Related papers: Uniqueness of MAP estimates for inverse problems u…
The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard…
In inverse reinforcement learning (IRL), a learning agent infers a reward function encoding the underlying task using demonstrations from experts. However, many existing IRL techniques make the often unrealistic assumption that the agent…
This study delves into the application of Conformal Field Theory (CFT) to understand information diffusion within digital media and its broader social implications. Focusing on the digital native generation, vulnerable to misinformation and…
Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…
In this paper we propose a state space modeling approach for trust evaluation in wireless sensor networks. In our state space trust model (SSTM), each sensor node is associated with a trust metric, which measures to what extent the data…
Integrability of equations of topological-antitopological fusion (being proposed by Cecotti and Vafa) describing ground state metric on given 2D topological field theory (TFT) model, is proved. For massive TFT models these equations are…
A computational scheme is developed to determine the response of a quantum field theory (QFT) with a factorized scattering operator under a variation of the Unruh temperature. To this end a new family of integrable systems is introduced,…
Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…
Originally conceived as a theory of consciousness, integrated information theory (IIT) provides a theoretical framework intended to characterize the compositional causal information that a system, in its current state, specifies about…
We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The…
In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…
Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models…
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…
Approximating marginals of a graphical model is one of the fundamental problems in the theory of networks. In a recent paper a method was shown to construct a variational free energy such that the linear response estimates, and maximum…
An information-theoretic framework is introduced to analyze last-layer embedding, focusing on learned representations for regression tasks. We define representation-rate and derive limits on the reliability with which input-output…
Inverse scattering aims to infer information about a hidden object by using the received scattered waves and training data collected from forward mathematical models. Recent advances in computing have led to increasing attention towards…
Bayesian inference provides principled uncertainty quantification but is often limited by the challenges of prior and likelihood elicitation. The martingale posterior (MGP) (Fong et al., 2023) offers an alternative by replacing these…
Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly…
We study the identifiability of parameters and falsifiability of predictions under the process of model expansion in a Bayesian setting. Identifiability is represented by the closeness of the posterior to the prior distribution and…
Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish…