Diversity prediction theorem
The wisdom of the crowd is the collective opinion of a group of individuals rather than that of a single expert.
Wisdom-of-the-crowds research routinely attributes the superiority of crowd averages over individual judgments to the elimination of individual noise, an explanation that assumes independence of the individual judgments from each other. Thus the crowd tends to make its best decisions if it is made up of diverse opinions and ideologies.
Scott E. Page introduced the diversity prediction theorem: "The squared error of the collective prediction equals the average squared error minus the predictive diversity". Therefore, when the diversity in a group is large, the error of the crowd is small.
- Average Individual Error: Average of the individual squared errors
- Collective Error: Squared error of the collective prediction
- Prediction Diversity: Average squared distance from the individual predictions to the collective prediction
So, The Diversity Prediction Theorem: Given a crowd of predictive models
Collective Error = Average Individual Error - Prediction Diversity
11l
<lang 11l>F average_square_diff(a, predictions)
R sum(predictions.map(x -> (x - @a) ^ 2)) / predictions.len
F diversity_theorem(truth, predictions)
V average = sum(predictions) / predictions.len print(‘average-error: ’average_square_diff(truth, predictions)"\n"‘’ ‘crowd-error: ’((truth - average) ^ 2)"\n"‘’ ‘diversity: ’average_square_diff(average, predictions))
diversity_theorem(49.0, [Float(48), 47, 51]) diversity_theorem(49.0, [Float(48), 47, 51, 42])</lang>
- Output:
average-error: 3 crowd-error: 0.111111111 diversity: 2.888888889 average-error: 14.5 crowd-error: 4 diversity: 10.5
C
Accepts inputs from command line, prints out usage on incorrect invocation. <lang C>
- include<string.h>
- include<stdlib.h>
- include<stdio.h>
float mean(float* arr,int size){ int i = 0; float sum = 0;
while(i != size) sum += arr[i++];
return sum/size; }
float variance(float reference,float* arr, int size){ int i=0; float* newArr = (float*)malloc(size*sizeof(float));
for(;i<size;i++) newArr[i] = (reference - arr[i])*(reference - arr[i]);
return mean(newArr,size); }
float* extractData(char* str, int *len){ float* arr; int i=0,count = 1; char* token;
while(str[i]!=00){ if(str[i++]==',') count++; }
arr = (float*)malloc(count*sizeof(float)); *len = count;
token = strtok(str,",");
i = 0;
while(token!=NULL){ arr[i++] = atof(token); token = strtok(NULL,","); }
return arr; }
int main(int argC,char* argV[]) { float* arr,reference,meanVal; int len; if(argC!=3) printf("Usage : %s <reference value> <observations separated by commas>"); else{ arr = extractData(argV[2],&len);
reference = atof(argV[1]);
meanVal = mean(arr,len);
printf("Average Error : %.9f\n",variance(reference,arr,len)); printf("Crowd Error : %.9f\n",(reference - meanVal)*(reference - meanVal)); printf("Diversity : %.9f",variance(meanVal,arr,len)); }
return 0; } </lang> Invocation and Output :
C:\rosettaCode>diversityTheorem.exe 49 48,47,51 Average Error : 3.000000000 Crowd Error : 0.111110263 Diversity : 2.888888597 C:\rosettaCode>diversityTheorem.exe 49 48,47,51,42 Average Error : 14.500000000 Crowd Error : 4.000000000 Diversity : 10.500000000
C#
<lang csharp> using System; using System.Linq; using System.Collections.Generic;
public class MainClass {
static double Square(double x) => x * x;
static double AverageSquareDiff(double a, IEnumerable<double> predictions) => predictions.Select(x => Square(x - a)).Average();
static void DiversityTheorem(double truth, IEnumerable<double> predictions) { var average = predictions.Average(); Console.WriteLine($@"average-error: {AverageSquareDiff(truth, predictions)}
