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文章目录
-
- CausalDiscoveryToolbox简介
- 因果建模的过程
-
- 图恢复算法 Graph recovery algorithms
-
- 二元依赖 (Bivariate dependencies)
- 多元方法 (Multivariate methods)
- 因果发现算法 Causal Discovery algorithms
-
- 成对建模（The pairwise setting）
- 全图建模（The graph setting）
- 安装Cdt工具包
- 使用示例
- 工具包模块
- 使用感想
最近在分析观测数据的因果关系时，发现一个很好用的工具包——CausalDiscoveryToolbox（以下简称Cdt），功能齐全，轻松上手因果发现。 下面简单整理下该工具包的原理 用法。
CausalDiscoveryToolbox简介
[Github] [论文] [文档]
- 用于在从数据的联合概率分布样本中学习因果图和相关的因果机制。
- 实现了端到端的因果发现方法，支持从观测数据中恢复直接依赖关系（因果图的骨架）和变量之间的因果关系。
- 实现了许多用于图结构恢复的算法（包括来自bnlearn1，pcalg2包的算法）。
- 基于Numpy，Scikit-learn，Pytorch和R开发。
- 支持GPU硬件加速。
因果建模的过程
Cdt工具包对一般的因果建模流程进行了概括：
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观测数据
因果发现算法
图恢复算法
无向图
因果有向图
Cdt工具包可以直接从观测数据中进行因果发现（获得因果有向图），也可以先恢复图结构（获得无向依赖图）之后，再进行因果发现（获得因果有向图）。
图恢复算法 Graph recovery algorithms
在Cdt工具包中实现了两种从原始数据中恢复无向依赖图的方法：
- 二元依赖 (Bivariate dependencies)
- 用于确定因果图中的（无向）边。
- 依赖于统计检验，例如皮尔逊相关性（Pearson’s correlation）或互信息分数（mutual information scores）3。在第一阶段中可以使用二元依赖关系来建立因果图骨架。
- 多元方法 (Multivariate methods)
- 目的是恢复全因果图。即为图的所有变量选择父、子和配偶节点（子的父母）。
- 输出一个networkx.Graph图对象。
因果发现算法 Causal Discovery algorithms
Cdt包的主要焦点是从观测数据中发现因果关系，从成对设置到全图建模。
- 成对建模（The pairwise setting）
- 把每一对变量作为因果对问题（CEP4，cause-effect pair problem）进行处理，从而确定这些变量之间的因果关系。 比如识别X→Y还是Y→X，或者X与Y没有关系。因果对参考教程
- 成对建模的两个经典方法：加性噪声模型（ANM）5和IGCI6 (Information-Geometric Causal Inference)，在有篇因果对的综述里有详细介绍，后面有空梳理下。
- 成对建模的前提假设是：这两个变量已经受到其他协变量的制约，并且剩余的潜在协变量几乎没有影响，可以被认为是“噪声”。
- 全图建模（The graph setting）
- 基于贝叶斯或基于分数的方法，输出有向无环图或部分有向无环图。
- ①依赖于条件独立性测试，称为基于约束的方法，如PC7或FCI8。
- ②依赖于基于分数的方法，通过图搜索启发式方法（如GES9或CAM10）找到使似然分数最大化的图。
- ③利用著名的对抗生成网络，例如CGNN11或SAM12。
安装Cdt工具包
直接使用pip安装：
代码语言：javascript复制pip install cdt使用示例
代码语言：javascript复制import cdt
from cdt import SETTINGS
SETTINGS.verbose=True
#SETTINGS.NJOBS=16
#SETTINGS.GPU=1
import networkx as nx
import matplotlib.pyplot as plt
plt.axis('off')
# Load data
data = pd.read_csv("lucas0_train.csv")
print(data.head())
# Finding the structure of the graph
glasso = cdt.independence.graph.Glasso()
skeleton = glasso.predict(data)
# Pairwise setting
model = cdt.causality.pairwise.ANM()
output_graph = model.predict(data, skeleton)
# Visualize causality graph
options = {
"node_color": "#A0CBE2",
"width": 1,
"node_size":400,
"edge_cmap": plt.cm.Blues,
"with_labels": True,
}
nx.draw_networkx(output_graph,**options)上述代码输出的因果图：
示例数据： https://download.csdn.net/download/Bit_Coders/16241408
网络结构的绘制参考networkx文档： https://networkx.org/documentation/stable/index.html
工具包模块
该软件包分为5个模块：
- 因果关系：cdt.causality在成对设置或图形设置中实施因果发现算法。
- 独立性：cdt.independence包括恢复数据依赖关系图的方法。
- 数据：cdt.data为用户提供生成数据和加载基准数据的工具。
- 实用程序：cdt.utils为用户提供用于模型构建，图形实用程序和设置的工具。
- 指标：cdt.metrics包括图表的评分指标，以输入为准 networkx.DiGraph 用于计算的所有方法，接口与Scikit-learn类似，在这里.predict() 发动对给定的数据到工具箱中的算法，.fit()使得训练学习算法大部分的算法是类，它们的参数可以在自定义.init()中设置。
程序包及其算法的结构：
代码语言：javascript复制 cdt package
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|- independence
| |- graph (Infering the skeleton from data)
| | |- Lasso variants (Randomized Lasso[1], Glasso[2], HSICLasso[3])
| | |- FSGNN (CGNN[12] variant for feature selection)
| | |- Skeleton recovery using feature selection algorithms (RFECV[5], LinearSVR[6], RRelief[7], ARD[8,9], DecisionTree)
