book

Causal AI

Name: Causal AI
Author: Robert Ness
ISBN: 9781633439917

by Robert Ness

February 2025

Beginner to intermediate

520 pages

17h 3m

English

Manning Publications

Audiobook available

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Causal AI
copyright
dedication
contents
foreword
preface
acknowledgments
about this book
What is the required mathematical and programming background?What programming tools will we use?Navigating this bookAbout the codeliveBook discussion forum
about the author
about the cover illustration

Part 1 Conceptual foundations
1 Why causal AI
1.1 What is causal AI?1.2 How this book approaches causal inference1.2.1 Emphasis on AI1.2.2 Focus on tech, retail, and business1.2.3 Parallel world counterfactuals and other queries beyond causal effects1.2.4 An assumption of commodification of inference1.2.5 Breaking down theory with code1.3 Causality’s role in modern AI workflows1.3.1 Better data science1.3.2 Better attribution, credit assignment, and root cause analysis1.3.3 More robust, decomposable, and explainable models1.3.4 Fairer AI1.4 How causality is driving the next AI wave1.4.1 Causal representation learning1.4.2 Causal reinforcement learning1.4.3 Large language models and foundation models1.5 A machine learning-themed primer on causality1.5.1 Queries, probabilities, and statistics1.5.2 Causality and MNIST1.5.3 Causal queries, probabilities, and statisticsSummary
2 A primer on probabilistic generative modeling
2.1 Primer on probability2.1.1 Random variables and probability2.1.2 Probability distributions and distribution functions2.1.3 Joint probability and conditional probability2.1.4 The chain rule, the law of total probability, and Bayes Rule2.1.5 Markovian assumptions and Markov kernels2.1.6 Parameters2.1.7 Canonical classes of probability distribution2.1.8 Visualizing distributions2.1.9 Independence and conditional independence2.1.10 Expected value2.2 Computational probability2.2.1 The physical interpretation of probability2.2.2 Random generation2.2.3 Coding random processes2.2.4 Monte Carlo simulation and expectation2.2.5 Programming probabilistic inference2.3 Data, populations, statistics, and models2.3.1 Probability distributions as models for populations2.3.2 From the observed data to the data generating process2.3.3 Statistical tests for independence2.3.4 Statistical estimation of model parameters2.4 Determinism and subjective probability2.4.1 Determinism2.4.2 Subjective probabilitySummary
Part 2 Building and validating a causal graph
3 Building a causal graphical model
3.1 Introducing the causal DAG3.1.1 Case study: A causal model for transportation3.1.2 Why use a causal DAG?3.1.3 DAGs are useful in communicating and visualizing causal assumptions3.1.4 We have many tools for computing over DAGs3.1.5 Causal DAGs can represent time3.1.6 DAGs link causality to conditional independence3.1.7 DAGs can provide scaffolding for probabilistic ML models3.1.8 Training a model on the causal DAG3.1.9 Different techniques for parameter learning3.1.10 Learning parameters when there are latent variables3.1.11 Inference with a trained causal probabilistic machine learning model3.2 Causal invariance and parameter modularity3.2.1 Independence of mechanism and parameter modularity3.2.2 Causal transfer learning, data fusion, and invariant prediction3.2.3 Fitting parameters with common sense3.3 Your causal question scopes the DAG3.3.1 Selecting variables for inclusion in the DAG3.3.2 Including variables in causal DAGs by their role in inference3.4 Looking ahead: Model testing and combining causal graphs with deep learningSummary
4 Testing the DAG with causal constraints
