A Brief Introduction to Causal Inference in Machine Learning (2405.08793v1)

Abstract: This is a lecture note produced for DS-GA 3001.003 "Special Topics in DS - Causal Inference in Machine Learning" at the Center for Data Science, New York University in Spring, 2024. This course was created to target master's and PhD level students with basic background in machine learning but who were not exposed to causal inference or causal reasoning in general previously. In particular, this course focuses on introducing such students to expand their view and knowledge of machine learning to incorporate causal reasoning, as this aspect is at the core of so-called out-of-distribution generalization (or lack thereof.)

• The paper introduces key concepts and techniques that extend traditional correlation analysis to reveal causal relationships.
• It details methodologies like PGMs, SCMs, regression, RCTs, and double machine learning to accurately estimate treatment effects.
• The study demonstrates practical applications in fields such as marketing, healthcare, and policy, enhancing decision-making processes.

Understanding Causal Inference in Machine Learning

What is Causal Inference?

Causal inference is all about figuring out the relationships between causes and outcomes. When working with machine learning models, we often strive to create predictions based on correlations. However, correlations don't necessarily mean one thing causes another. Causal inference steps beyond mere correlation to identify and verify these cause-effect relationships. This is critical, especially when our goal is to make decisions that generalize well beyond our training data.

Core Approaches

Several approaches to causal inference are outlined:

1. Probabilistic Graphical Models (PGMs): These models use vertices/nodes to represent variables and edges to depict dependencies. PGMs bring a structured method to capturing the joint distribution of these variables.
2. Structural Causal Models (SCMs): SCMs pair deterministic functions with external noise to depict how values are generated. This approach clarifies how changing one variable influences another, streamlining counterfactual reasoning.
3. Learning: This process involves training a machine learning model to represent relationships between variables. Typically, this uses probabilistic methods like the maximum likelihood to estimate these relationships accurately.

Causal Quantities of Interest

Average Treatment Effect (ATE):

• ATE measures the expected difference in outcomes between a treated and untreated group. Mathematically, it's captured as:

$$\mathrm{ATE} = \mathbb{E}[y | \mathrm{do}(a=1)] - \mathbb{E}[y | \mathrm{do}(a=0)]$$

Conditional ATE (CATE):

• CATE narrows ATE to subpopulations based on some characteristics. This helps understand treatment effects on specific groups within the data.

Major Techniques in Causal Inference

1. Regression:

- Assumes no unobserved confounders. It regresses the outcome on the action and covariates, effortlessly connecting machine learning methods.

2. Randomized Controlled Trials (RCTs):

- These are often considered the gold standard. RCTs remove confounders by randomly assigning subjects to treatment or control groups. This separation ensures that causal effects can be attributed directly to the treatment.

3. Inverse Probability Weighting (IPW):

- Accounts for situations where treatment assignment isn't random. It weights observations based on the inverse of their probability of receiving treatment, adjusting for confounding variables.

4. Instrumental Variables (IVs):

- When unobserved confounders are present, IVs can help. IVs affect the treatment but not directly the outcome, helping to isolate causal pathways.

Advanced Techniques

Difference-in-Difference:

• Used when you can measure outcomes before and after a treatment. It calculates the treatment effect by comparing the differences in outcomes over time between treated and control groups.

Regression Discontinuity:

• Applies when treatment assignment is based on a cutoff in a continuous variable. This method compares observations near the cutoff to estimate causal effects.

Double Machine Learning:

• Combines machine learning methods with traditional causal inference techniques. This approach can deal with high-dimensional covariates, leveraging the strengths of both fields to reduce bias and variance.

Putting It into Practice

Consider a scenario in which a company wants to evaluate the effectiveness of a new marketing strategy. Here’s how you can walk through it:

1. Defining the Variables:
   • Identify the causes (the marketing strategy) and the outcomes (sales increase).
2. Choosing an Approach:
   • If you have data from a randomized experiment, use RCTs.
   • For observational data with some known confounders, try IPW.
   • In the presence of unobserved confounders, consider using IVs.
3. Analyzing Results:
   • Apply one or more causal inference techniques.
   • Interpret the average treatment effect or conditional average treatment effect.

By following these steps, one can move beyond correlation and gain insights into causal relationships, ultimately making more informed and effective decisions.

Beyond Invariance

The concept of invariance suggests using stable relationships that hold across different environments to infer causality. However, finding these stable features isn't always simple. More flexible approaches tailor the stable feature selection to the specific task, potentially enhancing the robustness of machine learning models.

Conclusion

Understanding and applying causal inference can help improve decision-making processes in various fields, from healthcare to marketing to policy-making. By integrating causal reasoning with machine learning, one can build models that not only predict but also explain and guide better actions in real-world scenarios. Through approaches like regression, RCTs, IPW, and more advanced techniques, we can start uncovering these essential cause-and-effect relationships.