| |
| |- stats (pairwise methods for dependency)
| |- Correlation (Pearson, Spearman, KendallTau)
| |- Kernel based (NormalizedHSIC[10])
| |- Mutual information based (MIRegression, Adjusted Mutual Information[11], Normalized mutual information[11])
|
|- data
| |- CausalPairGenerator (Generate causal pairs)
| |- AcyclicGraphGenerator (Generate FCM-based graphs)
| |- load_dataset (load standard benchmark datasets)
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|- causality
| |- graph (methods for graph inference)
| | |- CGNN[12]
| | |- PC[13]
| | |- GES[13]
| | |- GIES[13]
| | |- LiNGAM[13]
| | |- CAM[13]
| | |- GS[23]
| | |- IAMB[24]
| | |- MMPC[25]
| | |- SAM[26]
| | |- CCDr[27]
| |
| |- pairwise (methods for pairwise inference)
| |- ANM[14] (Additive Noise Model)
| |- IGCI[15] (Information Geometric Causal Inference)
| |- RCC[16] (Randomized Causation Coefficient)
| |- NCC[17] (Neural Causation Coefficient)
| |- GNN[12] (Generative Neural Network -- Part of CGNN )
| |- Bivariate fit (Baseline method of regression)
| |- Jarfo[20]
| |- CDS[20]
| |- RECI[28]
|
|- metrics (Implements the metrics for graph scoring)
| |- Precision Recall
| |- SHD
| |- SID [29]
|
|- utils
|- Settings -> SETTINGS class (hardware settings)
|- loss -> MMD loss [21, 22] & various other loss functions
|- io -> for importing data formats
|- graph -> graph utilities使用感想
- 接口简单，文档清晰，易于上手。
- 不过目前还不支持使用干预措施。
- Cdt工具包是在观察环境进行因果发现的软件包，所以相当于还是在因果科学的第一层级“关联”。不过从当前的实际应用角度来说，“干预”和“反事实”的实施难度较大，“关联”层级的因果发现和推理已经能起到一定的作用。
- Marco Scutari. Package ‘bnlearn’, 2018. ↩︎
- Markus Kalisch, Alain Hauser, et al. Package ‘pcalg’. 2018. ↩︎
- Nguyen Xuan Vinh, Julien Epps, and James Bailey. Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research, 11(Oct):2837–2854, 2010. ↩︎
- Isabelle Guyon. Chalearn cause effect pairs challenge, 2013. URL http://www.causality.inf.ethz.ch/cause-effect.php. ↩︎
- Patrik O Hoyer, Dominik Janzing, Joris M Mooij, Jonas Peters, and Bernhard Sch¨olkopf. Nonlinear causal discovery with additive noise models. In Neural Information Processing Systems (NIPS), pages 689–696, 2009. ↩︎
- Janzing, D., Mooij, J., Zhang, K., Lemeire, et al… (2012). Information-geometric approach to inferring causal directions. Artificial Intelligence, 182, 1-31. ↩︎
- Peter Spirtes, Clark N Glymour, and Richard Scheines. Causation, prediction, and search.MIT press, 2000 ↩︎
- Eric V Strobl, Kun Zhang, and Shyam Visweswaran. Approximate kernel-based conditional independence tests for fast non-parametric causal discovery. 2017 ↩︎
- David Maxwell Chickering. Optimal structure identification with greedy search. Journal of machine learning research, 3(Nov):507–554, 2002. ↩︎
- Peter B¨uhlmann, Jonas Peters, Jan Ernest, et al. Cam: Causal additive models, highdimensional order search and penalized regression. The Annals of Statistics, 2014. ↩︎
- Olivier Goudet, Diviyan Kalainathan, et al. Learning functional causal models with generative neural networks. 2017. ↩︎
- Diviyan Kalainathan, Olivier Goudet, et al. Sam: Structural agnostic model, causal discovery and penalized adversarial learning. 2018. ↩︎
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