Related papers: Dynamical Kinds and their Discovery
Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may overlook the simultaneous and reciprocal nature of causal interactions observed in real world…
Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales.…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
We show a data-driven approach to discover the underlying structural form of the mathematical equation governing the dynamics of multiple but similar systems induced by the same mechanisms. This approach hinges on theories that we lay out…
Detecting anomalies and the corresponding root causes in multivariate time series plays an important role in monitoring the behaviors of various real-world systems, e.g., IT system operations or manufacturing industry. Previous anomaly…
Learning DAG structures from purely observational data remains a long-standing challenge across scientific domains. An emerging line of research leverages the score of the data distribution to initially identify a topological order of the…
Understanding which parts of a dynamical system cause each other is extremely relevant in fundamental and applied sciences. However, inferring causal links from observational data, namely without direct manipulations of the system, is still…
Discovering causal relationships in complex multivariate time series is a fundamental scientific challenge. Traditional methods often falter, either by relying on restrictive linear assumptions or on conditional independence tests that…
Motivated by the development and deployment of large-scale dynamical systems, often composed of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. In this work…
The discovery of causal relationships from high-dimensional data is a major open problem in bioinformatics. Machine learning and feature attribution models have shown great promise in this context but lack causal interpretation. Here, we…
We introduce a causal modeling framework that captures the input-output behavior of predictive models (e.g., machine learning models). The framework enables us to identify features that directly cause the predictions, which has broad…
We present a method of discovering governing differential equations from data without the need to specify a priori the terms to appear in the equation. The input to our method is a dataset (or ensemble of datasets) corresponding to a…
Structural Causal Models are widely used in causal modelling, but how they relate to other modelling tools is poorly understood. In this paper we provide a novel perspective on the relationship between Ordinary Differential Equations and…
This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance…
Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…
Dynamical systems of a new kind are described, which are motivated by the problem of constructing diffeomorphism invariant quantum theories. These are based on the extremization of a non-local and non-additive quantity that we call the…
Clustering aims to group unlabeled objects based on similarity inherent among them into clusters. It is important for many tasks such as anomaly detection, database sharding, record linkage, and others. Some clustering methods are taken as…
In this study, we present a novel constraint-based algorithm for causal structure learning specifically designed for nonlinear autoregressive time series. Our algorithm significantly reduces computational complexity compared to existing…
Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…
Computational analysis of time-course data with an underlying causal structure is needed in a variety of domains, including neural spike trains, stock price movements, and gene expression levels. However, it can be challenging to determine…