Related papers: Fisher Information Framework for Time Series Model…

In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…

We examine the prospect of learning ice sheet damage models from observational data. Our approach, implemented in CRIKit (the Constitutive Relation Inference Toolkit), is to model the material time derivative of damage as a frame-invariant…

We develop a general method to study the Fisher information distance in central limit theorem for nonlinear statistics. We first construct completely new representations for the score function. We then use these representations to derive…

We propose an unsupervised anomaly detection approach based on a physics-informed diffusion model for multivariate time series data. Over the past years, diffusion model has demonstrated its effectiveness in forecasting, imputation,…

A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…

A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the…

Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it…

Postselected weak measurement has shown significant potential for detecting small physical effects due to its unique weak-value-amplification phenomenon. Previous works suggest that Heisenberg-limit precision can be attained using only the…

Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…

Claeskens and Hjort (2003) constructed the focused information criterion (FIC) and developed frequentist model averaging methods using maximum likelihood estimators assuming the observations to be independent and identically distributed.…

A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an…

This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…

Results by van der Vaart (1991) from semi-parametric statistics about the existence of a non-zero Fisher information are reviewed in an infinite-dimensional non-linear Gaussian regression setting. Information-theoretically optimal inference…

Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…

Inference amortization methods share information across multiple posterior-inference problems, allowing each to be carried out more efficiently. Generally, they require the inversion of the dependency structure in the generative model, as…

Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…

This paper proposes an alternative approach for constructing invariant Jeffreys prior distributions tailored for hierarchical or multilevel models. In particular, our proposal is based on a flexible decomposition of the Fisher information…

Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…