4.1 How causality induces conditional independence4.1.1 Colliders4.1.2 Abstracting independence with a causal graph4.2 D-separation and conditional independence4.2.1 D-separation: A gateway to simplified causal analysis4.2.2 Examples of d-separating multiple paths4.2.3 D-separation in code4.3 Refuting a causal DAG4.3.1 Revisiting the causal Markov property4.3.2 Refutation using conditional independence tests4.3.3 Some tests are more important than others4.4 Caveats with conditional independence testing4.4.1 Statistical tests always have some chance of error4.4.2 Testing causal DAGs with traditional CI tests is flawed4.4.3 p-values vary with the size of the data4.4.4 The problem of multiple comparisons4.4.5 Conditional independence testing struggles in machine learning settings4.4.6 Final thoughts4.5 Refuting a causal DAG given latent variables4.5.1 An example of a testable implication that works with latent variables4.5.2 Libraries and perspectives on testing functional constraints4.5.3 Testing a functional constraint4.5.4 Final thoughts on testable implications4.6 Primer on (the perils of) causal discovery4.6.1 Approaches to causal discovery4.6.2 Causal discovery, causal faithfulness, and latent variable assumptions4.6.3 Equivalence classes and PDAGs4.6.4 How to think about causal discoverySummary
5 Connecting causality and deep learning
5.1 A causal model of a computer vision problem5.1.1 Leveraging the universal function approximator5.1.2 Causal abstraction and plate models5.2 Training a neural causal model5.2.1 Setting up the training data5.2.2 Setting up the variational autoencoder5.2.3 The training procedure5.2.4 Evaluating training5.2.5 How should we causally interpret Z?5.2.6 Advantages of this causal interpretation5.3 Using causal inference to enhance deep learning5.3.1 Independence of mechanism as an inductive bias5.3.2 Case study: Semi-supervised learning5.3.3 Demystifying deep learning with causalitySummary
Part 3 The causal hierarchy
6 Structural causal models
6.1 From a general causal graphical model to an SCM6.1.1 Forensics case study6.1.2 Converting to an SCM via reparameterization6.1.3 Formalizing the new model6.1.4 A discrete, imperative example of an SCM6.1.5 Why use SCMs?6.1.6 Differences from related approaches6.1.7 Causal determinism and implications to how we model6.2 Equivalence between SCMs6.2.1 Reparameterization is not enough6.2.2 Uniqueness and equivalence of SCMs6.3 Implementing SCMs for rule-based systems6.3.1 Case study: The Monty Hall problem6.3.2 A causal DAG for the Monty Hall problem6.3.3 Implementing Monty Hall as an SCM with pgmpy6.3.4 Exogenous variables in the rule-based system6.3.5 Applications of SCM-modeling of rule-based systems6.4 Training an SCM on data6.4.1 What assignment functions should I choose?6.4.2 How should I model the exogenous variable distributions?6.4.3 Additive models: A popular choice for SCM modeling6.4.4 Linear Gaussian additive model6.4.5 Linear non-Gaussian additive models6.4.6 Nonlinear additive noise models6.4.7 Training additive model SCMs with regression tools6.4.8 Beyond the additive model6.5 Combining SCMs with deep learning6.5.1 Implementing and training an SCM with basic PyTorch6.5.2 Training an SCM with probabilistic PyTorch6.5.3 Neural SCMs and normalizing flowsSummary
7 Interventions and causal effects
7.1 Case studies of interventions7.1.1 Case study: Predicting the weather vs. business performance7.1.2 Case study: Credit fraud detection7.1.3 Case study: Statistical analysis for an online role-playing game7.1.4 From randomized experiments to interventions7.1.5 From observations to experiments7.1.6 From experiments to interventions7.1.7 Recap7.2 The ideal intervention and intervention operator7.2.1 Intervention operators7.2.2 Ideal interventions in structural causal models7.2.3 Graph surgery: The ideal intervention in causal DAGs and causal graphical models7.2.4 Graph surgery and d-separation7.2.5 Ideal interventions and causal Markov kernels7.2.6 Ideal interventions in a causal program7.3 Intervention variables and distributions7.3.1 “Do” and counterfactual notation7.3.2 When causal notation reduces to traditional notation7.3.3 Causal models represent all intervention distributions7.4 Interventions and causal effects7.4.1 Average treatment effects with binary causes7.4.2 Average treatment effect with categorical causes7.4.3 Average treatment effect for continuous causes7.4.4 Conditional average treatment effect7.4.5 Statistical measures of association and causality7.4.6 Causality and regression models7.5 Stochastic interventions7.5.1 Random assignment in an experiment is a stochastic intervention7.5.2 Intervention policies7.6 Practical considerations in modeling interventions7.6.1 Reasoning about interventions that we can’t do in reality7.6.2 Refutation and real-world interventions7.6.3 “No causation without manipulation”7.6.4 Modeling “non-ideal” interventionsSummary
