causes and counterfactuals or the subtle wisdom of brainless robots

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CAUSES AND COUNTERFACTUALS OR THE SUBTLE WISDOM OF BRAINLESS ROBOTS

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CAUSES AND COUNTERFACTUALS OR THE SUBTLE WISDOM OF BRAINLESS ROBOTS. ANTIQUITY TO ROBOTICS. “I would rather discover one causal relation than be King of Persia” Democritus (430-380 BC). - PowerPoint PPT Presentation

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Page 1: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

CAUSES ANDCOUNTERFACTUALS

OR

THE SUBTLE WISDOMOF BRAINLESS ROBOTS

Page 2: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

ANTIQUITY TO ROBOTICS

“I would rather discover one causal relation than beKing of Persia”

Democritus (430-380 BC)

Development of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance).

A. Einstein, April 23, 1953

Page 3: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

David Hume (1711–1776)

Page 4: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

HUME’S LEGACYHUME’S LEGACY

1. Analytical vs. empirical claims

2. Causal claims are empirical

3. All empirical claims originate from experience.

Page 5: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

THE TWO RIDDLESTHE TWO RIDDLESOF CAUSATIONOF CAUSATION

What empirical evidence legitimizes a cause-effect connection?

What inferences can be drawn from causal information? and how?

Page 6: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS
Page 7: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

““Easy, man! that hurts!”Easy, man! that hurts!”

The Art ofCausal Mentoring

Page 8: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

1. How should a robot acquire causal information from the environment?

2. How should a robot process causal information received from its creator-programmer?

OLD RIDDLES IN NEW DRESSOLD RIDDLES IN NEW DRESS

Page 9: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

Input:1. “If the grass is wet, then it rained”2. “if we break this bottle, the grass

will get wet”

Output:“If we break this bottle, then it rained”

CAUSATION AS A CAUSATION AS A PROGRAMMER'S NIGHTMAREPROGRAMMER'S NIGHTMARE

Page 10: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

CAUSATION AS ACAUSATION AS APROGRAMMER'S NIGHTMARE PROGRAMMER'S NIGHTMARE

(Cont.) ( Lin, 1995)(Cont.) ( Lin, 1995)

Input:1. A suitcase will open iff both

locks are open.2. The right lock is open

Query:What if we open the left lock?

Output:The right lock might get closed.

Page 11: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

Y = 2X

BRAINLESS FIRST DISCOVERY:PHYSICS DESERVES A NEW ALGEBRA

Had X been 3, Y would be 6.If we raise X to 3, Y would be 6.Must “wipe out” X = 1.

X = 1 Y = 2

The solutionProcess information

Y := 2X

Correct notation:

X = 1

e.g., Length (Y) equals a constant (2) times the weight (X)

Scientific Equations (e.g., Hooke’s Law) are non-algebraic

Page 12: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

MATHEMATICAL EXTRAPOLATION:THE WORLD AS A COLLECTION

OF SPRINGS

Definition: A structural causal model is a 4-tupleV,U, F, P(u), where• V = {V1,...,Vn} are endogeneas variables• U = {U1,...,Um} are background variables• F = {f1,..., fn} are functions determining V,

vi = fi(v, u)• P(u) is a distribution over UP(u) and F induce a distribution P(v) over observable variables

Yuxy e.g.,

Page 13: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

Z

YX

INPUT OUTPUT

FAMILIAR CAUSAL MODELORACLE FOR COUNTERFACTUALS

Page 14: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

)()( uYuY xMx

The Fundamental Equation of Counterfactuals:

BRAINLESS SECOND DISCOVERY:COUNTERFACTUALS ARE EMBARRASINGLY SIMPLE

Definition: The sentence: “Y would be y (in situation u), had X been x,”

denoted Yx(u) = y, means:The solution for Y in a mutilated model Mx, (i.e., the equations

for X replaced by X = x) with input U=u, is equal to y.

