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.
Machine learning is often used in competitive scenarios: Participants learn and fit static models, and those models compete in a shared platform. The common assumption is that in order to win a competition one has to have the best predictive model, i.e., the model with the smallest out-sample error. Is that necessarily…
We discuss the finite sample theoretical properties of online predictions in non-stationary time series under model misspecification. To analyze the theoretical predictive properties of statistical methods under this setting, we first define the Kullback-Leibler risk, in order to place the problem within a decision the…
We show that model compression can improve the population risk of a pre-trained model, by studying the tradeoff between the decrease in the generalization error and the increase in the empirical risk with model compression. We first prove that model compression reduces an information-theoretic bound on the generalizati…
The choice of model class is fundamental in statistical learning and system identification, no matter whether the class is derived from physical principles or is a generic black-box. We develop a method to evaluate the specified model class by assessing its capability of reproducing data that is similar to the observed…
This paper establishes a theoretical foundation for consistency training in diffusion models.
problem Lack of a comprehensive theoretical understanding of consistency training in diffusion models.
method Demonstrates the necessity of a number of steps in consistency learning exceeding d5/2/ε for generating samples within ε proximity to the target distribution.
result Establishes rigorous insights into the validity and efficacy of consistency models, offering theoretical underpinnings for their utility.
Stochastic volatility models describe asset prices St as driven by an unobserved process capturing the random dynamics of volatility σt. Here, we quantify how much information about σt can be inferred from asset prices St in terms of Shannon's mutual information I(St:σt). This motivates a careful nume…
This article presents a theoretical model for a dynamic system based on sustainable development. Due to the relatively absence of theoretical studies and practical issues in the area of sustainable development, Romania aspires to the principles of sustainable development. Based on the concept as a process in which econ…
Model-based reinforcement learning (RL) is considered to be a promising approach to reduce the sample complexity that hinders model-free RL. However, the theoretical understanding of such methods has been rather limited. This paper introduces a novel algorithmic framework for designing and analyzing model-based RL algo…
The paper explores stability and generalization of deep GCNs.
problem Understanding the stability and generalization of deep GCNs from a theoretical perspective.
method Theoretical analysis of stability and generalization properties of deep GCNs.
result The stability and generalization of deep GCNs are influenced by the maximum absolute eigenvalue of the graph filter operators and the depth of the network.
Deep neural networks are often used to implement powerful generative models for real-world data. Notable applications include image denoising, as well as other classical inverse problems like compressed sensing and super-resolution. To provide a rigorous but simplified analysis of generative models, in this work, we in…
Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choi…
This research provides theoretical guarantees for hyperparameter estimation in complex network dynamical systems.
problem Theoretical guarantees for hyperparameter estimation in large, inhomogeneous complex network dynamical systems.
method Formulating the system's evolution in a measure transport perspective, proposing a theoretical framework for estimating hyperparameters with mean-type observations.
result A nonasymptotic bound for the deviation of hyperparameter estimates in inhomogeneous complex network dynamical systems with respect to network population size.
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of random regression forests and prove that our algorithm is consistent. We also prov…
Although initially originated as a totally empirical relationship to explain the volume of trade between two partners, gravity equation has been the focus of several theoretic models that try to explain it. Specialization models are of great importance in providing a solid theoretic ground for gravity equation in bilat…