conterfactuals srini narayanan icsi ntl meeting 10/30/2009

Conterfactuals

Srini Narayanan

ICSI NTL Meeting

10/30/2009

Alterations to reality If Ted Kennedy were alive, universal health care would

have an unshakable champion. If only we had left earlier, we would have avoided the

traffic. He almost made it to the track on time. I hope we find a gas station soon. He never would have made it without my help. If only I had ten dollars more, I could have bought that

shirt. If this had been an actual emergency, the signal you

just heard would have been followed by official information, news or instructions.

Counterfactuals

Counterfactuals are mental simulations of “variations on a theme”. They refer to imagined alternatives to something

that has actually occurred.

Basic to human cognition ubiquitous in commonsense reasoning as well as

in formalized discourse.

They play a significant role in other cognitive processes such as conceptual learning, planning, decision making,

social cognition, mood adjustment, and performance improvement.

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Computational treatments of counterfactuals

Material implication doesn’t workP => Q = ~P or QCostello and McCarthy (circumscription)Ginsburg (minimal worlds)

Structural equation semanticsGraphical Interventions (Pearl) vs. ObservationThe calculus of do(x)

Basic point: Structural theories must be enhanced by content to capture the richness of human counterfactual reasoning.

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Activation of counterfactuals(Markaman, Roese, Medvec, Bryne)

Behavior regulationMake salient a relationship between

resources, actions, and outcomes.Upward vs. downward counterfactuals.

Affect regulationContrast effects

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Minimal rewrite rule

Tetlock and Belkin (1996), Kahneman and Miller (Norm theory)

Small, minor changes to reality are acceptable, whereas bigger changes may be less so. Regrets with which people chastise themselves also

follow this minimal rewrite rule (Roese and Sommerville, 2005).

People typically focus on just one action to alter within the counterfactual. All other aspects of reality remain within the counterfactual exactly as they truly are.

Alternative histories:Few key differences between the story’s setting and

reality, framed by innumerable similarities, such as the laws of physics and basic characteristics of human nature.

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Summary of background research on counterfactual content

Counterfactuals manipulate the connection between actions, outcomes and goals (desired outcomes).

A proper understanding of counterfactual processes thus depends on a model of (the relationship between) goals, actions, and their outcomes.

Basic Assumption

Proposition 1. Counterfactuals exploit rich shared structure of human event and action representation. Encoding this structure provides the

basis for generating and simulating the effect of counterfactual reasoning.

The minimal rewrite rule pertains to locality in the space of actions and events

Preconditions, resources, fine control structure are important aspects of events

Active representations Many inferences about actions derive from what we

know about executing them X-net representation based on stochastic Petri nets

captures dynamic, parameterized nature of actions Used for acting, recognition, planning, and language

Walking:bound to a specific walker with a

direction or goalconsumes resources (e.g., energy)may have termination condition

(e.g., walker at goal) ongoing, iterative action

walker=Harry

goal=home

energy

walker at goal

Basic Features

Fine grained model of actions and eventsInterruption, hierarchy, concurrency,

synchronization, iteration

Models resources, preconditions, state changes

Active representationFeedback loops

Forward and backwardExtensions allow hybrid system models

States are DBN

Dynamic Bayesian Networks (D(T)BNs) are an extension of Bayesian networks for modeling dynamic systems. In a DBN, the state at time t is represented by a

set of random variables. The state at time t is dependent on the states at previous time steps.

Typically, we assume that each state only depends on the immediately preceding state (first-order Markovian), and thus we need to represent the transition distribution P(Zt+1 | Zt).

This can be done using a two-time-slice Bayesian network fragment (2-TBN) Bt+1, variables from Zt+1 whose parents are variables

from Zt and/or Zt+1, and variables from Zt without any parents.

Typically, we also assume that the process is stationary, i.e., the transition models for all time slices are identical:

A coordinated Model of Actions and events

Graphical Model A factorized probabilistic model of state

Based on Probabilistic Relational ModelsA fine grained model of events

Based on Stochastic Petri NetsModels primitives for concurrency, sequence, choice,

stochasticity, iteration, conditionals, synchronization.Partial order true concurrency semantics

CPRM combines PRM based state representation with coordinated actions.

