Related papers: MESSY Estimation: Maximum-Entropy based Stochastic…
This review describes recent advances by the authors and others on the topic of incorporating experimental data into molecular simulations through maximum entropy methods. Methods which incorporate experimental data improve accuracy in…
We introduce MeSys, a meaning-based approach, for solving English math word problems (MWPs) via understanding and reasoning in this paper. It first analyzes the text, transforms both body and question parts into their corresponding logic…
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…
This paper deals with the estimation of rare event probabilities using importance sampling (IS), where an optimal proposal distribution is computed with the cross-entropy (CE) method. Although, IS optimized with the CE method leads to an…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
Objective: Sparse Bayesian learning provides an effective scheme to solve the high-dimensional problem in brain signal decoding. However, traditional assumptions regarding data distributions such as Gaussian and binomial are potentially…
The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a…
Nonparametric methods for the estimation of the Levy density of a Levy process are developed. Estimators that can be written in terms of the ``jumps'' of the process are introduced, and so are discrete-data based approximations. A model…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
The Maximum Entropy Method (MEM) is a popular data analysis technique based on Bayesian inference, which has found various applications in the research literature. While the MEM itself is well-grounded in statistics, I argue that its…
The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an…
Model usage is the central challenge of model-based reinforcement learning. Although dynamics model based on deep neural networks provide good generalization for single step prediction, such ability is over exploited when it is used to…
The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm can be applied to stochastic differential equations to estimate the drift and the diffusion function using data from a realization of the SDE. The SINDy algorithm requires…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…
It is well known that semantic and structural features of the generated images emerge at different times during the reverse dynamics of diffusion, a phenomenon that has been connected to physical phase transitions in magnets and other…
A Massey-like inequality is any useful lower bound on guessing entropy in terms of the computationally scalable Shannon entropy. The asymptotically optimal Massey-like inequality is determined and further refined for finite-support…
Masked Diffusion Models (MDMs) offer flexible, non-autoregressive generation, but this freedom introduces a challenge: final output quality is highly sensitive to the decoding order. We are the first to formalize this issue, attributing the…
Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…