crowd-error: {Square(truth - average)} diversity: {AverageSquareDiff(average, predictions)}");
}
public static void Main() {
DiversityTheorem(49, new []{48d,47,51});
DiversityTheorem(49, new []{48d,47,51,42}); }
}</lang>
- Output:
average-error: 3 crowd-error: 0.11111 diversity: 2.88889 average-error: 14.5 crowd-error: 4 diversity: 10.5
C++
<lang Cpp>
- include <iostream>
- include <vector>
- include <numeric>
float sum(const std::vector<float> &array) {
return std::accumulate(array.begin(), array.end(), 0.0);
}
float square(float x) {
return x * x;
}
float mean(const std::vector<float> &array) {
return sum(array) / array.size();
}
float averageSquareDiff(float a, const std::vector<float> &predictions) {
std::vector<float> results; for (float x : predictions) results.push_back(square(x - a)); return mean(results);
}
void diversityTheorem(float truth, const std::vector<float> &predictions) {
float average = mean(predictions); std::cout << "average-error: " << averageSquareDiff(truth, predictions) << "\n" << "crowd-error: " << square(truth - average) << "\n" << "diversity: " << averageSquareDiff(average, predictions) << std::endl;
}
int main() {
diversityTheorem(49, {48,47,51}); diversityTheorem(49, {48,47,51,42}); return 0;
} </lang>
- Output:
average-error: 3 crowd-error: 0.11111 diversity: 2.88889 average-error: 14.5 crowd-error: 4 diversity: 10.5
Clojure
John Lawrence Aspden's code posted on Diversity Prediction Theorem. <lang Clojure> (defn diversity-theorem [truth predictions]
(let [square (fn[x] (* x x)) mean (/ (reduce + predictions) (count predictions)) avg-sq-diff (fn[a] (/ (reduce + (for [x predictions] (square (- x a)))) (count predictions)))] {:average-error (avg-sq-diff truth) :crowd-error (square (- truth mean)) :diversity (avg-sq-diff mean)}))
(println (diversity-theorem 49 '(48 47 51))) (println (diversity-theorem 49 '(48 47 51 42))) </lang>
- Output:
{:average-error 3, :crowd-error 1/9, :diversity 26/9} {:average-error 29/2, :crowd-error 4, :diversity 21/2}
D
<lang d>import std.algorithm; import std.stdio;
auto square = (real x) => x * x;
auto meanSquareDiff(R)(real a, R predictions) {
return predictions.map!(x => square(x - a)).mean;
}
void diversityTheorem(R)(real truth, R predictions) {
auto average = predictions.mean; writeln("average-error: ", meanSquareDiff(truth, predictions)); writeln("crowd-error: ", square(truth - average)); writeln("diversity: ", meanSquareDiff(average, predictions)); writeln;
}
void main() {
diversityTheorem(49.0, [48.0, 47.0, 51.0]); diversityTheorem(49.0, [48.0, 47.0, 51.0, 42.0]);
}</lang>
- Output:
average-error: 3 crowd-error: 0.111111 diversity: 2.88889 average-error: 14.5 crowd-error: 4 diversity: 10.5
Factor
<lang factor>USING: kernel math math.statistics math.vectors prettyprint ;
TUPLE: div avg-err crowd-err diversity ;
- diversity ( x seq -- obj )
[ n-v dup v* mean ] [ mean swap - sq ] [ nip dup mean v-n dup v* mean ] 2tri div boa ;
49 { 48 47 51 } diversity . 49 { 48 47 51 42 } diversity .</lang>
- Output:
T{ div { avg-err 3 } { crowd-err 1/9 } { diversity 2+8/9 } } T{ div { avg-err 14+1/2 } { crowd-err 4 } { diversity 10+1/2 } }
Fōrmulæ
In this page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
Go
<lang go>package main
import "fmt"
func averageSquareDiff(f float64, preds []float64) (av float64) {
for _, pred := range preds { av += (pred - f) * (pred - f) } av /= float64(len(preds)) return
}
func diversityTheorem(truth float64, preds []float64) (float64, float64, float64) {
av := 0.0 for _, pred := range preds { av += pred } av /= float64(len(preds)) avErr := averageSquareDiff(truth, preds) crowdErr := (truth - av) * (truth - av) div := averageSquareDiff(av, preds) return avErr, crowdErr, div