8 Counterfactuals and parallel worlds
8.1 Motivating counterfactual reasoning8.1.1 Online gaming8.1.2 The streaming wars8.1.3 Counterfactuals analysis of machine learning models8.1.4 Regret and why do we care about what “would have happened?”8.1.5 Reinforcement learning and automated decision-making8.1.6 Steps to answering a counterfactual query8.2 Symbolic representation of counterfactuals8.2.1 Hypothetical statements and questions8.2.2 Facts filter hypotheticals to a subpopulation8.2.3 Conditional hypotheticals, interventions, and simulation8.2.4 Counterfactual statements8.2.5 The consistency rule8.2.6 More examples8.3 Binary counterfactuals8.3.1 Probabilities of causation8.3.2 Probabilities of causation and attribution8.3.3 Binary counterfactuals and uplift modeling8.4 Possible worlds and parallel world graphs8.4.1 Potential outcomes in possible worlds8.4.2 The parallel world graph8.4.3 Applying the hypothetical condition via graph surgery8.4.4 Reasoning across more than two possible worlds8.4.5 Rule of thumb: Hypothetical worlds should be simplerSummary
9 The general counterfactual inference algorithm
9.1 Algorithm walkthrough9.1.1 Abduction: Infer the exogenous variables given the observed endogenous variables9.1.2 Action: Implementing the hypothetical causes9.1.3 Prediction: Inferring hypothetical outcomes9.1.4 Counterfactual Monte Carlo9.1.5 Introduction to the case studies9.2 Case study 1: Monty Hall problem9.2.1 Specifying the exogenous variables9.2.2 Specifying the assignment functions for the endogenous variables9.2.3 Building the parallel world graphical model9.2.4 Running the counterfactual inference algorithm9.3 Case study 2: Counterfactual variational inference9.3.1 Building the model9.3.2 Implementing an intervention with pyro.do9.3.3 Implementing the abduction step with variational inference9.3.4 Implementing the action and prediction steps9.4 Case study 3: Counterfactual image generation with a deep generative model9.4.1 The dSprites data9.4.2 Assumptions needed for counterfactual image generationSummary
10 Identification and the causal hierarchy
10.1 The causal hierarchy10.1.1 Where questions and queries fall on the hierarchy10.1.2 Where models and assumptions fall on the hierarchy10.1.3 Where data falls on the hierarchy10.1.4 The causal hierarchy theorem10.2 Identification and the causal inference workflow10.2.1 Defining identification10.2.2 The causal inference workflow10.2.3 Separating identification and estimation10.3 Identification with backdoor adjustment10.3.1 The backdoor adjustment formula10.3.2 Demystifying the back door10.4 Graphical identification with the do-calculus10.4.1 Demystifying the do-calculus10.4.2 Using the do-calculus for backdoor identification10.5 Graphical identification algorithms10.5.1 Case study: The front-door estimand10.5.2 Demystifying the front door10.6 General counterfactual identification10.6.1 The problem with the general algorithm for counterfactual inference10.6.2 Example: Monotonicity and the probabilities of causation10.7 Graphical counterfactual identification10.7.1 Effect of treatment on the treated10.7.2 Identification over the counterfactual graph10.7.3 Counterfactual identification with single-world intervention graphs10.7.4 Identification with SWIGs10.7.5 The single-world assumption10.8 Identification and probabilistic inference10.9 Partial identificationSummary
Part 4 Applications of causal inference
11 Building a causal inference workflow
