Related papers: Imaginary Time Formalism for Causal Nonlinear Resp…

The Schwinger-Keldysh diagram technique is usually involved in the calculation of real-time in-in correlation functions. In the case of a thermal state, one can analytically continue imaginary-time Matsubara correlation functions to real…

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…

An approach for computing Lyapunov functions for nonlinear continuous-time differential equations is developed via a new, Massera-type construction. This construction is enabled by imposing a finite-time criterion on the integrated…

We revisit the causal backreaction paradigm, in which the need for Dark Energy is eliminated via the generation of an apparent cosmic acceleration from the causal flow of inhomogeneity information coming in towards each observer from…

Estimating causal interactions in complex dynamical systems is an important problem encountered in many fields of current science. While a theoretical solution for detecting the causal interactions has been previously formulated in the…

A fundamental challenge of scientific research is inferring causal relations based on observed data. One commonly used approach involves utilizing structural causal models that postulate noisy functional relations among interacting…

Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to…

This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power…

Univariate or multivariate ordinal responses are often assumed to arise from a latent continuous parametric distribution, with covariate effects which enter linearly. We introduce a Bayesian nonparametric modeling approach for univariate…

In a recent work we have introduced a novel approach to study the effect of weak non-linearities in the transfer function on the information transmitted by an analogue channel, by means of a perturbative diagrammatic expansion. We extend…

The present work is based on the nonequilibrium perturbative formalism. There the self-energies are derived up to the forth-order. In consequence, it proves that the nonequilibrium (real-time) perturbative expansion can be connected with…

This paper develops a general causal inference method for treatment effects models with noisily measured confounders. The key feature is that a large set of noisy measurements are linked with the underlying latent confounders through an…

Causal representation learning is the task of identifying the underlying causal variables and their relations from high-dimensional observations, such as images. Recent work has shown that one can reconstruct the causal variables from…

In this paper we study linear non-Gaussian graphical models from the perspective of algebraic statistics. These are acyclic causal models in which each variable is a linear combination of its direct causes and independent noise. The…

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…

We propose a definition of causality for time series in terms of the effect of an intervention in one component of a multivariate time series on another component at some later point in time. Conditions for identifiability, comparable to…

Causal reasoning has gained great attention over the last half century as it allows (or at least intends) to answer questions which go above those within the capabilities of classical inferential statistics using just observational data. So…

Interpreting the inner function of neural networks is crucial for the trustworthy development and deployment of these black-box models. Prior interpretability methods focus on correlation-based measures to attribute model decisions to…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…