}
func main() {
predsArray := [2][]float64{{48, 47, 51}, {48, 47, 51, 42}} truth := 49.0 for _, preds := range predsArray { avErr, crowdErr, div := diversityTheorem(truth, preds) fmt.Printf("Average-error : %6.3f\n", avErr) fmt.Printf("Crowd-error : %6.3f\n", crowdErr) fmt.Printf("Diversity : %6.3f\n\n", div) }
}</lang>
- Output:
Average-error : 3.000 Crowd-error : 0.111 Diversity : 2.889 Average-error : 14.500 Crowd-error : 4.000 Diversity : 10.500
JavaScript
ES5
<lang JavaScript>'use strict';
function sum(array) {
return array.reduce(function (a, b) { return a + b; });
}
function square(x) {
return x * x;
}
function mean(array) {
return sum(array) / array.length;
}
function averageSquareDiff(a, predictions) {
return mean(predictions.map(function (x) { return square(x - a); }));
}
function diversityTheorem(truth, predictions) {
var average = mean(predictions); return { 'average-error': averageSquareDiff(truth, predictions), 'crowd-error': square(truth - average), 'diversity': averageSquareDiff(average, predictions) };
}
console.log(diversityTheorem(49, [48,47,51])) console.log(diversityTheorem(49, [48,47,51,42])) </lang>
- Output:
{ 'average-error': 3, 'crowd-error': 0.11111111111111269, diversity: 2.888888888888889 } { 'average-error': 14.5, 'crowd-error': 4, diversity: 10.5 }
ES6
<lang JavaScript>(() => {
'use strict';
// mean :: Num a => [a] -> b const mean = xs => { const lng = xs.length;
return lng > 0 ? ( xs.reduce((a, b) => a + b, 0) / lng ) : undefined; }
// meanErrorSquared :: Num a => a -> [a] -> b const meanErrorSquared = (observed, predictions) => mean(predictions.map(x => Math.pow(x - observed, 2)));
// diversityValues :: Num a => a -> [a] -> // {mean-Error :: b, crowd-error :: b, diversity :: b} const diversityValues = (observed, predictions) => { const predictionMean = mean(predictions);
return { 'mean-error': meanErrorSquared(observed, predictions), 'crowd-error': Math.pow(observed - predictionMean, 2), 'diversity': meanErrorSquared(predictionMean, predictions) }; }
// TEST
// show :: a -> String const show = x => JSON.stringify(x, null, 2);
return show([{ observed: 49, predictions: [48, 47, 51] }, { observed: 49, predictions: [48, 47, 51, 42] }].map(x => { const dctData = diversityValues(x.observed, x.predictions), dct = {};
return ( Object.keys(dctData) .forEach(k => dct[k] = dctData[k].toPrecision(3)), dct ); }));
})();</lang>
- Output:
[ { "mean-error": "3.00", "crowd-error": "0.111", "diversity": "2.89" }, { "mean-error": "14.5", "crowd-error": "4.00", "diversity": "10.5" } ]
Jsish
From Typescript entry. <lang javascript>/* Diverisity Prediction Theorem, in Jsish */ "use strict";
function sum(arr:array):number {
return arr.reduce(function(acc, cur, idx, arr) { return acc + cur; });
}
function square(x:number):number {
return x * x;
}
function mean(arr:array):number {
return sum(arr) / arr.length;
}
function averageSquareDiff(a:number, predictions:array):number {
return mean(predictions.map(function(x:number):number { return square(x - a); }));
}
function diversityTheorem(truth:number, predictions:array):object {
var average = mean(predictions); return { "average-error": averageSquareDiff(truth, predictions), "crowd-error": square(truth - average), "diversity": averageSquareDiff(average, predictions) };
}
- diversityTheorem(49, [48,47,51]);
- diversityTheorem(49, [48,47,51,42]);
/*
!EXPECTSTART!
diversityTheorem(49, [48,47,51]) ==> { "average-error":3, "crowd-error":0.1111111111111127, diversity:2.888888888888889 } diversityTheorem(49, [48,47,51,42]) ==> { "average-error":14.5, "crowd-error":4, diversity:10.5 }
!EXPECTEND!
