Alink漫谈(二十一) ：回归评估之源码分析
Alink漫谈(二十一) ：回归评估之源码分析
0x00 摘要
Alink 是阿里巴巴基于实时计算引擎 Flink 研发的新一代机器学习算法平台，是业界首个同时支持批式算法、流式算法的机器学习平台。本文和将带领大家来分析Alink中 回归评估 的实现。
这是剖析Alink以来，最轻松的一次了。因为这里的概念和实现逻辑都非常清晰。
0x01 背景概念
1.1 功能介绍
回归评估是对回归算法的预测结果进行效果评估，支持下列评估指标。这些指标基本都是统计领域概念。
1.2 具体指标
Alink 提供如下指标：
count 行数
SST 总平方和(Sum of Squared for Total)，度量了Y在样本中的分散程度。
\[SST=\sum_{i=1}^{N}(y_i-\bar{y})^2 \]
SSE 误差平方和(Sum of Squares for Error)，度量了总样本变异。
\[SSE=\sum_{i=1}^{N}(y_i-f_i)^2" \]
SSR 回归平方和(Sum of Squares for Regression)，度量了残差的样本变异。
\[SSR=\sum_{i=1}^{N}(f_i-\bar{y})^2 \]
R^2 判定系数(Coefficient of Determination)，用于估计回归方程是否很好的拟合了样本的数据，判定系数为估计的回归方程提供了一个拟合优度的度量。
\[R^2=1-\dfrac{SSE}{SST} \]
R 多重相关系数(Multiple Correlation Coeffient)，指一个随机变量与某一组随机变量间线性相依性的度量。
\[R=\sqrt{R^2} \]
MSE 均方误差(Mean Squared Error)，均方差（标准差）、方差都是用来描述数据集的离散程度。
均方误差是衡量“平均误差”的一种较方便的方法，可以评价数据的变化程度。从类别来看属于预测评价与预测组合；从字面上看来，“均”指的是平均，即求其平均值，“方差”即是在概率论中用来衡量随机变量和其估计值（其平均值）之间的偏离程度的度量值，“误”可以理解为测定值与真实值之间的误差。
\[MSE=\dfrac{1}{N}\sum_{i=1}^{N}(f_i-y_i)^2 \]
RMSE 均方根误差(Root Mean Squared Error)
\[RMSE=\sqrt{MSE} \]
SAE/SAD 绝对误差(Sum of Absolute Error/Difference)
\[SAE=\sum_{i=1}^{N}|f_i-y_i| \]
MAE/MAD 平均绝对误差(Mean Absolute Error/Difference)
\[MAE=\dfrac{1}{N}\sum_{i=1}^{N}|f_i-y_i| \]
MAPE 平均绝对百分误差(Mean Absolute Percentage Error)
\[MAPE=\dfrac{100}{N}\sum_{i=1}^{N}|\dfrac{f_i-y_i}{y_i}| \]
explained variance 解释方差
\[explained Variance=\dfrac{SSR}{N} \]
0x02 示例代码
直接拿出来Alink的示例代码。
public class EvalRegressionBatchOpExp {
public static void main(String[] args) throws Exception {
Row[] data =
new Row[] {
Row.of(0.4, 0.5),
Row.of(0.3, 0.5),
Row.of(0.2, 0.6),
Row.of(0.6, 0.7),
Row.of(0.1, 0.5)
};
MemSourceBatchOp input = new MemSourceBatchOp(data, new String[] {"label", "pred"});
RegressionMetrics metrics = new EvalRegressionBatchOp()
.setLabelCol("label")
.setPredictionCol("pred")
.linkFrom(input)
.collectMetrics();
System.out.println(metrics.getRmse());
System.out.println(metrics.getR2());
System.out.println(metrics.getSse());
System.out.println(metrics.getMape());
System.out.println(metrics.getMae());
System.out.println(metrics.getSsr());
System.out.println(metrics.getSst());
}
}输出为：
0.27568097504180444
-1.5675675675675653
0.38
141.66666666666669
0.24
0.31999999999999973
0.148000000000000130x03 总体逻辑
总体逻辑是：
- 调用 CalcLocal 进行分区计算各种统计数值；
- reduce 调用 ReduceBaseMetrics 进行归并各种统计数值；
- 调用 SaveDataAsParams 存储；
getLabelCol 就是 y，getPredictionCol 就是 y_hat。
public EvalRegressionBatchOp linkFrom(BatchOperator<?>... inputs) {
BatchOperator in = checkAndGetFirst(inputs);
// 这里就是找到y, y_hat
TableUtil.findColIndexWithAssertAndHint(in.getColNames(), this.getLabelCol());
TableUtil.findColIndexWithAssertAndHint(in.getColNames(), this.getPredictionCol());
// 利用y, y_hat来构建Metrics
TableUtil.assertNumericalCols(in.getSchema(), this.getLabelCol(), this.getPredictionCol());
DataSet<Row> out = in.select(new String[] {this.getLabelCol(), this.getPredictionCol()})
.getDataSet()
.rebalance()
.mapPartition(new CalcLocal())
.reduce(new EvaluationUtil.ReduceBaseMetrics())
.flatMap(new EvaluationUtil.SaveDataAsParams());
this.setOutputTable(DataSetConversionUtil.toTable(getMLEnvironmentId(),
out, new TableSchema(new String[] {"regression_eval_result"}, new TypeInformation[] {Types.STRING})
));
return this;
}0x04 分区计算统计数值
调用 CalcLocal 进行分区计算各种统计数值，间接调用getRegressionStatistics。
/**
* Get the label sum, predResult sum, SSE, MAE, MAPE of one partition.