CPRM inference Filtering

P(X_t | o_1…t,X_1…t) Update the state based on the observation sequence

and state set MAP Estimation

Argmaxh1…hnP(X_t | o_1…t, X_1…t) Return the best assignment of values to the hypothesis

variables given the observation and states Smoothing

P(X_t-k | o_1…t, X_1…t) modify assumptions about previous states, given

observation sequence and state set Projection/Prediction/Reachability

P(X_t+k | o_1..t, X_1..t)

Counterfactual generation

Principle 1. People imagine two possibilities when they generate counterfactuals. One possibility corresponds to the actual world and the

second corresponds to a variant of the actual world. This principle is adapted from (Bryne 2005)).

• Principle 2. The fine grained structure and evolution of events and actions includes multiple possibilities or branching points for counterfactuals. These branching points are likely candidates for generating

variants or changes to reality. Resources, preconditions, goals are all local to the action and

are altered in the generation of counterfactuals

Resource alterations

If I had more money, I could have gone to the game. (consumption)

If I had more energy, I could have completed the marathon. (consumption)

If you had reserved the room, you could have held the meeting here. (lock-release)

If we could produce more power, we could meet demands. (produce)

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Remove resource

Remove preconditi

on

Add resource

Add preconditi

on

Preconditions

If only I had not opened the gate, the dog would not have run out.

If only you had not dropped the banana peel, the old man would not have fallen.

If only I had fixed the lamp, there would have been more light.

If only I had removed the vase, it would not have been toppled.

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Resources

Shared responsibilityEach person in a group supplies a little

bit of poison to an individualFiring squad

Consumption/Production over timeEach day the food is poisoned

(accumulation)

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Alternative choice points

Bryne (2005) points of initiation as a choice point (action versus inaction)If the talks had continued, we would have

reached an agreement. (suspended and not resumed)

If we had stopped talking, we would have been able to listen. (action not suspended)

If we had canceled the game, we could have avoided getting wet. (action not canceled)

If the intifada had not restarted, peace talks would have continued. (one action interrupts another).

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Choice points and presuppositions

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Event 1: Intifada restarts

Start Ongoing Finish

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Event 1: Peace talks suspended

Temporal Order

(Bryne 2005) and colleagues have performed experiments suggesting a recency effect in counterfactual generation. Their test scenario involved imagining two individuals

who are in a game show. They are asked to pick a square which contains a blue or

red colored sports car. If they both pick the same color (red or blue), they each get to keep the car they picked. If they chose different colors, they don’t get anything.

Now suppose, the first person, John chose red. Then Jack, the second chooses blue.

When asked to complete the sentence, “The players would have won if only ...”, most people tended to say

The players would have won if only Jack had picked a red car’, even though the choices for John were equally likely.

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Simulation Local in the simulation space to pick the most recent

Undoing the most recent action is local in simulation

Defeasible due to other conditions Salient resources, sub-goals, salient preconditions

For instance, in the case where you go camping and stay an extra day you didn’t plan for, the initial resource of not having extra food or water (which

may be the usual practice) may be a more likely source of counterfactuals.

If only I had the usual extra food) than the most recent action (If only we hadn’t decided to stay longer).

Suggests many experiments of the trade-offs involved

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Semifactives-Even-if

Even if we had stayed together then, we would have broken up by now.

Even if I had taken the higher paying job, I would not have been able to afford the house.

Even if it had been sunny, the game would have been canceled.

Even if it had stopped raining, the levee would have collapsed.

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90

80

80

80

50

60

80

80

Even if I had loaned you $10, you couldn’t have bought the ticket.

Even if you had loaned me $10, you still could have bought the ticket

Concessive conditionals

(Dancygier & Sweetser 2005)

The would vote for him even if he were a criminal.

The concessive conditional above sets up an atypical situation in which the normal expectation is violated and an unusual situation is asserted where the people still vote for the criminal candidate.

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Voting.enable

Even-if network

vote

criminal(x)

vote

Default

elected(x)

criminal(x)

elected(x)

other causes NOISY-OR

Model of concessives Concessive conditions often highlight the relative

importance of canonically (in the default situation) non-salient factors for an outcome. In the example above, this could be the background of the

candidate, his past deeds, ethnicity or any number of other factors that could override the fact that he has committed a crime.

Concessive conditionals specify the extreme case of the specific value of the changed parameter that still maintains the outcome. Thus the conditional holds not just for the situation described

but for a whole range of situations which are less likely to change the outcome than the one described.

