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use linear weighted selection instead of softmax for choosing fad des…
…tinations this includes a bit of refactoring of the various `oneOf` methods in MasonUtils, which are now using precondition
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
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| package uk.ac.ox.oxfish.utility; | ||
|
|
||
| /****************************************************************************** | ||
| * File: AliasMethod.java | ||
| * Author: Keith Schwarz ([email protected]) | ||
| * | ||
| * An implementation of the alias method implemented using Vose's algorithm. | ||
| * The alias method allows for efficient sampling of random values from a | ||
| * discrete probability distribution (i.e. rolling a loaded die) in O(1) time | ||
| * each after O(n) preprocessing time. | ||
| * | ||
| * For a complete writeup on the alias method, including the intuition and | ||
| * important proofs, please see the article "Darts, Dice, and Coins: Smpling | ||
| * from a Discrete Distribution" at | ||
| * | ||
| * http://www.keithschwarz.com/darts-dice-coins/ | ||
| /****************************************************************************** | ||
| * Modified to use ec.util.MersenneTwisterFast instead of java.util.Random | ||
| * -- NP 2019-09-18. | ||
| */ | ||
|
|
||
| import java.util.ArrayDeque; | ||
| import java.util.ArrayList; | ||
| import java.util.Deque; | ||
| import java.util.List; | ||
| import ec.util.MersenneTwisterFast; | ||
|
|
||
| public final class AliasMethod { | ||
| /* The random number generator used to sample from the distribution. */ | ||
| private final MersenneTwisterFast random; | ||
|
|
||
| /* The probability and alias tables. */ | ||
| private final int[] alias; | ||
| private final double[] probability; | ||
|
|
||
| /** | ||
| * Constructs a new AliasMethod to sample from a discrete distribution and | ||
| * hand back outcomes based on the probability distribution. | ||
| * <p> | ||
| * Given as input a list of probabilities corresponding to outcomes 0, 1, | ||
| * ..., n - 1, along with the random number generator that should be used | ||
| * as the underlying generator, this constructor creates the probability | ||
| * and alias tables needed to efficiently sample from this distribution. | ||
| * | ||
| * @param probabilities The list of probabilities. | ||
| * @param random The random number generator | ||
| */ | ||
| public AliasMethod(List<Double> probabilities, MersenneTwisterFast random) { | ||
| /* Begin by doing basic structural checks on the inputs. */ | ||
| if (probabilities == null || random == null) | ||
| throw new NullPointerException(); | ||
| if (probabilities.size() == 0) | ||
| throw new IllegalArgumentException("Probability vector must be nonempty."); | ||
|
|
||
| /* Allocate space for the probability and alias tables. */ | ||
| probability = new double[probabilities.size()]; | ||
| alias = new int[probabilities.size()]; | ||
|
|
||
| /* Store the underlying generator. */ | ||
| this.random = random; | ||
|
|
||
| /* Compute the average probability and cache it for later use. */ | ||
| final double average = 1.0 / probabilities.size(); | ||
|
|
||
| /* Make a copy of the probabilities list, since we will be making | ||
| * changes to it. | ||
| */ | ||
| probabilities = new ArrayList<Double>(probabilities); | ||
|
|
||
| /* Create two stacks to act as worklists as we populate the tables. */ | ||
| Deque<Integer> small = new ArrayDeque<Integer>(); | ||
| Deque<Integer> large = new ArrayDeque<Integer>(); | ||
|
|
||
| /* Populate the stacks with the input probabilities. */ | ||
| for (int i = 0; i < probabilities.size(); ++i) { | ||
| /* If the probability is below the average probability, then we add | ||
| * it to the small list; otherwise we add it to the large list. | ||
| */ | ||
| if (probabilities.get(i) >= average) | ||
| large.add(i); | ||
| else | ||
| small.add(i); | ||
| } | ||
|
|
||
| /* As a note: in the mathematical specification of the algorithm, we | ||
| * will always exhaust the small list before the big list. However, | ||
| * due to floating point inaccuracies, this is not necessarily true. | ||
| * Consequently, this inner loop (which tries to pair small and large | ||
| * elements) will have to check that both lists aren't empty. | ||
| */ | ||
| while (!small.isEmpty() && !large.isEmpty()) { | ||
| /* Get the index of the small and the large probabilities. */ | ||
| int less = small.removeLast(); | ||
| int more = large.removeLast(); | ||
|
|
||
| /* These probabilities have not yet been scaled up to be such that | ||
| * 1/n is given weight 1.0. We do this here instead. | ||
| */ | ||
| probability[less] = probabilities.get(less) * probabilities.size(); | ||
| alias[less] = more; | ||
|
|
||
| /* Decrease the probability of the larger one by the appropriate | ||
| * amount. | ||
| */ | ||
| probabilities.set(more, | ||
| (probabilities.get(more) + probabilities.get(less)) - average); | ||
|
|
||
| /* If the new probability is less than the average, add it into the | ||
| * small list; otherwise add it to the large list. | ||
| */ | ||
| if (probabilities.get(more) >= 1.0 / probabilities.size()) | ||
| large.add(more); | ||
| else | ||
| small.add(more); | ||
| } | ||
|
|
||
| /* At this point, everything is in one list, which means that the | ||
| * remaining probabilities should all be 1/n. Based on this, set them | ||
| * appropriately. Due to numerical issues, we can't be sure which | ||
| * stack will hold the entries, so we empty both. | ||
| */ | ||
| while (!small.isEmpty()) | ||
| probability[small.removeLast()] = 1.0; | ||
| while (!large.isEmpty()) | ||
| probability[large.removeLast()] = 1.0; | ||
| } | ||
|
|
||
| /** | ||
| * Samples a value from the underlying distribution. | ||
| * | ||
| * @return A random value sampled from the underlying distribution. | ||
| */ | ||
| public int next() { | ||
| /* Generate a fair die roll to determine which column to inspect. */ | ||
| int column = random.nextInt(probability.length); | ||
|
|
||
| /* Generate a biased coin toss to determine which option to pick. */ | ||
| boolean coinToss = random.nextDouble() < probability[column]; | ||
|
|
||
| /* Based on the outcome, return either the column or its alias. */ | ||
| return coinToss ? column : alias[column]; | ||
| } | ||
| } |
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