This contains the reference information for the books about causal inference. List of helpful books about causal inference:
1. The Book of Why
2. Causal inference in statistics : A primer
3. Explanation in Causal Inference: Methods for Mediation and Interaction 1st Edition (2015).  Author: VanderWeele, Tyler

Causal Inference Books

This contains the reference information for papers about causal inference. List of helpful papers about causal inference:

- Computer-Aided Experiment Planning toward Causal Discovery in Neuroscience
- Causal inference Based on Counterfactuals
- Illustrating bias due to conditioning on a collider
- Towards Clarifying the Theory of the Deconfounder
- On Geometry of Information Flow for Causal Inference
- Directed Acyclic Graphs and causal thinking in clinical risk prediction modeling
- A Crash Course in Good and Bad Controls
- The Seven Tools of Causal Inference, with Reﬂections on Machine Learning
- Generalizing Experimental Results by Leveraging Knowledge of Mechanisms
- Note on ‘‘Generalizability of Study Results‘‘
- THE LIMITATIONS OF OPAQUE LEARNING MACHINES
- Sensitivity Analysis of Linear Structural Causal Models
- The Environment and Disease: Association or Causation?
- Confounding and Collapsibility in Causal Inference
- Causal Inference-so much more than statistics

Causal Inference Papers

This contains useful videos to help learn about or discuss causal inference. List of causal inference videos: 

Counterfactuals:
https://www.youtube.com/watch?v=9j_HWkrSxzI

Judea Pearl as Keynote speaker on cause and effect:
https://www.youtube.com/watch?v=ZaPV1OSEpHw

Causal Inference Videos

- Causal Inference Books
- Causal Inference Papers

University of Michigan - Ann Arbor

Causal inference refers to making conclusions about finding the reasonings behind the relationship of two or more variables. After coming to some conclusions about statistical data, we ask why such relationships exist between variables.

Causal Inference

A machine passes this test if a human could perceive their interactions with the machine as human, indicating that the machine has successfully emulated human reasoning. 

Turing Test

Causal Inference References

The calculus of causation is formed of:
1. Causal diagrams (the language of knowledge)
2. Causal symbolic language (the language of queries)

The calculus of causation

Organisms, as well as ML, can be divided into 3 levels of causation corresponding to three cognitive abilities: seeing, doing, and imagining.
1. Association
2. Intervention
3. Counterfactuals


Ladder of Causation 

Bayes Theorem is about predicting the probability of an event A occurring given an event B has already occurred. We can use the inverse probability of this statment and the probability of each event to find this value. 
P(A) is called prior probability, P(B|A) is Likelihood, P(B) is evidence, and P(A|B) is posterior probability.


Bayes Theorem Overview

Most of the statistical methods are entirely objective, which means reasoning exclusively from data and experiments. But causal analysis and Bayesian analysis are different in that they involves some subjectivity.

Causal analysis requires some subjective commitments based on one's knowledge in the field before the causal digram is drawn and data is explored.

Similarly, Bayesian analysis combines objective evidence with the prior subjective belief.

From objectivity to subjectivity

Both Induction and Deduction are necessary within casual inference because they are two ways of approaching a problem and often go hand in hand. Induction goes from evidence -> hypothesis while deduction works in the forward direction; cause (hypothesis) -> effect (theory, conclusion). Artificial Intelligence has started automating Induction and Deduction, an example is Bayesian networks. 

Stages of Casual Inference: Induction and Deduction

Logical reasoning is the process of using a rational, systematic series of steps based on sound certain mathematical procedures and statements to arrive at a conclusion. 

There are three types of the reasoning:
- Abductive Reasoning 
- Deductive Reasoning 
- Inductive Reasoning

Reasoning

Hill's Criteria is a collection of nine informal guidelines ("viewpoints" as supposed to requirements) used to determine whether a causal relationship exists within an observed association.  Initially, five out of the nine viewpoints were proposed by the surgeon general's advisory committee, to which Bradford Hill later added four more.  Hill's Criteria is not meant to be the necessary conditions to support or refute a cause-and-effect hypothesis.  The debate over the causality between cigarette and lung cancer prompted the criteria, which were used for the proponent of the causal relationship to justify their claim that cigarette smoking is indeed causally related to lung cancer.  

Hill's Criteria

1. necessary causation (but-for causation)
2. sufficient causation
3. necessary-and-sufficient causation

Three different kinds of causation

1. The Law of Counterfactuals
2. The Law of Conditional Independence

The Two Fundamental Laws of Causal Inference

A Randomized Controlled Trial (RCT) or a Controlled Experiment is a method to eliminate unmeasurable confounders effect on causal inference by implementing an intervention on a randomly selected group of individuals (treatment/intervened group) while keeping other individuals unchanged (controlled group, placebo, not-intervened group) to observe the changes in outcomes due to the intervention effect. The RCTs are intended to "disarm" confounders (confounding variables).

Randomized Controlled Trial (RCT) = Controlled Experiment

List of techniques that help solve intractable inference problems in machine learning that usually arise from interactions between latent variables in a structured graphical model.

-Expectation Maximization

-MAP Inference and Sparse Coding

-Variational Inference and Learning

-Learned Approximate Inference



Approximate Inference 

"The estimand is the target quantity—the purpose of the statistical analysis ... the thing we are estimating" " that connects statistical evidence to theory."

It refers "to both the theoretical and the empirical estimands."

Estimand

1- "Set a **theoretical estimand**, clearly connecting this quantity to theory"

2- "Link to an **empirical estimand**, which is informative about the theoretical estimand under some identification assumptions"

3- Use "an **estimation strategy** to learn the empirical estimand (e.g., a regression model) ... from data."

Three Critical Choices in Causal Inference

- Correlation does not imply causation.
- Causation does not imply correlation either.

Correlation vs. Causation

Establishing causality in economics is a significant challenge for two main reasons. First, unlike in many natural sciences, it is often impossible to conduct controlled experiments to isolate a single variable. The economy is a dynamic system where numerous factors change simultaneously, creating confounding variables that can lead to misleading correlations. Second, the economy's fundamental complexity, arising from the interactions of millions of people, makes it impossible to measure and understand every variable. This inherent complexity means economists must be skeptical of simple claims that one complex phenomenon, like capitalism, is the direct cause of another, such as a rise in living standards. To address these challenges, economists use methods like natural experiments and advanced statistical techniques to infer causal relationships from observational data.

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