Related papers: Statistical description and dimension reduction of…
We present an efficient approach, based on a number-conditioned master equation, for large-deviation analysis in mesoscopic transports. Beyond the conventional full-counting-statistics study, the large-deviation approach encodes complete…
Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…
In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
We introduce an infinite-dimensional version of the Christoffel function, where now (i) its argument lies in a Hilbert space of functions, and (ii) its associated underlying measure is supported on a compact subset of the Hilbert space. We…
Using first principles from inference, we design a set of functionals for the purposes of \textit{ranking} joint probability distributions with respect to their correlations. Starting with a general functional, we impose its desired…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
We propose a simple method to estimate the parameters of a continuously measured quantum system, by fitting correlation functions of the measured signal. We demonstrate the approach in simulation, both on toy examples and on a recent…
We propose a flexible regression framework to model the conditional distribution of multilevel generalized multivariate functional data of potentially mixed type, e.g. binary and continuous data. We make pointwise parametric distributional…
This paper jointly addresses the challenges of non-stationarity and high dimensionality in analysing multivariate time series. Building on the classical concept of cointegration, we introduce a more flexible notion, called stability space,…
In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to…
In two recent papers by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects,…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
In observational studies, the causal effect of a treatment may be confounded with variables that are related to both the treatment and the outcome of interest. In order to identify a causal effect, such studies often rely on the…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…