11.1 Step 1: Select the query11.2 Step 2: Build the model11.3 Step 3: Identify the estimand11.3.1 The backdoor adjustment estimand11.3.2 The instrumental variable estimand11.3.3 The front-door adjustment estimand11.3.4 Choosing estimands and reducing “DAG anxiety”11.3.5 When you don’t have identification11.4 Step 4: Estimate the estimand11.4.1 Linear regression estimation of the backdoor estimand11.4.2 Propensity score estimators of the backdoor estimand11.4.3 Backdoor estimation with machine learning11.4.4 Front-door estimation11.4.5 Instrumental variable methods11.4.6 Comparing and selecting estimators11.5 Step 5: Refutation11.5.1 Data size reduction11.5.2 Adding a dummy confounder11.5.3 Replacing treatment with a dummy11.5.4 Replacing outcome with a dummy outcome11.5.5 Testing robustness to unmodeled confounders11.6 Causal inference with causal generative models11.6.1 Transformations for causal inference11.6.2 Steps for inferring a causal query with a causal generative model11.6.3 Extending inference to estimation11.6.4 A VAE-inspired model for causal inference11.6.5 Setting up posterior inference with SVI11.6.6 Posterior predictive inference of the ATE11.6.7 On the identifiability of the Bayesian causal generative inference11.6.8 Closing thoughts on causal latent variable modelsSummary
12 Causal decisions and reinforcement learning
12.1 A causal primer on decision theory12.1.1 Utility, reward, loss, and cost12.1.2 Uncertainty comes from other causes12.2 Causal decision theory12.2.1 Decisions as a level 2 query12.2.2 Causal characterization of decision rules and policies12.2.3 Causal probabilistic decision-modeling and admissibility12.2.4 The deceptive alignment of argmax values of causal and non-causal expectations12.2.5 Newcomb’s paradox12.2.6 Newcomb’s paradox with a causal model12.2.7 Introspection in causal decision theory12.3 Causal DAGs and sequential decisions12.3.1 Bandit feedback12.3.2 Contextual bandit feedback12.3.3 Delayed feedback12.3.4 Causal queries on a sequential model12.4 Policies as stochastic interventions12.4.1 Examples in sequential decision-making12.4.2 How policies can introduce confounding12.5 Causal reinforcement learning12.5.1 Connecting causality and Markov decision processes12.5.2 The MDP as a causal DAG12.5.3 Partially observable MDPs12.5.4 Policy in an MDP12.5.5 Causal Bellman equation12.6 Counterfactual reasoning for decision-theory12.6.1 Counterfactual policy evaluation12.6.2 Counterfactual regret minimization12.6.3 Making level 3 assumptions in decision problemsSummary
13 Causality and large language models
13.1 LLMs as a causal knowledgebase13.1.1 Building a causal DAG13.1.2 Generating code for DAGs, models, and causal analyses13.1.3 Explanations and mechanism13.1.4 The causal frame problem and AI alignment13.1.5 Understanding and contextualizing causal concepts13.1.6 Formalization of causal queries13.1.7 Beware: LLMs hallucinate13.2 A causality-themed LLM primer13.2.1 A probabilistic ML view of LLMs13.2.2 The attention mechanism13.2.3 From tokens to causal representation13.2.4 Hallucination, attention, and causal identification13.3 Forging your own causal LLM13.3.1 An LLM for script writing13.3.2 Using pretrained models for causal Markov kernels13.3.3 Sampling from the interventional and observational distributions13.3.4 Closing thoughtsSummary
index

Content preview from Causal AI

foreword

Twenty-seven lawyers in the room, anybody know ‘post hoc, ergo propter hoc?’

—President Josiah Bartlett ( The West Wing)

“Post hoc ergo propter hoc” is a logical fallacy regarding causation: “After it, therefore because of it.” The idea dates back at least to Aristotle (the fallacy appears in On Sophistical Refutations). More than two thousand years after Aristotle, Welsh economic theorist Sir Clive Granger inverted “post hoc ergo propter hoc” to provide one of the two principles underlying what is now known as Granger Causality, namely that something cannot cause something if it happened before it.

Humans have been fascinated by the notion of causality—what causes what—since their early recorded writing. Indeed, causal ...

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Causal AI

by Robert Ness

foreword

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