L10: Causality Flashcards
Factorise problem on slides 6-8?
Yes?
Marginalise problem on slides 10-13?
Yes?
Definition of causal inference?
X causes Y if and only if changing X leads to a change in (the distribution of) Y, keeping all else constant.
Existence of causal effect
X has a causal effect on Y if there are values a and b for X such that p(Y |do(X = a)) not equal to p(Y |do(X = b))
What is the danger of observational studies?
Can mistake correlation for causation. Need to try to control for confounders and compare similar subgroups (usually still not enough for a causal discovery in general)
What is Simpson’s Paradox?
Simpson’s paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combine
Definition causal effect
The causal effect is the magnitude by which Y is changed by a (unit) change in X.
What is the interventionist approach to causality?
Taking an action while keeping other relevant factors constant.
Describe counterfactual thinking
From time t − 1 to time t, we decide to change from Y_old to Y_new .
* Yold and Ynew represent two options that we are investigating about which one is best – they are not related to time.
* What would have happened
had we not done what we did?
* Estimating the effect
of the intervention:
* Naive: E[Ynew (t)] − E[Yold (t − 1)]
* Causal: E[Ynew (t)] − E[Yold (t)] (compare the effect of both options at the same time against each other)
Describe the three methods for answering causal questions and some examples
- Randomization (harder but most valid)
* A/B test
* Multi-armed bandits - Natural Experiments (intermediate)
* Regression discontinuity
* Instrumental Variables - Conditioning (easy but less valid)
* Stratification
* Matching
Difference between internal and external validity
Internal validity
Validity of conclusions drawn within context of particular study
External validity
Generalizability of empirical findings to new environments, settings or populations
Give examples of do-operations
Do-operation on switch S = on:
“glue the switch in the position on”.
Do-operation on B = bright:
“short-cut the electrical circuit
such that there is always light”.
p(Y = 1|do(X = 1)):
probability of re-arrest if program were compulsory for all prisoners
Note that generally p(Y = 1|X = 1) not equal to p(Y = 1|do(X = 1)).
Definition of Causal Bayesian Network
A Causal Bayesian Network is a tuple (G,P(· | ·)) where
* G is a DAG with vertices X1, . . . , Xn, and
* P(· | ·) is a family of conditional probability tables.
The model encodes the PMF p(X1, . . . , Xn) = Product of P(Xi| pa(Xi))
AND
For any subset W of V = {1, . . . , n} and joint configuration xW = {Xj = xj
: j ∈ W },
we have (truncated factorisation formula)
p(X1, . . . , Xn|do(xW )) = Y
i∈V \W
P(Xi
| pa(Xi)) ·
Y
j∈W
I(Xj = xj)
Describe the Bayesian Networks for slide 59 and whether the causal Bayesian networks are the same
Yes?
Write down the formula after the intervention on X2 in slide 61-62
Yes?
Describe the formulas for causal effect
Total average causal effect (ACE) of X = a with respect to X = b on Y is
ACE(a, b) = E(Y |do(X = a)) − E(Y |do(X = b))
The amount of causal effect (CE) of X = a with respect to X = b on Y = y is
CE(a, b, y) = p(Y = y|do(X = a)) − p(Y = y|do(X = b))
