Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables
- URL: http://arxiv.org/abs/2308.06718v2
- Date: Sun, 9 Jun 2024 16:07:50 GMT
- Title: Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables
- Authors: Feng Xie, Biwei Huang, Zhengming Chen, Ruichu Cai, Clark Glymour, Zhi Geng, Kun Zhang,
- Abstract summary: We propose a Generalized Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models.
We show that the causal structure of a LiNGLaH is identifiable in light of GIN conditions.
- Score: 28.44175079713669
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate the task of learning causal structure in the presence of latent variables, including locating latent variables and determining their quantity, and identifying causal relationships among both latent and observed variables. To this end, we propose a Generalized Independent Noise (GIN) condition for linear non-Gaussian acyclic causal models that incorporate latent variables, which establishes the independence between a linear combination of certain measured variables and some other measured variables. Specifically, for two observed random vectors $\bf{Y}$ and $\bf{Z}$, GIN holds if and only if $\omega^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are independent, where $\omega$ is a non-zero parameter vector determined by the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. We then give necessary and sufficient graphical criteria of the GIN condition in linear non-Gaussian acyclic models. Roughly speaking, GIN implies the existence of a set $\mathcal{S}$ such that $\mathcal{S}$ is causally earlier (w.r.t. the causal ordering) than $\mathbf{Y}$, and that every active (collider-free) path between $\mathbf{Y}$ and $\mathbf{Z}$ must contain a node from $\mathcal{S}$. Interestingly, we find that the independent noise condition (i.e., if there is no confounder, causes are independent of the residual derived from regressing the effect on the causes) can be seen as a special case of GIN. With such a connection between GIN and latent causal structures, we further leverage the proposed GIN condition, together with a well-designed search procedure, to efficiently estimate Linear, Non-Gaussian Latent Hierarchical Models (LiNGLaHs), where latent confounders may also be causally related and may even follow a hierarchical structure. We show that the causal structure of a LiNGLaH is identifiable in light of GIN conditions. Experimental results show the effectiveness of the proposed method.
Related papers
- Causal Discovery from Poisson Branching Structural Causal Model Using High-Order Cumulant with Path Analysis [24.826219353338132]
One of the most common characteristics of count data is the inherent branching structure described by a binomial thinning operator.
A single causal pair is Markov equivalent, i.e., $Xrightarrow Y$ and $Yrightarrow X$ are distributed equivalent.
We propose a Poisson Branching Structure Causal Model (PB-SCM) and perform a path analysis on PB-SCM using high-order cumulants.
arXiv Detail & Related papers (2024-03-25T08:06:08Z) - A Unified Framework for Uniform Signal Recovery in Nonlinear Generative
Compressed Sensing [68.80803866919123]
Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously.
Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples.
We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
arXiv Detail & Related papers (2023-09-25T17:54:19Z) - Reinterpreting causal discovery as the task of predicting unobserved
joint statistics [15.088547731564782]
We argue that causal discovery can help inferring properties of the unobserved joint distributions'
We define a learning scenario where the input is a subset of variables and the label is some statistical property of that subset.
arXiv Detail & Related papers (2023-05-11T15:30:54Z) - Statistical Learning under Heterogeneous Distribution Shift [71.8393170225794]
Ground-truth predictor is additive $mathbbE[mathbfz mid mathbfx,mathbfy] = f_star(mathbfx) +g_star(mathbfy)$.
arXiv Detail & Related papers (2023-02-27T16:34:21Z) - On counterfactual inference with unobserved confounding [36.18241676876348]
Given an observational study with $n$ independent but heterogeneous units, our goal is to learn the counterfactual distribution for each unit.
We introduce a convex objective that pools all $n$ samples to jointly learn all $n$ parameter vectors.
We derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality.
arXiv Detail & Related papers (2022-11-14T04:14:37Z) - On the Identifiability and Estimation of Causal Location-Scale Noise
Models [122.65417012597754]
We study the class of location-scale or heteroscedastic noise models (LSNMs)
We show the causal direction is identifiable up to some pathological cases.
We propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks.
arXiv Detail & Related papers (2022-10-13T17:18:59Z) - The Sample Complexity of Robust Covariance Testing [56.98280399449707]
We are given i.i.d. samples from a distribution of the form $Z = (1-epsilon) X + epsilon B$, where $X$ is a zero-mean and unknown covariance Gaussian $mathcalN(0, Sigma)$.
In the absence of contamination, prior work gave a simple tester for this hypothesis testing task that uses $O(d)$ samples.
We prove a sample complexity lower bound of $Omega(d2)$ for $epsilon$ an arbitrarily small constant and $gamma
arXiv Detail & Related papers (2020-12-31T18:24:41Z) - Generalized Independent Noise Condition for Estimating Latent Variable
Causal Graphs [39.24319581164022]
We propose a Generalized Independent Noise (GIN) condition to estimate latent variable graphs.
We show that GIN helps locate latent variables and identify their causal structure, including causal directions.
arXiv Detail & Related papers (2020-10-10T06:11:06Z) - Agnostic Learning of a Single Neuron with Gradient Descent [92.7662890047311]
We consider the problem of learning the best-fitting single neuron as measured by the expected square loss.
For the ReLU activation, our population risk guarantee is $O(mathsfOPT1/2)+epsilon$.
For the ReLU activation, our population risk guarantee is $O(mathsfOPT1/2)+epsilon$.
arXiv Detail & Related papers (2020-05-29T07:20:35Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.