Related papers: Comparing statistical and deep learning techniques…

In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…

We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an instance of the GDN model of Kratsios and Papon (2022) solves…

The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…

We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that…

Learning is a fundamental property of intelligent systems, observed across biological organisms and engineered systems. While modern intelligent systems typically rely on gradient descent for learning, the need for exact gradients and…

We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from…

Recurrent neural networks (RNNs) have many advantages over more traditional system identification techniques. They may be applied to linear and nonlinear systems, and they require fewer modeling assumptions. However, these neural network…

In this study, we generalize a problem of sampling a scalar Gauss Markov Process, namely, the Ornstein-Uhlenbeck (OU) process, where the samples are sent to a remote estimator and the estimator makes a causal estimate of the observed…

The advent of fast sensing technologies allows for real-time model updates in many applications where the model parameters are uncertain. Bayesian algorithms, such as ensemble smoothers, offer a real-time probabilistic inversion accounting…

This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and…

In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type \[ X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right), \] where \(\xi_s\) is a L{\'e}vy process.…

This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent…

Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…

In this study, an efficient stochastic gradient-free method, the ensemble neural networks (ENN), is developed. In the ENN, the optimization process relies on covariance matrices rather than derivatives. The covariance matrices are…

This paper presents a novel parameter calibration approach for power system stability models using automatic data generation and advanced deep learning technology. A PMU-measurement-based event playback approach is used to identify…

We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or…

Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this…