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[SPARK-26351][mllib]Update doc and minor correction in the mllib evaluation metrics #23589

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[SPARK-26351][mllib]Update doc and minor correction in the mllib evaluation metrics #23589

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update doc for evaluation metrics
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12 changes: 6 additions & 6 deletions docs/mllib-evaluation-metrics.md
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Expand Up @@ -439,21 +439,21 @@ $$rel_D(r) = \begin{cases}1 & \text{if $r \in D$}, \\ 0 & \text{otherwise}.\end{
Precision at k
</td>
<td>
$p(k)=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{k} \sum_{j=0}^{\text{min}(\left|D\right|, k) - 1} rel_{D_i}(R_i(j))}$
$p(k)=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{k} \sum_{j=0}^{\text{min}(\left|R_i\right|, k) - 1} rel_{D_i}(R_i(j))}$
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@srowen srowen Jan 19, 2019

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Although we usually have k <= |D| and k <= |R_i|, I agree that this is technically what must have been meant. How about using Q here instead of |R_i|? it was already used in the following formula. You can change both, sure, either way, as long as they're consistent.

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@shahidki31 shahidki31 Jan 19, 2019

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Actually the Q will vary with i, that is why I gave the notation |R_i|.

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@srowen srowen Jan 19, 2019

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Maybe; it could be the same for all users, or not. The documentation above this suggests there are equal numbers of recommended and relevant docs for each user (Q and N) but at least, it will almost never be true that |D_i| is the same for all users. Q could well be a constant.

But the implementation doesn't assume that and it's not necessary to, so I might even just remove the references to Q and N, or label them "Q_i" and "N_i" if you really want to be complete.

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@shahidki31 shahidki31 Jan 20, 2019

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Thanks. updated.

</td>
<td>
<a href="https://en.wikipedia.org/wiki/Information_retrieval#Precision_at_K">Precision at k</a> is a measure of
<a href="https://en.wikipedia.org/wiki/Evaluation_measures_(information_retrieval)#Precision_at_K">Precision at k</a> is a measure of
how many of the first k recommended documents are in the set of true relevant documents averaged across all
users. In this metric, the order of the recommendations is not taken into account.
</td>
</tr>
<tr>
<td>Mean Average Precision</td>
<td>
$MAP=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{\left|D_i\right|} \sum_{j=0}^{Q-1} \frac{rel_{D_i}(R_i(j))}{j + 1}}$
$MAP=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{\left|R_i\right|} \sum_{j=0}^{\left|R_i\right|-1} \frac{rel_{D_i}(R_i(j))}{j + 1}}$
</td>
<td>
<a href="https://en.wikipedia.org/wiki/Information_retrieval#Mean_average_precision">MAP</a> is a measure of how
<a href="https://en.wikipedia.org/wiki/Evaluation_measures_(information_retrieval)#Mean_average_precision">MAP</a> is a measure of how
many of the recommended documents are in the set of true relevant documents, where the
order of the recommendations is taken into account (i.e. penalty for highly relevant documents is higher).
</td>
Expand All @@ -462,10 +462,10 @@ $$rel_D(r) = \begin{cases}1 & \text{if $r \in D$}, \\ 0 & \text{otherwise}.\end{
<td>Normalized Discounted Cumulative Gain</td>
<td>
$NDCG(k)=\frac{1}{M} \sum_{i=0}^{M-1} {\frac{1}{IDCG(D_i, k)}\sum_{j=0}^{n-1}
\frac{rel_{D_i}(R_i(j))}{\text{ln}(j+2)}} \\
\frac{rel_{D_i}(R_i(j))}{log_2(j+2)}} \\
\text{Where} \\
\hspace{5 mm} n = \text{min}\left(\text{max}\left(|R_i|,|D_i|\right),k\right) \\
\hspace{5 mm} IDCG(D, k) = \sum_{j=0}^{\text{min}(\left|D\right|, k) - 1} \frac{1}{\text{ln}(j+2)}$
\hspace{5 mm} IDCG(D, k) = \sum_{j=0}^{\text{min}(\left|D\right|, k) - 1} \frac{1}{log_2(j+2)}$
</td>
<td>
<a href="https://en.wikipedia.org/wiki/Discounted_cumulative_gain#Normalized_DCG">NDCG at k</a> is a
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4 changes: 3 additions & 1 deletion mllib/src/main/scala/org/apache/spark/mllib/evaluation/RankingMetrics.scala
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Expand Up @@ -100,7 +100,7 @@ class RankingMetrics[T: ClassTag](predictionAndLabels: RDD[(Array[T], Array[T])]
}
i += 1
}
precSum / labSet.size
precSum / n
} else {
logWarning("Empty ground truth set, check input data")
0.0
Expand Down Expand Up @@ -138,6 +138,8 @@ class RankingMetrics[T: ClassTag](predictionAndLabels: RDD[(Array[T], Array[T])]
var dcg = 0.0
var i = 0
while (i < n) {
// Base of the log doesn't matter for calculating NDCG,
// if the relevance value is binary.
val gain = 1.0 / math.log(i + 2)
if (i < pred.length && labSet.contains(pred(i))) {
dcg += gain
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2 changes: 1 addition & 1 deletion mllib/src/test/java/org/apache/spark/mllib/evaluation/JavaRankingMetricsSuite.java
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Expand Up @@ -49,7 +49,7 @@ public void setUp() throws IOException {
public void rankingMetrics() {
@SuppressWarnings("unchecked")
RankingMetrics<?> metrics = RankingMetrics.of(predictionAndLabels);
Assert.assertEquals(0.355026, metrics.meanAveragePrecision(), 1e-5);
Assert.assertEquals(0.147989, metrics.meanAveragePrecision(), 1e-5);
Assert.assertEquals(0.75 / 3.0, metrics.precisionAt(4), 1e-5);
}
}
2 changes: 1 addition & 1 deletion mllib/src/test/scala/org/apache/spark/mllib/evaluation/RankingMetricsSuite.scala
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Expand Up @@ -43,7 +43,7 @@ class RankingMetricsSuite extends SparkFunSuite with MLlibTestSparkContext {
assert(metrics.precisionAt(10) ~== 0.8/3 absTol eps)
assert(metrics.precisionAt(15) ~== 8.0/45 absTol eps)

assert(map ~== 0.355026 absTol eps)
assert(map ~== 0.147989 absTol eps)

assert(metrics.ndcgAt(3) ~== 1.0/3 absTol eps)
assert(metrics.ndcgAt(5) ~== 0.328788 absTol eps)
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2 changes: 1 addition & 1 deletion python/pyspark/mllib/evaluation.py
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Expand Up @@ -324,7 +324,7 @@ class RankingMetrics(JavaModelWrapper):
>>> metrics.precisionAt(15)
0.17...
>>> metrics.meanAveragePrecision
0.35...
0.14...
>>> metrics.ndcgAt(3)
0.33...
>>> metrics.ndcgAt(10)
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