Related papers: Causal Homotopy
Learning the unique directed acyclic graph corresponding to an unknown causal model is a challenging task. Methods based on functional causal models can identify a unique graph, but either suffer from the curse of dimensionality or impose…
In observational studies, when a total causal effect of interest is not identified, the set of all possible effects can be reported instead. This typically occurs when the underlying causal DAG is only known up to a Markov equivalence…
In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology…
Predicting causal structure from time series data is crucial for understanding complex phenomena in physiology, brain connectivity, climate dynamics, and socio-economic behaviour. Causal discovery in time series is hindered by the…
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…
In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established…
Directed acyclic graphs (DAGs) are frequently used in epidemiology as a method to encode causal inference assumptions. We propose the DAGWOOD framework to bring many of those encoded assumptions to the forefront. DAGWOOD combines a root DAG…
The language and methods of algebraic topology, particularly homotopy theory, have been extensively used in the study of the identification, the classification and the evolution of defects. Topological methods provide the means for the…
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…
The causal dependence in data is often characterized by Directed Acyclic Graphical (DAG) models, widely used in many areas. Causal discovery aims to recover the DAG structure using observational data. This paper focuses on causal discovery…
We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be…
Structural discovery amongst a set of variables is of interest in both static and dynamic settings. In the presence of lead-lag dependencies in the data, the dynamics of the system can be represented through a structural equation model…
Simulated DAG models may exhibit properties that, perhaps inadvertently, render their structure identifiable and unexpectedly affect structure learning algorithms. Here, we show that marginal variance tends to increase along the causal…
We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…
We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…
The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of…
Identification theory for causal effects in causal models associated with hidden variable directed acyclic graphs (DAGs) is well studied. However, the corresponding algorithms are underused due to the complexity of estimating the…
A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of…
We consider the problem of learning the structure of a causal directed acyclic graph (DAG) model in the presence of latent variables. We define latent factor causal models (LFCMs) as a restriction on causal DAG models with latent variables,…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…