- /</lang>
- Output:
prompt$ jsish -u diversityPrediction.jsi [PASS] diversityPrediction.jsi
Julia
<lang julia>import Statistics: mean
function diversitytheorem(truth::T, pred::Vector{T}) where T<:Number
μ = mean(pred) avgerr = mean((pred .- truth) .^ 2) crderr = (μ - truth) ^ 2 divers = mean((pred .- μ) .^ 2) avgerr, crderr, divers
end
for (t, s) in [(49, [48, 47, 51]),
(49, [48, 47, 51, 42])] avgerr, crderr, divers = diversitytheorem(t, s) println(""" average-error : $avgerr crowd-error : $crderr diversity : $divers """)
end</lang>
- Output:
average-error : 3.0 crowd-error : 0.11111111111111269 diversity : 2.888888888888889 average-error : 14.5 crowd-error : 4.0 diversity : 10.5
Kotlin
<lang scala>// version 1.1.4-3
fun square(d: Double) = d * d
fun averageSquareDiff(d: Double, predictions: DoubleArray) =
predictions.map { square(it - d) }.average()
fun diversityTheorem(truth: Double, predictions: DoubleArray): String {
val average = predictions.average() val f = "%6.3f" return "average-error : ${f.format(averageSquareDiff(truth, predictions))}\n" + "crowd-error : ${f.format(square(truth - average))}\n" + "diversity : ${f.format(averageSquareDiff(average, predictions))}\n"
}
fun main(args: Array<String>) {
println(diversityTheorem(49.0, doubleArrayOf(48.0, 47.0, 51.0))) println(diversityTheorem(49.0, doubleArrayOf(48.0, 47.0, 51.0, 42.0)))
}</lang>
- Output:
average-error : 3.000 crowd-error : 0.111 diversity : 2.889 average-error : 14.500 crowd-error : 4.000 diversity : 10.500
Perl
<lang perl>sub diversity {
my($truth, @pred) = @_; my($ae,$ce,$cp,$pd,$stats);
$cp += $_/@pred for @pred; # collective prediction $ae = avg_error($truth, @pred); # average individual error $ce = ($cp - $truth)**2; # collective error $pd = avg_error($cp, @pred); # prediction diversity
my $fmt = "%13s: %6.3f\n"; $stats = sprintf $fmt, 'average-error', $ae; $stats .= sprintf $fmt, 'crowd-error', $ce; $stats .= sprintf $fmt, 'diversity', $pd;
}
sub avg_error {
my($m, @v) = @_; my($avg_err); $avg_err += ($_ - $m)**2 for @v; $avg_err/@v;
}
print diversity(49, qw<48 47 51>) . "\n"; print diversity(49, qw<48 47 51 42>);</lang>
- Output:
average-error: 3.000 crowd-error: 0.111 diversity: 2.889 average-error: 14.500 crowd-error: 4.000 diversity: 10.500
Phix
<lang Phix>function mean(sequence s)
return sum(s)/length(s)
end function
function variance(sequence s, atom d)
return mean(sq_power(sq_sub(s,d),2))
end function
function diversity_theorem(atom reference, sequence observations)
atom average_error = variance(observations,reference), average = mean(observations), crowd_error = power(reference-average,2), diversity = variance(observations,average) return {{"average_error",average_error}, {"crowd_error",crowd_error}, {"diversity",diversity}}
end function
procedure test(atom reference, sequence observations)
sequence res = diversity_theorem(reference, observations) for i=1 to length(res) do printf(1," %14s : %g\n",res[i]) end for
end procedure test(49, {48, 47, 51}) test(49, {48, 47, 51, 42})</lang>
- Output:
average_error : 3 crowd_error : 0.111111 diversity : 2.88889 average_error : 14.5 crowd_error : 4 diversity : 10.5
Python
By composition of pure functions:
<lang python>Diversity prediction theorem
from itertools import chain from functools import reduce
- main :: IO ()
def main():
Observed value: 49, prediction lists: various.
