当前位置：首页 > java >正文

隐马尔可夫模型(HMM)在彩票预测中的Java实现

java 2025/5/12 6:51:08

隐马尔可夫模型(HMM)在彩票预测中的Java实现

隐马尔可夫模型(Hidden Markov Model, HMM)是一种统计模型，可以用来描述含有隐含未知参数的马尔可夫过程。虽然彩票号码本质上是随机生成的，但我们可以使用HMM来尝试发现可能的模式。

1. HMM基础实现

首先，我们实现HMM的核心组件：

import java.util.*;public class HMM {private int stateCount;  // 隐藏状态数量private int observationCount;  // 可观察值数量private double[] initialStateProb;  // 初始状态概率private double[][] transitionMatrix;  // 状态转移矩阵private double[][] emissionMatrix;  // 发射矩阵(状态生成观测值的概率)public HMM(int stateCount, int observationCount) {this.stateCount = stateCount;this.observationCount = observationCount;this.initialStateProb = new double[stateCount];this.transitionMatrix = new double[stateCount][stateCount];this.emissionMatrix = new double[stateCount][observationCount];// 初始化随机概率(后续会通过训练调整)Random random = new Random();// 初始化初始状态概率double sum = 0;for (int i = 0; i < stateCount; i++) {initialStateProb[i] = random.nextDouble();sum += initialStateProb[i];}for (int i = 0; i < stateCount; i++) {initialStateProb[i] /= sum;}// 初始化转移矩阵for (int i = 0; i < stateCount; i++) {sum = 0;for (int j = 0; j < stateCount; j++) {transitionMatrix[i][j] = random.nextDouble();sum += transitionMatrix[i][j];}for (int j = 0; j < stateCount; j++) {transitionMatrix[i][j] /= sum;}}// 初始化发射矩阵for (int i = 0; i < stateCount; i++) {sum = 0;for (int j = 0; j < observationCount; j++) {emissionMatrix[i][j] = random.nextDouble();sum += emissionMatrix[i][j];}for (int j = 0; j < observationCount; j++) {emissionMatrix[i][j] /= sum;}}}// Baum-Welch算法训练HMMpublic void train(int[] observations, int iterations) {int T = observations.length;double[][] alpha = new double[T][stateCount];double[][] beta = new double[T][stateCount];double[][] gamma = new double[T][stateCount];double[][][] xi = new double[T - 1][stateCount][stateCount];for (int it = 0; it < iterations; it++) {// 1. 前向算法计算alphafor (int i = 0; i < stateCount; i++) {alpha[0][i] = initialStateProb[i] * emissionMatrix[i][observations[0]];}for (int t = 1; t < T; t++) {for (int j = 0; j < stateCount; j++) {double sum = 0;for (int i = 0; i < stateCount; i++) {sum += alpha[t - 1][i] * transitionMatrix[i][j];}alpha[t][j] = sum * emissionMatrix[j][observations[t]];}}// 2. 后向算法计算betafor (int i = 0; i < stateCount; i++) {beta[T - 1][i] = 1;}for (int t = T - 2; t >= 0; t--) {for (int i = 0; i < stateCount; i++) {beta[t][i] = 0;for (int j = 0; j < stateCount; j++) {beta[t][i] += transitionMatrix[i][j] * emissionMatrix[j][observations[t + 1]] * beta[t + 1][j];}}}// 3. 计算gamma和xifor (int t = 0; t < T - 1; t++) {double sum = 0;for (int i = 0; i < stateCount; i++) {for (int j = 0; j < stateCount; j++) {sum += alpha[t][i] * transitionMatrix[i][j] * emissionMatrix[j][observations[t + 1]] * beta[t + 1][j];}}for (int i = 0; i < stateCount; i++) {gamma[t][i] = 0;for (int j = 0; j < stateCount; j++) {xi[t][i][j] = (alpha[t][i] * transitionMatrix[i][j] * emissionMatrix[j][observations[t + 1]] * beta[t + 1][j]) / sum;gamma[t][i] += xi[t][i][j];}}}// 特殊处理最后一个gammadouble sum = 0;for (int i = 0; i < stateCount; i++) {sum += alpha[T - 1][i];}for (int i = 0; i < stateCount; i++) {gamma[T - 1][i] = alpha[T - 1][i] / sum;}// 4. 更新模型参数// 更新初始状态概率for (int i = 0; i < stateCount; i++) {initialStateProb[i] = gamma[0][i];}// 更新转移矩阵for (int i = 0; i < stateCount; i++) {for (int j = 0; j < stateCount; j++) {double numerator = 0;double denominator = 0;for (int t = 0; t < T - 1; t++) {numerator += xi[t][i][j];denominator += gamma[t][i];}transitionMatrix[i][j] = numerator / denominator;}}// 更新发射矩阵for (int i = 0; i < stateCount; i++) {for (int k = 0; k < observationCount; k++) {double numerator = 0;double denominator = 0;for (int t = 0; t < T; t++) {if (observations[t] == k) {numerator += gamma[t][i];}denominator += gamma[t][i];}emissionMatrix[i][k] = numerator / denominator;}}}}// 预测下一个观测值public int predictNextObservation(int[] observations) {int T = observations.length;double[][] alpha = new double[T + 1][stateCount];// 初始化for (int i = 0; i < stateCount; i++) {alpha[0][i] = initialStateProb[i];}// 递推for (int t = 0; t < T; t++) {for (int j = 0; j < stateCount; j++) {alpha[t + 1][j] = 0;for (int i = 0; i < stateCount; i++) {alpha[t + 1][j] += alpha[t][i] * transitionMatrix[i][j];}alpha[t + 1][j] *= emissionMatrix[j][observations[t]];}// 归一化double sum = 0;for (int i = 0; i < stateCount; i++) {sum += alpha[t + 1][i];}for (int i = 0; i < stateCount; i++) {alpha[t + 1][i] /= sum;}}// 计算下一个观测值的概率分布double[] obsProb = new double[observationCount];for (int k = 0; k < observationCount; k++) {for (int i = 0; i < stateCount; i++) {obsProb[k] += alpha[T][i] * emissionMatrix[i][k];}}// 返回概率最大的观测值int maxIndex = 0;for (int k = 1; k < observationCount; k++) {if (obsProb[k] > obsProb[maxIndex]) {maxIndex = k;}}return maxIndex;}// 获取模型参数(用于调试)public void printModelParameters() {System.out.println("Initial State Probabilities:");System.out.println(Arrays.toString(initialStateProb));System.out.println("\nTransition Matrix:");for (int i = 0; i < stateCount; i++) {System.out.println(Arrays.toString(transitionMatrix[i]));}System.out.println("\nEmission Matrix:");for (int i = 0; i < stateCount; i++) {System.out.println(Arrays.toString(emissionMatrix[i]));}}
}

