Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models

• URL: http://arxiv.org/abs/2402.14777v1
• Date: Thu, 22 Feb 2024 18:37:33 GMT
• Title: Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models
• Authors: Alvaro Ribot, Chandler Squires, Caroline Uhler
• Abstract summary: We consider the task of causal imputation, where we aim to predict the outcomes of some set of actions across a wide range of possible contexts. We introduce a novel SCM-based model class, where the outcome is expressed as a counterfactual. We show that, under a linearity assumption, this setup induces a latent factor model over the matrix of outcomes.
• Score: 9.722250595763386
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the task of causal imputation, where we aim to predict the outcomes of some set of actions across a wide range of possible contexts. As a running example, we consider predicting how different drugs affect cells from different cell types. We study the index-only setting, where the actions and contexts are categorical variables with a finite number of possible values. Even in this simple setting, a practical challenge arises, since often only a small subset of possible action-context pairs have been studied. Thus, models must extrapolate to novel action-context pairs, which can be framed as a form of matrix completion with rows indexed by actions, columns indexed by contexts, and matrix entries corresponding to outcomes. We introduce a novel SCM-based model class, where the outcome is expressed as a counterfactual, actions are expressed as interventions on an instrumental variable, and contexts are defined based on the initial state of the system. We show that, under a linearity assumption, this setup induces a latent factor model over the matrix of outcomes, with an additional fixed effect term. To perform causal prediction based on this model class, we introduce simple extension to the Synthetic Interventions estimator (Agarwal et al., 2020). We evaluate several matrix completion approaches on the PRISM drug repurposing dataset, showing that our method outperforms all other considered matrix completion approaches.

Related papers

• Induced Covariance for Causal Discovery in Linear Sparse Structures [55.2480439325792]
  Causal models seek to unravel the cause-effect relationships among variables from observed data. This paper introduces a novel causal discovery algorithm designed for settings in which variables exhibit linearly sparse relationships.
  arXiv  Detail & Related papers  (2024-10-02T04:01:38Z)
• Structured Learning of Compositional Sequential Interventions [5.8613343090506556]
  We consider sequential treatment regimes where each unit is exposed to combinations of interventions over time. Standard black-box approaches mapping sequences of categorical variables to outputs are applicable. We pose an explicit model for composition, that is, how the effect of sequential interventions can be isolated into modules.
  arXiv  Detail & Related papers  (2024-06-09T11:36:36Z)
• Generating collective counterfactual explanations in score-based classification via mathematical optimization [4.281723404774889]
  A counterfactual explanation of an instance indicates how this instance should be minimally modified so that the perturbed instance is classified in the desired class. Most of the Counterfactual Analysis literature focuses on the single-instance single-counterfactual setting. By means of novel Mathematical Optimization models, we provide a counterfactual explanation for each instance in a group of interest.
  arXiv  Detail & Related papers  (2023-10-19T15:18:42Z)
• The Ordered Matrix Dirichlet for Modeling Ordinal Dynamics [54.96229007229786]
  We propose the Ordered Matrix Dirichlet (OMD) to map latent states to observed action types. Models built on the OMD recover interpretable latent states and show superior forecasting performance in few-shot settings.
  arXiv  Detail & Related papers  (2022-12-08T08:04:26Z)
• Mutual Exclusivity Training and Primitive Augmentation to Induce Compositionality [84.94877848357896]
  Recent datasets expose the lack of the systematic generalization ability in standard sequence-to-sequence models. We analyze this behavior of seq2seq models and identify two contributing factors: a lack of mutual exclusivity bias and the tendency to memorize whole examples. We show substantial empirical improvements using standard sequence-to-sequence models on two widely-used compositionality datasets.
  arXiv  Detail & Related papers  (2022-11-28T17:36:41Z)
• Learning Invariant Representations under General Interventions on the Response [2.725698729450241]
  We focus on linear structural causal models (SCMs) and introduce invariant matching property (IMP) We analyze the generalization errors of our method under both the discrete and continuous environment settings.
  arXiv  Detail & Related papers  (2022-08-22T03:09:17Z)
• Mitigating multiple descents: A model-agnostic framework for risk monotonization [84.6382406922369]
  We develop a general framework for risk monotonization based on cross-validation. We propose two data-driven methodologies, namely zero- and one-step, that are akin to bagging and boosting.
  arXiv  Detail & Related papers  (2022-05-25T17:41:40Z)
• Scalable Intervention Target Estimation in Linear Models [52.60799340056917]
  Current approaches to causal structure learning either work with known intervention targets or use hypothesis testing to discover the unknown intervention targets. This paper proposes a scalable and efficient algorithm that consistently identifies all intervention targets. The proposed algorithm can be used to also update a given observational Markov equivalence class into the interventional Markov equivalence class.
  arXiv  Detail & Related papers  (2021-11-15T03:16:56Z)
• CausalX: Causal Explanations and Block Multilinear Factor Analysis [3.087360758008569]
  We propose a unified multilinear model of wholes and parts. We introduce an incremental bottom-up computational alternative, the Incremental M-mode Block SVD. The resulting object representation is an interpretable choice of intrinsic causal factor representations related to an object's hierarchy of wholes and parts.
  arXiv  Detail & Related papers  (2021-02-25T13:49:01Z)
• Performance metrics for intervention-triggering prediction models do not reflect an expected reduction in outcomes from using the model [71.9860741092209]
  Clinical researchers often select among and evaluate risk prediction models. Standard metrics calculated from retrospective data are only related to model utility under certain assumptions. When predictions are delivered repeatedly throughout time, the relationship between standard metrics and utility is further complicated.
  arXiv  Detail & Related papers  (2020-06-02T16:26:49Z)

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.