Related papers: Statistical Cryptography using a Fisher-Schr\"{o}d…
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…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…
The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…
Privacy regulations require the erasure of data from deep learning models. This is a significant challenge that is amplified in Federated Learning, where data remains on clients, making full retraining or coordinated updates often…
We introduce a nonparametric model for inferring time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and…
This paper presents a simple yet efficient method for statistical inference of tensor linear forms using incomplete and noisy observations. Under the Tucker low-rank tensor model and the missing-at-random assumption, we utilize an…
A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing…
Statistical Inference is the process of determining a probability distribution over the space of parameters of a model given a data set. As more data becomes available this probability distribution becomes updated via the application of…
Graphs are playing a crucial role in different fields since they are powerful tools to unveil intrinsic relationships among signals. In many scenarios, an accurate graph structure representing signals is not available at all and that…
In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but…
When training data are fragmented across batches or federated-learned across different geographic locations, trained models manifest performance degradation. That degradation partly owes to covariate shift induced by data having been…
Diffraction on the slit can be interpreted in accordance with the Heisenberg uncertainty principle. This elementary example hints at the importance of the information theory for the quantum physics. The role played by one particularly…
Persistence diagrams provide stable, interpretable summaries of geometric and topological structure and are useful for simulation-based inference when low-order statistics miss key information. Yet persistence-based pipelines require…
In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are…
Traditional approaches to Quantitative Information Flow (QIF) represent the adversary's prior knowledge of possible secret values as a single probability distribution. This representation may miss important structure. For instance,…
We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon$ under local differential privacy constraints. These bounds are valid under general…
In the realm of deep learning, the Fisher information matrix (FIM) gives novel insights and useful tools to characterize the loss landscape, perform second-order optimization, and build geometric learning theories. The exact FIM is either…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
In biomedical studies, it is often desirable to characterize the interactive mode of multiple disease outcomes beyond their marginal risk. Ising model is one of the most popular choices serving for this purpose. Nevertheless, learning…