Related papers: Deep Koopman operator framework for causal discove…

Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and prediction of these systems remains a challenge. Koopman operator theory circumvents some of these issues by considering the dynamics in the space of…

Causal discovery from time series is a fundamental task in machine learning. However, its widespread adoption is hindered by a reliance on untestable causal assumptions and by the lack of robustness-oriented evaluation in existing…

Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose…

Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or…

Causal inference in a nonlinear system of multivariate timeseries is instrumental in disentangling the intricate web of relationships among variables, enabling us to make more accurate predictions and gain deeper insights into real-world…

Reachability analysis of nonlinear dynamical systems is a challenging and computationally expensive task. Computing the reachable states for linear systems, in contrast, can often be done efficiently in high dimensions. In this paper, we…

Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…

Many frameworks exist to infer cause and effect relations in complex nonlinear systems but a complete theory is lacking. A new framework is presented that is fully nonlinear, provides a complete information theoretic disentanglement of…

Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical…

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large…

The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect…

Causal discovery is challenging in general dynamical systems because, without strong structural assumptions, the underlying causal graph may not be identifiable even from interventional data. However, many real-world systems exhibit…

This article presents a novel method for causal discovery with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data. Causal discovery often faces challenges…

Causal discovery from observational data is an important tool in many branches of science. Under certain assumptions it allows scientists to explain phenomena, predict, and make decisions. In the large sample limit, sound and complete…

Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable…

Recently Koopman operator has become a promising data-driven tool to facilitate real-time control for unknown nonlinear systems. It maps nonlinear systems into equivalent linear systems in embedding space, ready for real-time linear control…

Causal discovery in time-series is a fundamental problem in the machine learning community, enabling causal reasoning and decision-making in complex scenarios. Recently, researchers successfully discover causality by combining neural…

Classical machine learning techniques often struggle with overfitting and unreliable predictions when exposed to novel conditions. Introducing causality into the modelling process offers a promising way to mitigate these challenges by…

Exploratory analysis of time series data can yield a better understanding of complex dynamical systems. Granger causality is a practical framework for analysing interactions in sequential data, applied in a wide range of domains. In this…

Causal discovery aims to infer causal relationships among variables from observational data, typically represented by a directed acyclic graph (DAG). Most existing methods assume independent and identically distributed observations, an…