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Merge pull request #8 from daimpi/wip-computation-performance
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Wip computation performance
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daimpi authored May 14, 2017
2 parents 6fd56a7 + cbfa7e0 commit fd1911f
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4 changes: 2 additions & 2 deletions README.md
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Expand Up @@ -18,10 +18,10 @@ B/c the normal distribution is a continuous distribution the outcome is rounded

## Variables

Default-values have been set to mirror Zollman's (2010) model. The slider ranges are mostly set to mirror the ranges considered by Rosenstock et al. (2016). The exceptions are:
Default-values have been set to mirror Zollman's (2010) model. The slider ranges are mostly set to mirror the ranges considered by Rosenstock et al. (2016) ( pulls correspond to `n` in Rosenstock et al.(2016)). The exceptions are:

* The signal ranges have a larger interval
* The pulls range doesn't start at 1 but at 100 because of the normal approximation potentially not being accurate enough for low numbers of pulls. ( pulls correspond to `n` in Rosenstock et al.(2016))


### Globals

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150 changes: 55 additions & 95 deletions SocNetABM.nlogo
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@@ -1,10 +1,11 @@
turtles-own [a b theory-jump times-jumped cur-best-th current-theory-info
mytheory successes subj-th-i-signal crit-interact-lock confidence]
mytheory successes subj-th-i-signal crit-interact-lock confidence
avg-neighbor-signal]

globals [th-i-signal indiff-count crit-interactions-th1 crit-interactions-th2
confidence-cutoff converged-ticks last-converged-th max-confidence
confidence-cutoff converged-ticks last-converged-th
max-ticks converge-reporters converge-reporters-values
run-start-scientists-save rndseed]
run-start-scientists-save rndseed g-confidence g-depressed-confidence]

__includes ["protocol.nls"]

Expand All @@ -27,12 +28,11 @@ to setup [rs]
let a2 init-ab
let b2 init-ab
set a list a1 a2
; b contains the denominator of the mean of the beta distribution (i.e.
; alpha + beta): the first (second) entry is the denominator for
; b contains the denominator of the mean of the beta distribution (i.e.
; alpha + beta): the first (second) entry is the denominator for
; theory 1 (2).
set b (list (a1 + b1) (a2 + b2))
set current-theory-info [0 0]
; calculate the prior (i.e. mean of the beta distribution) from the random
; calculate the prior (i.e. mean of the beta distribution) from the random
; alphas / betas.
calc-posterior
compute-strategies
Expand Down Expand Up @@ -92,8 +92,7 @@ end

; initializes the hidden variables (= not set in the interface)
to init-hidden-variables
set confidence-cutoff 10 ^ 4
set max-confidence 10 ^ 5
set confidence-cutoff 1 - (1 / 10 ^ 4)
set max-ticks 10000
end

Expand Down Expand Up @@ -186,6 +185,15 @@ end



; reports a draw from the binomial distribution with n pulls and probability p
to-report binomial [n p]
report length filter [ ?1 -> ?1 < p ] n-values n [random-float 1]
end





; Researchers pull from their respective slot machine:
; the binomial distribution is approximated by the normal distribution with
; the same mean and variance. This approximation is highly accurate for all
Expand All @@ -197,6 +205,7 @@ end
to pull
let mysignal item mytheory subj-th-i-signal
set successes [0 0]
ifelse pulls > 100 [
let successes-normal round random-normal
(pulls * mysignal) sqrt (pulls * mysignal * (1 - mysignal) )
ifelse successes-normal > 0 and successes-normal <= pulls [
Expand All @@ -206,6 +215,10 @@ to pull
set successes replace-item mytheory successes pulls
]
]
][
let successes-binomial binomial pulls mysignal
set successes replace-item mytheory successes successes-binomial
]
end


Expand All @@ -223,7 +236,7 @@ end



; the sharing of information between researchers optionally including
; the sharing of information between researchers optionally including
; critical-interaction
to share
let cur-turtle self
Expand All @@ -234,7 +247,7 @@ to share
ask link-neighbors [
ifelse mytheory = cur-turtle-th or not critical-interaction [
set successvec (map + successvec successes)
set pullcounter replace-item mytheory pullcounter
set pullcounter replace-item mytheory pullcounter
(item mytheory pullcounter + pulls)
][
let other-successes successes
Expand All @@ -243,7 +256,7 @@ to share
if other-success-ratio > item mytheory [current-theory-info] of
cur-turtle [
ask cur-turtle [
evaluate-critically
evaluate-critically
]
]
ask cur-turtle [
Expand All @@ -262,7 +275,7 @@ end


