Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View

Gene regulatory network inference (GRNI) is a challenging problem, particularly owing to the presence of zeros in single-cell RNA sequencing data: some are biological zeros representing no gene expression, while some others are technical zeros arising from the sequencing procedure (aka dropouts), which may bias GRNI by distorting the joint distribution of the measured gene expressions. Existing approaches typically handle dropout error via imputation, which may introduce spurious relations as the true joint distribution is generally unidentifiable. To tackle this issue, we introduce a causal graphical model to characterize the dropout mechanism, namely, Causal Dropout Model. We provide a simple yet effective theoretical result: interestingly, the conditional independence (CI) relations in the data with dropouts, after deleting the samples with zero values (regardless if technical or not) for the conditioned variables, are asymptotically identical to the CI relations in the original data without dropouts. This particular test-wise deletion procedure, in which we perform CI tests on the samples without zeros for the conditioned variables, can be seamlessly integrated with existing structure learning approaches including constraint-based and greedy score-based methods, thus giving rise to a principled framework for GRNI in the presence of dropouts. We further show that the causal dropout model can be validated from data, and many existing statistical models to handle dropouts fit into our model as specific parametric instances. Empirical evaluation on synthetic, curated, and real-world experimental transcriptomic data comprehensively demonstrate the efficacy of our method.

Steering LLMs Towards Unbiased Responses: A Causality-Guided Debiasing Framework

Large language models (LLMs) can easily generate biased and discriminative responses. As LLMs tap into consequential decision-making (e.g., hiring and healthcare), it is of crucial importance to develop strategies to mitigate these biases. This paper focuses on social bias, tackling the association between demographic information and LLM outputs. We propose a causality-guided debiasing framework that utilizes causal understandings of (1) the data-generating process of the training corpus fed to LLMs, and (2) the internal reasoning process of LLM inference, to guide the design of prompts for debiasing LLM outputs through selection mechanisms. Our framework unifies existing de-biasing prompting approaches such as inhibitive instructions and in-context contrastive examples, and sheds light on new ways of debiasing by encouraging bias-free reasoning. Our strong empirical performance on real-world datasets demonstrates that our framework provides principled guidelines on debiasing LLM outputs even with only the black-box access.

A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of observed variables), based on rank information of covariance matrix over observed variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases.

Causal-learn: Causal Discovery in Python

Causal discovery aims at revealing causal relations from observational data, which is a fundamental task in science and engineering. We describe $\textit{causal-learn}$, an open-source Python library for causal discovery. This library focuses on bringing a comprehensive collection of causal discovery methods to both practitioners and researchers. It provides easy-to-use APIs for non-specialists, modular building blocks for developers, detailed documentation for learners, and comprehensive methods for all. Different from previous packages in R or Java, $\textit{causal-learn}$ is fully developed in Python, which could be more in tune with the recent preference shift in programming languages within related communities. The library is available at https://github.com/py-why/causal-learn.

The m-connecting imset and factorization for ADMG models

Directed acyclic graph (DAG) models have become widely studied and applied in statistics and machine learning -- indeed, their simplicity facilitates efficient procedures for learning and inference. Unfortunately, these models are not closed under marginalization, making them poorly equipped to handle systems with latent confounding. Acyclic directed mixed graph (ADMG) models characterize margins of DAG models, making them far better suited to handle such systems. However, ADMG models have not seen wide-spread use due to their complexity and a shortage of statistical tools for their analysis. In this paper, we introduce the m-connecting imset which provides an alternative representation for the independence models induced by ADMGs. Furthermore, we define the m-connecting factorization criterion for ADMG models, characterized by a single equation, and prove its equivalence to the global Markov property. The m-connecting imset and factorization criterion provide two new statistical tools for learning and inference with ADMG models. We demonstrate the usefulness of these tools by formulating and evaluating a consistent scoring criterion with a closed form solution.