How useful is the NOISY-OR (exception independence) combination?

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Counterfactual Evaluation

Model includes the state model and event model To evaluate “what would the value of Y be if X

were a, given that X is b. Y and X could be events transitions or state

variables Algorithm

Assert X is b (fire a transition or do(X=b)) on the PRM Propagate to the Context (background) (P(Context |

X=b) Assert “X* is a” in the counterfactual network Use temporal projection to compute the value of Y.

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NYT, Sept 18, 2009 Context:

American diplomats were unable on Friday to bridge gaps between Israel and the Palestinians onrestarting peace talks, meaning that while their leaders will likely meet with President Obama next week at the United Nations General Assembly, they will not announce a renewal of negotiations, officials on all sides said.

Sentence 1: The goal of the meetings this week was to produce conditions for a summit

meeting in New York, led by Mr. Obama, at which Prime Minister Benjamin Netanyahu of Israel and President Abbas would say they were starting peace talks again.

Sentence 2: Mr. Erekat and others said there were two sets of problems, the first having to

do with the length and extent of an Israeli settlement freeze in the West Bank and Jerusalem, and the second having to do with the basis for the negotiations themselves. Mr. Erekat said that without a freeze in advance, negotiations were pointless.

Sentence 3: Mr. Mitchell also met twice on Friday with Mr. Netanyahu. An aide to Mr.

Netanyahu said only that the prime minister would leave for New York as planned onWednesday and that Israel was willing to restart negotiations immediately, so the difficulty lay not with Israel but with the Palestinians.

Sentence 4: The Americans and Palestinians have been pushing Israel to agree to freeze

settlement building entirely as evidence of its seriousness about peace talks. The settlements are on land that the Palestinians wantfor their future state. But Mr. Netanyahu has declined to do so, saying that he would be willing to reduce orslow building, but not freeze it, because he would not turn his back on Israelis living there.

Events modeled

Context: Peace talks suspendedEvent 1: Preparatory meeting (week of Sept

18)Event 2: Talks between Israel and Palestine

(Context.status)Event 2 depends on both parties agreeing to talk.

Facts/Evidence: Meeting failed, Talks remain suspended, Israel will not freeze settlements

US role can be modeled but is not in the current version.

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Event 1: Meeting This week


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Produce resource: conditions for restarting talks

Part 1 = Palestine Part 2 = Israel

Agree(P, T)

Agree(I, T)

If Israel had agreed to freeze settlements, the peace talks could restart in New York this week

If the meeting had succeeded, talks could restart in New York this week

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Done

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Done

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Succeed



Agree(P, T)

Agree(I, T)


F(I,S)

A(P, T) A(I, T)

Precond(T)


F(I,S)

A(P, T) A(I, T)

Precond(T)

ACTUAL SPACE COUNTERFACTUAL SPACE

BACKGROUND: SUSPENDED(PT)

Evaluation Algorithm

If Israel had frozen settlements, the peace talks could have resumed in New York.

Running the algorithm on the dual networkDo ~I(F,S) Propagate evidence to the backgroundDo I*(F,S)Compute P(Precond*(T))Run X-net with new value of Precond*(T).

Return X-net state.

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F(I,S)

A(P, T) A(I, T)

Precond(T)


F(I,S)

A(P, T) A(I, T)

Precond(T)

ACTUAL SPACE COUNTERFACTUAL SPACE

BACKGROUND: SUSPENDED(PT)

Assert Evidence do(~F(I,S)) Assert Evidence F*(I,S)

Propagate Evidence to Background

Compute P(Precond(T))



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Agree(P, T)

Agree(I, T)

Precondition (T) holds



Done

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Agree(P, T)

Agree(I, T)


Restart Talks



Done

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Succeed



Agree(P, T)

Agree(I, T)


Restart Talks

Talks ready

Evaluation Algorithm

If the meeting had succeeded, talks could restart in New York this week

Running the algorithm on the dual networkAssert Evidence: Do Fire FailPropagate evidence to the background contextP(talks=suspended | Fail)Assert counterfactual (Fire Succeed)Run X-net with new value of Precond*(T).

Return X-net state.