; If researchers communicate with researchers from another theory they might
; interact critically
; interact critically
to evaluate-critically
let actual-prob-suc 0
ifelse mytheory = 0 [
Expand All @@ -283,7 +296,7 @@ end



; calculates from a given a (= alpha) and b (= alpha + beta) the belief of a
; calculates from a given a (= alpha) and b (= alpha + beta) the belief of a
; researcher i.e. the mean of the beta distribution
to calc-posterior
set current-theory-info (map / a b)
Expand Down Expand Up @@ -335,74 +348,6 @@ to set-researcher-colors
set color turquoise
]
end





; Calculates how confident the researcher is in the fact that her current best
; theory is actually the best theory (i.e. how unlikely it is that she will
; change her mind). This calculation only makes sense in case researchers have
; converged.
to calc-confidence
let worst-signal [item mytheory subj-th-i-signal] of min-one-of turtles [
item mytheory subj-th-i-signal]
ask turtles [
let belief-to-beat item ((mytheory + 1) mod 2) current-theory-info
* strategy-threshold
let cur-theory mytheory
let avg-neighbor-signal mean [item cur-theory subj-th-i-signal] of
(turtle-set link-neighbors self)
; if the scientist would be given sufficient time for her belief to
; converge to the average signal of her and her link-neighbors, would
; this be enough for her to abandon her current theory? If so, she's not
; confident enough.
if avg-neighbor-signal <= belief-to-beat [
set confidence 0
stop
]
; the following calculations are based on probability maximization of the
; normal-distribution. This is separately documented at [placeholder].
let alpha item mytheory a
let varepsilon avg-neighbor-signal - belief-to-beat
let delta item mytheory current-theory-info - belief-to-beat
if (2 * alpha - 1) * delta <= belief-to-beat [
set confidence 0
stop
]
let exit-probability 0.5 + 0.5 * erf (
((0 - 2 * alpha + 1) * delta + belief-to-beat)
/ (sqrt((0 - 2 * alpha * delta + delta + belief-to-beat)
* (belief-to-beat + varepsilon) * (0 - 1 + belief-to-beat + varepsilon)
/ (varepsilon * (belief-to-beat + delta)))
* (belief-to-beat + delta)))
ifelse exit-probability > 0 [
set confidence 1 / exit-probability
if confidence > max-confidence [
set confidence max-confidence
]
][
set confidence max-confidence
]
]
end





; reports a numerical approximation for the error-function function on its
; negative domain, therefore the argument (x) must be smaller than 0. For
; sources see infotab.
to-report erf [x]
let t (1 - .5 * x)
report exp ( 0 - x ^ 2 - 1.26551223 + 1.00002368 / t
+ .37409196 / t ^ 2 + 0.09678418 / t ^ 3
- .18628806 / t ^ 4 + .27886807 / t ^ 5
- 1.13520398 / t ^ 6 + 1.48851587 / t ^ 7
- .82215223 / t ^ 8 + .17087277 / t ^ 9)
/ t - 1
end
@#$#@#$#@
GRAPHICS-WINDOW
210
Expand Down Expand Up @@ -468,10 +413,10 @@ SLIDER
288
pulls
pulls
100
1
6000
1000.0
100
1
1
NIL
HORIZONTAL
Expand Down Expand Up @@ -678,10 +623,10 @@ B/c the normal distribution is a continuous distribution the outcome is rounded

## Variables

Default-values have been set to mirror Zollman's (2010) model. The slider ranges are mostly set to mirror the ranges considered by Rosenstock et al. (2016). The exceptions are:
Default-values have been set to mirror Zollman's (2010) model. The slider ranges are mostly set to mirror the ranges considered by Rosenstock et al. (2016) ( pulls correspond to `n` in Rosenstock et al.(2016)). The exceptions are:

* The signal ranges have a larger interval
* The pulls range doesn't start at 1 but at 100 because of the normal approximation potentially not being accurate enough for low numbers of pulls. ( pulls correspond to `n` in Rosenstock et al.(2016))


### Globals

Expand Down Expand Up @@ -709,9 +654,10 @@ The sum of critical interactions scientists on theory 1(2) encountered.
#### confidence-cutoff

* type: integer
* example: 10000
* example: 0.9999

The global-confidence `g-confidence` must be higher than this value for the run to be terminated.

A hidden variable: the confidence that the least confident scientist has to reach before the run is terminated.

#### converged-ticks

Expand All @@ -727,13 +673,6 @@ The number of ticks which have passed since the researchers converged for the la

The theory the researchers converged on the last time they converged: 0 = th1, 1 = th2

#### max-confidence

* type: integer
* example: 100000

A hidden variable: the maximal confidence a researcher can reach.