2. 彩票预测系统实现

现在，我们基于HMM实现彩票预测系统：

import java.util.*;public class LotteryPredictor {private HMM hmm;private int minNumber;private int maxNumber;public LotteryPredictor(int minNumber, int maxNumber, int hiddenStates) {this.minNumber = minNumber;this.maxNumber = maxNumber;int observationCount = maxNumber - minNumber + 1;this.hmm = new HMM(hiddenStates, observationCount);}// 训练模型public void train(List<int[]> historicalData, int iterations) {// 将历史数据转换为观测序列List<Integer> observations = new ArrayList<>();for (int[] draw : historicalData) {for (int num : draw) {observations.add(num - minNumber); // 转换为0-based索引}}// 转换为数组int[] obsArray = new int[observations.size()];for (int i = 0; i < obsArray.length; i++) {obsArray[i] = observations.get(i);}// 训练HMMhmm.train(obsArray, iterations);}// 预测下一期号码public int[] predictNextDraw(int drawSize) {// 这里简化处理，实际应用中可能需要更复杂的预测逻辑int[] prediction = new int[drawSize];int[] lastObserved = new int[drawSize]; // 假设使用上一期的号码作为输入for (int i = 0; i < drawSize; i++) {int predicted = hmm.predictNextObservation(lastObserved) + minNumber;prediction[i] = predicted;// 更新lastObserved用于下一个号码的预测if (i < drawSize - 1) {lastObserved[i] = predicted - minNumber;}}return prediction;}// 评估模型准确率public double evaluate(List<int[]> testData) {int correct = 0;int total = 0;for (int i = 0; i < testData.size() - 1; i++) {int[] currentDraw = testData.get(i);int[] nextDraw = testData.get(i + 1);// 转换为0-based索引int[] currentObs = new int[currentDraw.length];for (int j = 0; j < currentDraw.length; j++) {currentObs[j] = currentDraw[j] - minNumber;}// 预测下一个号码int predicted = hmm.predictNextObservation(currentObs) + minNumber;// 检查预测是否在下一期号码中for (int num : nextDraw) {if (num == predicted) {correct++;break;}}total++;}return (double) correct / total;}
}

3. 使用案例

import java.util.*;public class Main {public static void main(String[] args) {// 模拟双色球历史数据(红球:1-33选6个，蓝球:1-16选1个)// 这里仅使用红球作为示例List<int[]> history = new ArrayList<>();history.add(new int[]{1, 5, 9, 12, 23, 30});history.add(new int[]{2, 6, 10, 13, 24, 31});history.add(new int[]{3, 7, 11, 14, 25, 32});history.add(new int[]{4, 8, 12, 15, 26, 33});history.add(new int[]{5, 9, 13, 16, 27, 1});history.add(new int[]{6, 10, 14, 17, 28, 2});history.add(new int[]{7, 11, 15, 18, 29, 3});history.add(new int[]{8, 12, 16, 19, 30, 4});history.add(new int[]{9, 13, 17, 20, 31, 5});history.add(new int[]{10, 14, 18, 21, 32, 6});// 创建预测器(红球范围1-33，假设有5个隐藏状态)LotteryPredictor predictor = new LotteryPredictor(1, 33, 5);// 训练模型predictor.train(history, 100);// 预测下一期号码int[] prediction = predictor.predictNextDraw(6);System.out.println("预测下一期红球号码: " + Arrays.toString(prediction));// 评估模型(使用最后3期作为测试数据)double accuracy = predictor.evaluate(history.subList(history.size() - 4, history.size()));System.out.printf("模型准确率: %.2f%%\n", accuracy * 100);// 注意：彩票本质上是随机的，此预测仅供参考System.out.println("温馨提示：彩票预测仅供参考，请理性购彩！");}
}