print(unlines(map( showDiversityValues(49), [ [48, 47, 51], [48, 47, 51, 42], [50, '?', 50, {}, 50], # Non-numeric values. [] # Missing predictions. ] ))) print(unlines(map( showDiversityValues('49'), # String in place of number. [ [50, 50, 50], [40, 35, 40], ] )))
- meanErrorSquared :: Num -> [Num] -> Num
def meanErrorSquared(x):
The mean of the squared differences between the observed value x and a non-empty list of predictions ps. return lambda ps: mean(list(map( lambda y: pow(y - x, 2), ps )))
- diversityValues :: Num a => a -> [a] ->
- {mean-Error :: a, crowd-error :: a, diversity :: a}
def diversityValues(x):
The mean error, crowd error and diversity, for a given observation x and a non-empty list of predictions ps. def go(ps): mp = mean(ps) return { 'mean-error': meanErrorSquared(x)(ps), 'crowd-error': pow(x - mp, 2), 'diversity': meanErrorSquared(mp)(ps) } return lambda ps: go(ps)
- FORMATTING ----------------------------------------------
- showDiversityValues :: Num -> [Num] -> Either String String
def showDiversityValues(x):
Formatted string representation of diversity values for a given observation x and a non-empty list of predictions p. def go(x, ps): def showDict(dct): w = 4 + max(map(len, dct.keys()))
def showKV(a, kv): k, v = kv return a + k.rjust(w, ' ') + ( ' : ' + showPrecision(3)(v) + '\n' ) return 'Predictions: ' + showList(ps) + ' ->\n' + ( reduce(showKV, dct.items(), ) )
def showProblem(e): return ( unlines(map(indent(1), e)) if ( isinstance(e, list) ) else indent(1)(repr(e)) ) + '\n'
return 'Observation: ' + repr(x) + '\n' + ( either(showProblem)(showDict)( bindLR(numLR(x))( lambda n: bindLR(numsLR(ps))( compose(Right)(diversityValues(n)) ) ) ) ) return lambda ps: go(x, ps)
- GENERIC -------------------------------------------------
- Right :: b -> Either a b
def Right(x):
Constructor for a populated Either (option type) value return {'type': 'Either', 'Left': None, 'Right': x}
- Left :: a -> Either a b
def Left(x):
Constructor for an empty Either (option type) value with an associated string. return {'type': 'Either', 'Right': None, 'Left': x}
- bindLR (>>=) :: Either a -> (a -> Either b) -> Either b
def bindLR(m):
Either monad injection operator. Two computations sequentially composed, with any value produced by the first passed as an argument to the second. return lambda mf: ( mf(m.get('Right')) if None is m.get('Left') else m )
- compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
Right to left function composition. return lambda f: lambda x: g(f(x))
- concatMap :: (a -> [b]) -> [a] -> [b]
def concatMap(f):
Concatenated list over which a function has been mapped. The list monad can be derived by using a function f which wraps its output in a list, (using an empty list to represent computational failure). return lambda xs: list( chain.from_iterable( map(f, xs) ) )
- either :: (a -> c) -> (b -> c) -> Either a b -> c
def either(fl):
The application of fl to e if e is a Left value, or the application of fr to e if e is a Right value. return lambda fr: lambda e: fl(e['Left']) if ( None is e['Right'] ) else fr(e['Right'])
- indent :: Int -> String -> String
def indent(n):
String indented by n multiples of four spaces return lambda s: (n * 4 * ' ') + s
- mean :: [Num] -> Float
def mean(xs):
Arithmetic mean of a list of numeric values. return sum(xs) / float(len(xs))
- numLR :: a -> Either String Num
def numLR(x):
Either Right x if x is a float or int, or a Left explanatory message. return Right(x) if ( isinstance(x, (float, int)) ) else Left('Expected number, saw: ' + str(type(x)) + ' ' + repr(x))
- numsLR :: [a] -> Either String [Num]
def numsLR(xs):
Either Right xs if all xs are float or int, or a Left explanatory message. def go(ns): ls, rs = partitionEithers(map(numLR, ns)) return Left(ls) if ls else Right(rs) return bindLR( Right(xs) if ( bool(xs) and isinstance(xs, list) ) else Left( 'Expected a non-empty list, saw: ' + ( str(type(xs)) + ' ' + repr(xs) ) ) )(go)