*/
public static class CalcLocal implements MapPartitionFunction<Row, BaseMetricsSummary> {
@Override
public void mapPartition(Iterable<Row> rows, Collector<BaseMetricsSummary> collector)
throws Exception {
collector.collect(getRegressionStatistics(rows));
}
}getRegressionStatistics作用是遍历输入数据，在本Partition内部计算各种累积数值，为后续做准备。
/**
* Calculate the RegressionMetrics from local data.
*
* @param rows Input rows, the first field is label value, the second field is prediction value.
* @return RegressionMetricsSummary.
*/
public static RegressionMetricsSummary getRegressionStatistics(Iterable<Row> rows) {
RegressionMetricsSummary regressionSummary = new RegressionMetricsSummary();
for (Row row : rows) {
if (checkRowFieldNotNull(row)) {
double yVal = ((Number)row.getField(0)).doubleValue();
double predictVal = ((Number)row.getField(1)).doubleValue();
double diff = Math.abs(yVal - predictVal);
regressionSummary.ySumLocal += yVal;
regressionSummary.ySum2Local += yVal * yVal;
regressionSummary.predSumLocal += predictVal;
regressionSummary.predSum2Local += predictVal * predictVal;
regressionSummary.maeLocal += diff;
regressionSummary.sseLocal += diff * diff;
regressionSummary.mapeLocal += Math.abs(diff / yVal);
regressionSummary.total++;
}
}
return regressionSummary.total == 0 ? null : regressionSummary;
}0x05 归并统计数值
reduce 调用 ReduceBaseMetrics 进行归并各种统计数值：
/**
* Merge the BaseMetrics calculated locally.
*/
public static class ReduceBaseMetrics implements ReduceFunction<BaseMetricsSummary> {
@Override
public BaseMetricsSummary reduce(BaseMetricsSummary t1, BaseMetricsSummary t2) throws Exception {
return null == t1 ? t2 : t1.merge(t2);
}
}0x06 存储模型
这里调用SaveDataAsParams来存储模型。
/**
* After merging all the BaseMetrics, we get the total BaseMetrics. Calculate the indexes and save them into params.
*/
public static class SaveDataAsParams implements FlatMapFunction<BaseMetricsSummary, Row> {
@Override
public void flatMap(BaseMetricsSummary t, Collector<Row> collector) throws Exception {
collector.collect(t.toMetrics().serialize());
}
}0x07 toMetrics
最后呈现出统计指标。
public RegressionMetrics toMetrics() {
Params params = new Params();
params.set(RegressionMetrics.SST, ySum2Local - ySumLocal * ySumLocal / total);
params.set(RegressionMetrics.SSE, sseLocal);
params.set(RegressionMetrics.SSR,
predSum2Local - 2 * ySumLocal * predSumLocal / total + ySumLocal * ySumLocal / total);
params.set(RegressionMetrics.R2, 1 - params.get(RegressionMetrics.SSE) / params.get(RegressionMetrics.SST));
params.set(RegressionMetrics.R, Math.sqrt(params.get(RegressionMetrics.R2)));
params.set(RegressionMetrics.MSE, params.get(RegressionMetrics.SSE) / total);
params.set(RegressionMetrics.RMSE, Math.sqrt(params.get(RegressionMetrics.MSE)));
params.set(RegressionMetrics.SAE, maeLocal);
params.set(RegressionMetrics.MAE, params.get(RegressionMetrics.SAE) / total);
params.set(RegressionMetrics.COUNT, (double)total);
params.set(RegressionMetrics.MAPE, mapeLocal * 100 / total);
params.set(RegressionMetrics.Y_MEAN, ySumLocal / total);
params.set(RegressionMetrics.PREDICTION_MEAN, predSumLocal / total);
params.set(RegressionMetrics.EXPLAINED_VARIANCE, params.get(RegressionMetrics.SSR) / total);
return new RegressionMetrics(params);
}最后得到结果
params = {Params@9098} "Params {R2=-1.5675675675675693, predictionMean=0.5599999999999999, SSE=0.38, count=5.0, MAPE=141.66666666666666, RMSE=0.27568097504180444, MAE=0.24, R=NaN, SSR=0.3200000000000002, yMean=0.32, SST=0.1479999999999999, SAE=1.2, Explained Variance=0.06400000000000003, MSE=0.076}"
params = {HashMap@9101} size = 14
"R2" -> "-1.5675675675675693"
"predictionMean" -> "0.5599999999999999"
"SSE" -> "0.38"
"count" -> "5.0"
"MAPE" -> "141.66666666666666"
"RMSE" -> "0.27568097504180444"
"MAE" -> "0.24"
"R" -> "NaN"
"SSR" -> "0.3200000000000002"
"yMean" -> "0.32"
"SST" -> "0.1479999999999999"
"SAE" -> "1.2"
"Explained Variance" -> "0.06400000000000003"
"MSE" -> "0.076"