Causal discovery for observational sciences using supervised machine learning

Causal inference can estimate causal effects, but unless data are collected experimentally, statistical analyses must rely on pre-specified causal models. Causal discovery algorithms are empirical methods for constructing such causal models from data. Several asymptotically correct methods already exist, but they generally struggle on smaller samples. Moreover, most methods focus on very sparse causal models, which may not always be a realistic representation of real-life data generating mechanisms. Finally, while causal relationships suggested by the methods often hold true, their claims about causal non-relatedness have high error rates. This non-conservative error tradeoff is not ideal for observational sciences, where the resulting model is directly used to inform causal inference: A causal model with many missing causal relations entails too strong assumptions and may lead to biased effect estimates. We propose a new causal discovery method that addresses these three shortcomings: Supervised learning discovery (SLdisco). SLdisco uses supervised machine learning to obtain a mapping from observational data to equivalence classes of causal models. We evaluate SLdisco in a large simulation study based on Gaussian data and we consider several choices of model size and sample size. We find that SLdisco is more conservative, only moderately less informative and less sensitive towards sample size than existing procedures. We furthermore provide a real epidemiological data application. We use random subsampling to investigate real data performance on small samples and again find that SLdisco is less sensitive towards sample size and hence seems to better utilize the information available in small datasets.

A Uniformly Consistent Estimator of non-Gaussian Causal Effects Under the k-Triangle-Faithfulness Assumption

Kalisch and B\"{u}hlmann (2007) showed that for linear Gaussian models, under the Causal Markov Assumption, the Strong Causal Faithfulness Assumption, and the assumption of causal sufficiency, the PC algorithm is a uniformly consistent estimator of the Markov Equivalence Class of the true causal DAG for linear Gaussian models; it follows from this that for the identifiable causal effects in the Markov Equivalence Class, there are uniformly consistent estimators of causal effects as well. The $k$-Triangle-Faithfulness Assumption is a strictly weaker assumption that avoids some implausible implications of the Strong Causal Faithfulness Assumption and also allows for uniformly consistent estimates of Markov Equivalence Classes (in a weakened sense), and of identifiable causal effects. However, both of these assumptions are restricted to linear Gaussian models. We propose the Generalized $k$-Triangle Faithfulness, which can be applied to any smooth distribution. In addition, under the Generalized $k$-Triangle Faithfulness Assumption, we describe the Edge Estimation Algorithm that provides uniformly consistent estimates of causal effects in some cases (and otherwise outputs "can't tell"), and the \textit{Very Conservative }$SGS$ Algorithm that (in a slightly weaker sense) is a uniformly consistent estimator of the Markov equivalence class of the true DAG.

Learning from Positive and Unlabeled Data by Identifying the Annotation Process

In binary classification, Learning from Positive and Unlabeled data (LePU) is semi-supervised learning but with labeled elements from only one class. Most of the research on LePU relies on some form of independence between the selection process of annotated examples and the features of the annotated class, known as the Selected Completely At Random (SCAR) assumption. Yet the annotation process is an important part of the data collection, and in many cases it naturally depends on certain features of the data (e.g., the intensity of an image and the size of the object to be detected in the image). Without any constraints on the model for the annotation process, classification results in the LePU problem will be highly non-unique. So proper, flexible constraints are needed. In this work we incorporate more flexible and realistic models for the annotation process than SCAR, and more importantly, offer a solution for the challenging LePU problem. On the theory side, we establish the identifiability of the properties of the annotation process and the classification function, in light of the considered constraints on the data-generating process. We also propose an inference algorithm to learn the parameters of the model, with successful experimental results on both simulated and real data. We also propose a novel real-world dataset forLePU, as a benchmark dataset for future studies.

Causal Discovery in the Presence of Measurement Error: Identifiability Conditions

Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model for the measurement-error-free variables can be identified in the presence of measurement error with unknown variance. In this paper, we study precise sufficient identifiability conditions for the measurement-error-free causal model and show what information of the causal model can be recovered from observed data. In particular, we present two different sets of identifiability conditions, based on the second-order statistics and higher-order statistics of the data, respectively. The former was inspired by the relationship between the generating model of the measurement-error-contaminated data and the factor analysis model, and the latter makes use of the identifiability result of the over-complete independent component analysis problem.