#### max-ticks

* type: integer
Expand Down Expand Up @@ -769,6 +708,20 @@ The number of scientists on [th1 th2] at the beginning of the run.

Stores the random-seed of the current run.

#### g-confidence

* format: float
* example: 0.9993

Global-confidence: the probability that not a single researcher will switch theories i.e. the probability that this convergence is final. Range: [0,1]

#### g-depressed-confidence

* format: boolean
* example: false

If there is a researcher for whom, if given sufficient time for her belief to converge to the average signal of her and her link-neighbors, this would this be enough to abandon her current theory, her confidence will always be zero and therefore `g-confidence` will also be zero. In this case `g-depressed-confidence` will be set to true in order to avoid redundant confidence calculations.


### Turtles-own

Expand Down Expand Up @@ -848,6 +801,13 @@ For how many more rounds the researcher is blocked from pursuing strategies (i.e

How confident the researcher is in the fact that her current best theory is actually the best theory (i.e. how unlikely it is that she will change her mind). Only calculated once all researchers have converged to one theory.

#### avg-neighbor-signal

* type: float
* example: 0.499

Only set once all researchers converged. This is the average signal the researcher and her link-neighbors currently observe for the theory they converged on.


## CREDITS AND REFERENCES

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83 changes: 81 additions & 2 deletions protocol.nls
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Expand Up @@ -62,6 +62,85 @@ end



; Calculates how confident the researcher is in the fact that her current best
; theory is actually the best theory (i.e. how unlikely it is that she will
; change her mind). This calculation only makes sense in case researchers have
; converged.
to calc-confidence
if converged-ticks = 0 [
set g-depressed-confidence false
]
if g-depressed-confidence [stop]
let stop? false
ask turtles [
if stop? [stop]
let belief-to-beat item ((mytheory + 1) mod 2) current-theory-info
* strategy-threshold
let cur-theory mytheory
if converged-ticks = 0 [
set avg-neighbor-signal mean [item cur-theory subj-th-i-signal] of
(turtle-set link-neighbors self)
]
; if the scientist would be given sufficient time for her belief to
; converge to the average signal of her and her link-neighbors, would
; this be enough for her to abandon her current theory? If so, she's not
; confident enough.
if avg-neighbor-signal <= belief-to-beat [
set confidence 0
set stop? true
set g-depressed-confidence true
stop
]
; the following calculations are based on probability maximization of the
; normal-distribution. This is separately documented at [placeholder].
let alpha item mytheory a
let varepsilon avg-neighbor-signal - belief-to-beat
let delta item mytheory current-theory-info - belief-to-beat
if (2 * alpha - 1) * delta <= belief-to-beat [
set confidence 0
set stop? true
stop
]
let exit-probability 0.5 + 0.5 * erf (
((0 - 2 * alpha + 1) * delta + belief-to-beat)
/ (sqrt((0 - 2 * alpha * delta + delta + belief-to-beat)
* (belief-to-beat + varepsilon) * (0 - 1 + belief-to-beat + varepsilon)
/ (varepsilon * (belief-to-beat + delta)))
* (belief-to-beat + delta)))
ifelse exit-probability > 0 [
set confidence 1 - exit-probability
][
set confidence 1
]
]
ifelse stop? [
set g-confidence 0
][
set g-confidence reduce * [confidence] of turtles
]
end





; reports a numerical approximation for the error-function function on its
; negative domain, therefore the argument (x) must be smaller than 0. For
; sources see infotab.
to-report erf [x]
let t (1 - .5 * x)
report exp ( 0 - x ^ 2 - 1.26551223 + 1.00002368 / t
+ .37409196 / t ^ 2 + 0.09678418 / t ^ 3
- .18628806 / t ^ 4 + .27886807 / t ^ 5
- 1.13520398 / t ^ 6 + 1.48851587 / t ^ 7
- .82215223 / t ^ 8 + .17087277 / t ^ 9)
/ t - 1
end





; reports 1 if scientists converged on the best theory (th1) by the end of the
; run, 0 otherwise
to-report successful-run
Expand Down Expand Up @@ -227,10 +306,10 @@ end
to-report average-confidence [rec?]
let identifier "avgconfidence"
ifelse rec? [
if not converged [
if ticks >= max-ticks and not converged [
report (list identifier 0)
]
let avg-confidence mean [confidence] of turtles
let avg-confidence g-confidence
report (list identifier avg-confidence)
][
let avg-confidence item 1 first filter [curitem ->
Expand Down

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