Optimal transport for causal discovery

• URL: http://arxiv.org/abs/2201.09366v1
• Date: Sun, 23 Jan 2022 21:09:45 GMT
• Title: Optimal transport for causal discovery
• Authors: Ruibo Tu, Kun Zhang, Hedvig Kjellstr\"om, Cheng Zhang
• Abstract summary: We provide a novel dynamical-system view of Functional Causal Models (FCMs) We then propose a new framework for identifying causal direction in the bivariate case. Our method demonstrated state-of-the-art results on both synthetic and causal discovery benchmark datasets.
• Score: 13.38095181298957
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Approaches based on Functional Causal Models (FCMs) have been proposed to determine causal direction between two variables, by properly restricting model classes; however, their performance is sensitive to the model assumptions, which makes it difficult for practitioners to use. In this paper, we provide a novel dynamical-system view of FCMs and propose a new framework for identifying causal direction in the bivariate case. We first show the connection between FCMs and optimal transport, and then study optimal transport under the constraints of FCMs. Furthermore, by exploiting the dynamical interpretation of optimal transport under the FCM constraints, we determine the corresponding underlying dynamical process of the static cause-effect pair data under the least action principle. It provides a new dimension for describing static causal discovery tasks, while enjoying more freedom for modeling the quantitative causal influences. In particular, we show that Additive Noise Models (ANMs) correspond to volume-preserving pressureless flows. Consequently, based on their velocity field divergence, we introduce a criterion to determine causal direction. With this criterion, we propose a novel optimal transport-based algorithm for ANMs which is robust to the choice of models and extend it to post-noninear models. Our method demonstrated state-of-the-art results on both synthetic and causal discovery benchmark datasets.

Related papers

• Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flows [6.954510776782872]
  Post-nonlinear (PNL) causal models stand out as a versatile and adaptable framework for modeling causal relationships. We introduce CAF-PoNo, harnessing the power of the normalizing flows architecture to enforce the crucial invertibility constraint in PNL models. Our method precisely reconstructs the hidden noise, which plays a vital role in cause-effect identification.
  arXiv  Detail & Related papers  (2024-07-06T07:19:21Z)
• DA-Flow: Dual Attention Normalizing Flow for Skeleton-based Video Anomaly Detection [52.74152717667157]
  We propose a lightweight module called Dual Attention Module (DAM) for capturing cross-dimension interaction relationships in-temporal skeletal data. It employs the frame attention mechanism to identify the most significant frames and the skeleton attention mechanism to capture broader relationships across fixed partitions with minimal parameters and flops.
  arXiv  Detail & Related papers  (2024-06-05T06:18:03Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Robust Estimation of Causal Heteroscedastic Noise Models [7.568978862189266]
  Student's $t$-distribution is known for its robustness in accounting for sampling variability with smaller sample sizes and extreme values without significantly altering the overall distribution shape. Our empirical evaluations demonstrate that our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.
  arXiv  Detail & Related papers  (2023-12-15T02:26:35Z)
• Unifying Distributionally Robust Optimization via Optimal Transport Theory [13.19058156672392]
  This paper introduces a novel approach that unifies these methods into a single framework based on optimal transport. Our proposed approach makes it possible for optimal adversarial distributions to simultaneously perturb likelihood and outcomes. The paper investigates several duality results and presents tractable reformulations that enhance the practical applicability of this unified framework.
  arXiv  Detail & Related papers  (2023-08-10T08:17:55Z)
• Perimeter Control Using Deep Reinforcement Learning: A Model-free Approach towards Homogeneous Flow Rate Optimization [28.851432612392436]
  Perimeter control maintains high traffic efficiency within protected regions by controlling transfer flows among regions to ensure that their traffic densities are below critical values. Existing approaches can be categorized as either model-based or model-free, depending on whether they rely on network transmission models (NTMs) and macroscopic fundamental diagrams (MFDs)
  arXiv  Detail & Related papers  (2023-05-29T21:22:08Z)
• Improving and generalizing flow-based generative models with minibatch optimal transport [90.01613198337833]
  We introduce the generalized conditional flow matching (CFM) technique for continuous normalizing flows (CNFs) CFM features a stable regression objective like that used to train the flow in diffusion models but enjoys the efficient inference of deterministic flow models. A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference.
  arXiv  Detail & Related papers  (2023-02-01T14:47:17Z)
• When to Update Your Model: Constrained Model-based Reinforcement Learning [50.74369835934703]
  We propose a novel and general theoretical scheme for a non-decreasing performance guarantee of model-based RL (MBRL) Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns.
  arXiv  Detail & Related papers  (2022-10-15T17:57:43Z)
• Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
  We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
  arXiv  Detail & Related papers  (2022-06-29T22:19:03Z)
• Estimation of Bivariate Structural Causal Models by Variational Gaussian Process Regression Under Likelihoods Parametrised by Normalising Flows [74.85071867225533]
  Causal mechanisms can be described by structural causal models. One major drawback of state-of-the-art artificial intelligence is its lack of explainability.
  arXiv  Detail & Related papers  (2021-09-06T14:52:58Z)
• Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approach [1.6242924916178285]
  This study presents a microscopic traffic model that can capture randomness and measure errors in the real world. Since one unique feature of the proposed framework is the capability of capturing both car-following and lane-changing behaviors with one single model, numerical tests are carried out with two separated datasets.
  arXiv  Detail & Related papers  (2020-07-17T06:03:32Z)

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.