Page 15: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

),|(),|'(

)()()|(

')(':'

)(:

yxuPyxyYPN

uPyYPyP

yuxYux

yuxYux

In particular:

)(xdo

BRAINLESS SECOND DISCOVERY:COUNTERFACTUALS ARE EMBARRASINGLY SIMPLE

Definition: The sentence: “Y would be y (in situation u), had X been x,”

denoted Yx(u) = y, means:The solution for Y in a mutilated model Mx, (i.e., the equations

for X replaced by X = x) with input U=u, is equal to y.•

)(),()(,)(:

uPzZyYPzuZyuYu

wxwx

Joint probabilities of counterfactuals:

Page 16: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

Data

Inference

Q(M)(Aspects of M)

Data Generating

Model

M – Invariant strategy (mechanism, recipe, law, protocol) by which Nature assigns values to variables in the analysis.

JointDistribution

THE STRUCTURAL MODELPARADIGM

M

“Think Nature, not experiment!”•

Page 17: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

THE PUZZLE OF COUNTERFACTUAL CONSENSUS

• Indicative: “If Oswald didn’t kill Kennedy, someone else did,”

• Subjunctive: “If Oswald hadn’t killed Kennedy, someone else would have.”

(Adams 1975)

Page 18: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

THE PUZZLING UBIQUITYOF COUNTERFACTUALS

Hume’s Definition of “cause”: We may define a cause to be an object followed by another, and where all the objects, similar to the first, are followed by objects similar to the second, Or, in other words, where, if the first object had not been, the second never had existed (Hume 1748/1958, sec. VII).

Lewis’s Definition of “cause”: “A has caused B” if “B would not have occurred if it were not

for A (Lewis 1986).

• Why not define counterfactuals in terms of causes?(Pearl 2000)

Page 19: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

w

STRUCTURAL AND SIMILARITY-BASED COUNTERFACTUALS

Lewis’s account (1973): The counterfactual “B if it were A” is true in a world w just in case B is true in all the closest A-worlds to w.

B

A

.)( yuY xM

Structural account (1995): “Y would be y if X were x” is true in situation u just in case

Page 20: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

OS

true

false

P (SE) = 1

true

true

true

P (SE) = P (SE)

S1: “IF OSWALD DIDN’T KILL KENNEDY, SOMEONE ELSE DID”

MOS

true

Oswald killed Kennedy

K

MSE

SE OS

true

Prior knowledge

OS

MSE MOS

K

SE

Realizing Oswald did not

kill Kennedy

K

MSE MOS

SE OS

true

false

P (SE)

MOS = true

Page 21: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

K

SE OS

MSE

true

true

After learning Oswald killed

Kennedy

MOSMOS = true

P (SE) = P (SE)

S2: “IF OSWALD HADN’T KILLED KENNEDY, SOMEONE ELSE WOULD HAVE?”

Prior knowledge

K

SE OS

MSE MOS

Oswald refraining from

killing

P (SE)

K

MOS

SE OS

trueMSE

Page 22: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

K

SE OS

true

true

MSE M

OS = true

S2: “IF OSWALD HADN’T KILLED KENNEDY, SOMEONE ELSE WOULD HAVE?”

Prior knowledge

K

SE OS

MSE MOS

Oswald refraining from

killing

After learning Oswald killed

Kennedy

P (SE)

K

MOS

SE OS

trueMSE

P (SE) = P (SE)

false

P (SE) = P (SE)

Page 23: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

BRAINLESS THIRD DISCOVERY:HIGH SCHOOL COUNTERFACTUALS

CAN BE USEFUL

• Solidify and unify (all?) other approaches to causation(e.g., PO, SEM, DA, Prob., SC)

• Demystify enigmatic notions and weed out myths and misconceptions(e.g., ignorability, exogeneity, exchangeability, confounding, mediation, attribution, regret)

• Algorithmitize causal inference tasks (e.g., covariate-selection, identification, c-equivalence, effect-restoration, experimental integration, sufficiency)

• Resolve lingering puzzles

Page 24: CAUSES  AND COUNTERFACTUALS OR THE  SUBTLE  WISDOM OF  BRAINLESS  ROBOTS

CONCLUSIONS

• If Oswald had not used counterfactuals, brainless would have.

• Much of modern thinking is owed to brainless robots.

• I compute, therefore I think.