- partitionEithers :: [Either a b] -> ([a],[b])
def partitionEithers(lrs):
A list of Either values partitioned into a tuple of two lists, with all Left elements extracted into the first list, and Right elements extracted into the second list. def go(a, x): ls, rs = a r = x.get('Right') return (ls + [x.get('Left')], rs) if None is r else ( ls, rs + [r] ) return reduce(go, lrs, ([], []))
- showList :: [a] -> String
def showList(xs):
Compact string representation of a list return '[' + ','.join(str(x) for x in xs) + ']'
- showPrecision Int -> Float -> String
def showPrecision(n):
A string showing a floating point number at a given degree of precision. return lambda x: str(round(x, n))
- unlines :: [String] -> String
def unlines(xs):
A single string derived by the intercalation of a list of strings with the newline character. return '\n'.join(xs)
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
Observation: 49 Predictions: [48,47,51] -> mean-error : 3.0 crowd-error : 0.111 diversity : 2.889 Observation: 49 Predictions: [48,47,51,42] -> mean-error : 14.5 crowd-error : 4.0 diversity : 10.5 Observation: 49 Expected number, saw: <class 'str'> '?' Expected number, saw: <class 'dict'> {} Observation: 49 "Expected a non-empty list, saw: <class 'list'> []" Observation: '49' "Expected number, saw: <class 'str'> '49'" Observation: '49' "Expected number, saw: <class 'str'> '49'"
Raku
(formerly Perl 6) <lang perl6>sub diversity-calc($truth, @pred) {
my $ae = avg-error($truth, @pred); # average individual error my $cp = ([+] @pred)/+@pred; # collective prediction my $ce = ($cp - $truth)**2; # collective error my $pd = avg-error($cp, @pred); # prediction diversity return $ae, $ce, $pd;
}
sub avg-error ($m, @v) { ([+] (@v X- $m) X**2) / +@v }
sub diversity-format (@stats) {
gather { for <average-error crowd-error diversity> Z @stats -> ($label,$value) { take $label.fmt("%13s") ~ ':' ~ $value.fmt("%7.3f"); } }
}
.say for diversity-format diversity-calc(49, <48 47 51>); .say for diversity-format diversity-calc(49, <48 47 51 42>);</lang>
- Output:
average-error: 3.000 crowd-error: 0.111 diversity: 2.889 average-error: 14.500 crowd-error: 4.000 diversity: 10.500
REXX
version 1
<lang rexx>/* REXX */ Numeric Digits 20 Call diversityTheorem 49,'48 47 51' Say '--------------------------------------' Call diversityTheorem 49,'48 47 51 42' Exit
diversityTheorem:
Parse Arg truth,list average=average(list) Say 'average-error='averageSquareDiff(truth,list) Say 'crowd-error='||(truth-average)**2 Say 'diversity='averageSquareDiff(average,list) Return
average: Procedure
Parse Arg list res=0 Do i=1 To words(list) res=res+word(list,i) /* accumulate list elements */ End Return res/words(list) /* return the average */
averageSquareDiff: Procedure
Parse Arg a,list res=0 Do i=1 To words(list) x=word(list,i) res=res+(x-a)**2 /* accumulate square of differences */ End Return res/words(list) /* return the average */</lang>
- Output:
average-error=3 crowd-error=0.11111111111111111089 diversity=2.8888888888888888889 -------------------------------------- average-error=14.5 crowd-error=4 diversity=10.5
version 2
Uses greater precision, but rounds the output to six decimal digits past the decimal point (see the last comment in the program). <lang rexx>/*REXX program calculates the average error, crowd error, and prediction diversity. */
numeric digits 50 /*use precision of fifty decimal digits*/
call diversity 49, 48 47 51 /*true value and the crowd predictions.*/ call diversity 49, 48 47 51 42 /* " " " " " " */ exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ avg: $=0; do j=1 for #; $= $ + word(x, j) ; end; return $/# avgSD: $=0; arg y; do j=1 for #; $= $ + (word(x, j) - y)**2; end; return $/# /*──────────────────────────────────────────────────────────────────────────────────────*/ diversity: parse arg true, x; #= words(x); avg$= avg() /*get args; count #est; avg.*/
