms [7.283533791778357]
  This paper addresses optimization in a streaming setting with time-dependent and biased estimates. We analyze several first-order methods, including Gradient Descent (SGD), mini-batch SGD, and time-varying mini-batch SGD, along with their Polyak-Ruppert averages.
  arXiv  Detail & Related papers  (2022-05-25T07:53:51Z)
• Solving Multistage Stochastic Linear Programming via Regularized Linear Decision Rules: An Application to Hydrothermal Dispatch Planning [77.34726150561087]
  We propose a novel regularization scheme for linear decision rules (LDR) based on the AdaSO (adaptive least absolute shrinkage and selection operator) Experiments show that the overfit threat is non-negligible when using the classical non-regularized LDR to solve MSLP. For the LHDP problem, our analysis highlights the following benefits of the proposed framework in comparison to the non-regularized benchmark.
  arXiv  Detail & Related papers  (2021-10-07T02:36:14Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.