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Done

Canceled

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Ready

PrepareEnabled

Restart Suspended

Stop Stopped

Suspend

Iterate

Resume

Fail Failed

Enable Disable


Done

Canceled

Cancel

Ready

PrepareEnabled

Restart Suspended

Stop Stopped

Suspend

Iterate

Resume

Undo Undone

Enable Disable


Succeed



Agree(P, T)

Agree(I, T)



Done

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Ready

PrepareEnabled

Restart Suspended

Stop Stopped

Suspend

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Fail Failed

Enable Disable


Done

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Ready

PrepareEnabled

Restart Suspended

Stop Stopped

Suspend

Iterate

Resume

Undo Undone

Enable Disable


Succeed



Agree(P, T)

Agree(I, T)


Restart Talks

Talks ready

Conclusion

Counterfactuals depend on The relationship between actions, outcomes

and goalsThe fine-grained structure of events and actionsResources, control, and complex interactions

between events and stateInterventions on both events and state (Pearl

2000)

The CPRM framework provides a computationally adequate framework.

Biological implications (in reading).

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Metaphoric Counterfacuals

If Israel had turned around on the settlement issue, Abbas would have moved forward on the peace talks.

Basic Features

Control and responsibility Control of an action implies

Adequate state information (world and agent) For action selection and effect evaluation

Have resources Ways of acquiring it

Preconditions Ways of setting it.

Have resources and preconditions to choose at branch points

Control + execution interacts with responsibility To claim responsibility

find the minimal, relevant action under my control that I performed that changed the outcome

To claim that I am not responsible find the minimal action not under my control that changes the

outcome.

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Control and responsibility Control of an action implies

Adequate state information (world and agent) For action selection and effect evaluation

Have resources Ways of acquiring it

Preconditions Ways of setting it.

Have resources and preconditions to choose at branch points

Control + execution interacts with responsibility To claim responsibility

find the minimal, relevant action under my control that I performed that changed the outcome

To claim that I am not responsible find the minimal action not under my control that changes the

outcome.

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Counterfactual probes

Find the minimal perturbations that could disambiguate hypotheses about a partially observable system (diagnostic probes)

Find the minimal changes to change the outcome (influence probe)

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Probe AnalysisSystem Design (Steve Sinha)

Coordination links between path segments

Ongoing segment N-19 is 24% complete

Completed segments (S4 has completed)

segment S-5 is ready to start

history

Infer

Current resource loading

Inputs: Resource values for each

segment Simulation:

X-net model simulates the progress of every pathway segment over time

Decision making: Selects best (least cost)

alternate pathway dynamically for blocked pathways

Outputs Degree of completion of every

path segment Status of every path segment

Inputs: Resource values for each

segment Simulation:

X-net model simulates the progress of every pathway segment over time

Decision making: Selects best (least cost)

alternate pathway dynamically for blocked pathways

Outputs Degree of completion of every

path segment Status of every path segment

ICSI System

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Desired Simulated Outcome

Blocked resources result in delays in the program and reallocation of resources to different pathway segments.

Manifests as delays in completion of pathway segments and changes to completion rates

Segment Delay

Change in Rate

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Demonstrated Results

In system demonstration, different probes yield different results Block resources to a segment in both hypotheses early

in the business development Block resources to a segment only money laundering

hypothesis midway through the business development Complex Probe:

Combination of both actions at the appropriate time

Garbage Disposal Segs

Garbage Disposal Segs

Money Laundering Front

Garbage Disposal Hyp

LecturesI. Overview2. Simulation Semantics3. ECG and Best-fit Analysis4. Compositionality5. Simulation, Counterfactuals, and Inference

Constructions

Simulation

Utterance Discourse & Situational Context

Semantic Specification:image schemas, bindings,

action schemas

Analyzer:

incremental,competition-based,

psychologically plausible

X-net Extensions to Petri Nets Parameterization

x-schemas take parameter values (speed, force) Walk(speed = slow, destination = store1)

Dynamic Binding X-schemas allow run-time binding to different

objects/entities Grasp(cup1), push(cart1)

Hierarchical control and durative transitions Walk is composed of steps which are composed

of stance and swing phases

Stochasticity and Inhibition Uncertainties in world evolution and in action

selection Factorized state

Resources and actions

conterfactuals srini narayanan icsi ntl meeting 10/30/2009

Documents

downward counterfactuals

human cognition basic

human cognition ubiquitous

structural theories

q costello

social cognition

commonsense reasoning

basic point