Related papers: Learning Sparse Causal Models is not NP-hard
Graphical structures estimated by causal learning algorithms from time series data can provide misleading causal information if the causal timescale of the generating process fails to match the measurement timescale of the data. Existing…
Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…
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…
Causal discovery from observational data holds great promise, but existing methods rely on strong assumptions about the underlying causal structure, often requiring full observability of all relevant variables. We tackle these challenges by…
The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…
A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their…
Much of the causal discovery literature prioritises guaranteeing the identifiability of causal direction in statistical models. For structures within a Markov equivalence class, this requires strong assumptions which may not hold in…
The use of simulated data in the field of causal discovery is ubiquitous due to the scarcity of annotated real data. Recently, Reisach et al., 2021 highlighted the emergence of patterns in simulated linear data, which displays increasing…
We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude polynomial…
Causal structure learning has been a challenging task in the past decades and several mainstream approaches such as constraint- and score-based methods have been studied with theoretical guarantees. Recently, a new approach has transformed…
Structural causal models postulate noisy functional relations among a set of interacting variables. The causal structure underlying each such model is naturally represented by a directed graph whose edges indicate for each variable which…
Noise Contrastive Estimation (NCE) is a powerful parameter estimation method for log-linear models, which avoids calculation of the partition function or its derivatives at each training step, a computationally demanding step in many cases.…
The assumption of independence between observations (units) in a dataset is prevalent across various methodologies for learning causal graphical models. However, this assumption often finds itself in conflict with real-world data, posing…
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…
We consider learning a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are…
Causal Bayesian networks are widely used tools for summarising the dependencies between variables and elucidating their putative causal relationships. By restricting the search to trees, for example, learning the optimum from data is…
In this paper we present a comprehensive view of prominent causal discovery algorithms, categorized into two main categories (1) assuming acyclic and no latent variables, and (2) allowing both cycles and latent variables, along with…
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…
In this paper, we focus on learning sparse graphs with a core-periphery structure. We propose a generative model for data associated with core-periphery structured networks to model the dependence of node attributes on core scores of the…
The PC and FCI algorithms are popular constraint-based methods for learning the structure of directed acyclic graphs (DAGs) in the absence and presence of latent and selection variables, respectively. These algorithms (and their…