say ' the true value: ' true copies("═", 20) 'crowd estimates: ' x say ' the average error: ' format( avgSD(true) , , 6) / 1 say ' the crowd error: ' format( (true-avg$)**2 , , 6) / 1 say 'prediction diversity: ' format( avgSD(avg$) , , 6) / 1; say; say return /*show 6──┘ decimal digits*/</lang>
- output when using the default inputs:
the true value: 49 ════════════════════ crowd estimates: 48 47 51 the average error: 3 the crowd error: 0.111111 prediction diversity: 2.888889 the true value: 49 ════════════════════ crowd estimates: 48 47 51 42 the average error: 14.5 the crowd error: 4 prediction diversity: 10.5
Scala
<lang scala>object DiversityPredictionTheorem {
def square(d: Double): Double = d * d
def average(a: Array[Double]): Double = a.sum / a.length
def averageSquareDiff(d: Double, predictions: Array[Double]): Double = average(predictions.map(it => square(it - d)))
def diversityTheorem(truth: Double, predictions: Array[Double]): String = { val avg = average(predictions) f"average-error : ${averageSquareDiff(truth, predictions)}%6.3f\n" + f"crowd-error : ${square(truth - avg)}%6.3f\n"+ f"diversity : ${averageSquareDiff(avg, predictions)}%6.3f\n" }
def main(args: Array[String]): Unit = { println(diversityTheorem(49.0, Array(48.0, 47.0, 51.0))) println(diversityTheorem(49.0, Array(48.0, 47.0, 51.0, 42.0))) }
}</lang>
- Output:
average-error : 3.000 crowd-error : 0.111 diversity : 2.889 average-error : 14.500 crowd-error : 4.000 diversity : 10.500
Sidef
<lang ruby>func avg_error(m, v) {
v.map { (_ - m)**2 }.sum / v.len
}
func diversity_calc(truth, pred) {
var ae = avg_error(truth, pred) var cp = pred.sum/pred.len var ce = (cp - truth)**2 var pd = avg_error(cp, pred) return [ae, ce, pd]
}
func diversity_format(stats) {
gather { for t,v in (%w(average-error crowd-error diversity) ~Z stats) { take(("%13s" % t) + ':' + ('%7.3f' % v)) } }
}
diversity_format(diversity_calc(49, [48, 47, 51])).each{.say} diversity_format(diversity_calc(49, [48, 47, 51, 42])).each{.say}</lang>
- Output:
average-error: 3.000 crowd-error: 0.111 diversity: 2.889 average-error: 14.500 crowd-error: 4.000 diversity: 10.500
TypeScript
<lang TypeScript> function sum(array: Array<number>): number {
return array.reduce((a, b) => a + b)
}
function square(x : number) :number {
return x * x
}
function mean(array: Array<number>): number {
return sum(array) / array.length
}
function averageSquareDiff(a: number, predictions: Array<number>): number {
return mean(predictions.map(x => square(x - a)))
}
function diversityTheorem(truth: number, predictions: Array<number>): Object {
const average: number = mean(predictions) return { "average-error": averageSquareDiff(truth, predictions), "crowd-error": square(truth - average), "diversity": averageSquareDiff(average, predictions) }
}
console.log(diversityTheorem(49, [48,47,51])) console.log(diversityTheorem(49, [48,47,51,42])) </lang>
- Output:
{ 'average-error': 3, 'crowd-error': 0.11111111111111269, diversity: 2.888888888888889 } { 'average-error': 14.5, 'crowd-error': 4, diversity: 10.5 }
zkl
<lang zkl>fcn avgError(m,v){ v.apply('wrap(n){ (n - m).pow(2) }).sum(0.0)/v.len() }
fcn diversityCalc(truth,pred){ //(Float,List of Float)
ae,cp := avgError(truth,pred), pred.sum(0.0)/pred.len(); ce,pd := (cp - truth).pow(2), avgError(cp, pred); return(ae,ce,pd)
}
fcn diversityFormat(stats){ // ( (averageError,crowdError,diversity) )
T("average-error","crowd-error","diversity").zip(stats) .pump(String,Void.Xplode,"%13s :%7.3f\n".fmt)
}</lang> <lang zkl>diversityCalc(49.0, T(48.0,47.0,51.0)) : diversityFormat(_).println(); diversityCalc(49.0, T(48.0,47.0,51.0,42.0)) : diversityFormat(_).println();</lang>
- Output:
average-error : 3.000 crowd-error : 0.111 diversity : 2.889 average-error : 14.500 crowd-error : 4.000 diversity : 10.500