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Introduction + + </a> + + + + </li> + + <li class="chapter " data-level="1.2" data-path="../getting_started/"> + + <a href="../getting_started/"> + + + <b>1.2.</b> + + Getting Started + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="1.2.1" data-path="../getting_started/installation.html"> + + <a href="../getting_started/installation.html"> + + + <b>1.2.1.</b> + + Installation + + </a> + + + + </li> + + <li class="chapter " data-level="1.2.2" data-path="../getting_started/permanent-functions.html"> + + <a href="../getting_started/permanent-functions.html"> + + + <b>1.2.2.</b> + + Install as permanent functions + + </a> + + + + </li> + + <li class="chapter " data-level="1.2.3" data-path="../getting_started/input-format.html"> + + <a href="../getting_started/input-format.html"> + + + <b>1.2.3.</b> + + Input Format + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="1.3" data-path="../tips/"> + + <a href="../tips/"> + + + <b>1.3.</b> + + Tips for Effective Hivemall + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="1.3.1" data-path="../tips/addbias.html"> + + <a href="../tips/addbias.html"> + + + <b>1.3.1.</b> + + Explicit addBias() for better prediction + + </a> + + + + </li> + + <li class="chapter " data-level="1.3.2" data-path="../tips/rand_amplify.html"> + + <a href="../tips/rand_amplify.html"> + + + <b>1.3.2.</b> + + Use rand_amplify() to better prediction results + + </a> + + + + </li> + + <li class="chapter " data-level="1.3.3" data-path="../tips/rt_prediction.html"> + + <a href="../tips/rt_prediction.html"> + + + <b>1.3.3.</b> + + Real-time Prediction on RDBMS + + </a> + + + + </li> + + <li class="chapter " data-level="1.3.4" data-path="../tips/ensemble_learning.html"> + + <a href="../tips/ensemble_learning.html"> + + + <b>1.3.4.</b> + + Ensemble learning for stable prediction + + </a> + + + + </li> + + <li class="chapter " data-level="1.3.5" data-path="../tips/mixserver.html"> + + <a href="../tips/mixserver.html"> + + + <b>1.3.5.</b> + + Mixing models for a better prediction convergence (MIX server) + + </a> + + + + </li> + + <li class="chapter " data-level="1.3.6" data-path="../tips/emr.html"> + + <a href="../tips/emr.html"> + + + <b>1.3.6.</b> + + Run Hivemall on Amazon Elastic MapReduce + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="1.4" data-path="../tips/general_tips.html"> + + <a href="../tips/general_tips.html"> + + + <b>1.4.</b> + + General Hive/Hadoop tips + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="1.4.1" data-path="../tips/rowid.html"> + + <a href="../tips/rowid.html"> + + + <b>1.4.1.</b> + + Adding rowid for each row + + </a> + + + + </li> + + <li class="chapter " data-level="1.4.2" data-path="../tips/hadoop_tuning.html"> + + <a href="../tips/hadoop_tuning.html"> + + + <b>1.4.2.</b> + + Hadoop tuning for Hivemall + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="1.5" data-path="../troubleshooting/"> + + <a href="../troubleshooting/"> + + + <b>1.5.</b> + + Troubleshooting + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="1.5.1" data-path="../troubleshooting/oom.html"> + + <a href="../troubleshooting/oom.html"> + + + <b>1.5.1.</b> + + OutOfMemoryError in training + + </a> + + + + </li> + + <li class="chapter " data-level="1.5.2" data-path="../troubleshooting/mapjoin_task_error.html"> + + <a href="../troubleshooting/mapjoin_task_error.html"> + + + <b>1.5.2.</b> + + SemanticException Generate Map Join Task Error: Cannot serialize object + + </a> + + + + </li> + + <li class="chapter " data-level="1.5.3" data-path="../troubleshooting/asterisk.html"> + + <a href="../troubleshooting/asterisk.html"> + + + <b>1.5.3.</b> + + Asterisk argument for UDTF does not work + + </a> + + + + </li> + + <li class="chapter " data-level="1.5.4" data-path="../troubleshooting/num_mappers.html"> + + <a href="../troubleshooting/num_mappers.html"> + + + <b>1.5.4.</b> + + The number of mappers is less than input splits in Hadoop 2.x + + </a> + + + + </li> + + <li class="chapter " data-level="1.5.5" data-path="../troubleshooting/mapjoin_classcastex.html"> + + <a href="../troubleshooting/mapjoin_classcastex.html"> + + + <b>1.5.5.</b> + + Map-side Join causes ClassCastException on Tez + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part II - Generic Features</li> + + + + <li class="chapter " data-level="2.1" data-path="../misc/generic_funcs.html"> + + <a href="../misc/generic_funcs.html"> + + + <b>2.1.</b> + + List of generic Hivemall functions + + </a> + + + + </li> + + <li class="chapter " data-level="2.2" data-path="../misc/topk.html"> + + <a href="../misc/topk.html"> + + + <b>2.2.</b> + + Efficient Top-K query processing + + </a> + + + + </li> + + <li class="chapter " data-level="2.3" data-path="../misc/tokenizer.html"> + + <a href="../misc/tokenizer.html"> + + + <b>2.3.</b> + + English/Japanese Text Tokenizer + + </a> + + + + </li> + + + + + <li class="header">Part III - Feature Engineering</li> + + + + <li class="chapter " data-level="3.1" data-path="../ft_engineering/scaling.html"> + + <a href="../ft_engineering/scaling.html"> + + + <b>3.1.</b> + + Feature Scaling + + </a> + + + + </li> + + <li class="chapter " data-level="3.2" data-path="../ft_engineering/hashing.html"> + + <a href="../ft_engineering/hashing.html"> + + + <b>3.2.</b> + + Feature Hashing + + </a> + + + + </li> + + <li class="chapter " data-level="3.3" data-path="../ft_engineering/tfidf.html"> + + <a href="../ft_engineering/tfidf.html"> + + + <b>3.3.</b> + + TF-IDF calculation + + </a> + + + + </li> + + <li class="chapter " data-level="3.4" data-path="../ft_engineering/ft_trans.html"> + + <a href="../ft_engineering/ft_trans.html"> + + + <b>3.4.</b> + + FEATURE TRANSFORMATION + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="3.4.1" data-path="../ft_engineering/vectorizer.html"> + + <a href="../ft_engineering/vectorizer.html"> + + + <b>3.4.1.</b> + + Vectorize Features + + </a> + + + + </li> + + <li class="chapter " data-level="3.4.2" data-path="../ft_engineering/quantify.html"> + + <a href="../ft_engineering/quantify.html"> + + + <b>3.4.2.</b> + + Quantify non-number features + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="3.5" data-path="../ft_engineering/feature_selection.html"> + + <a href="../ft_engineering/feature_selection.html"> + + + <b>3.5.</b> + + Feature selection + + </a> + + + + </li> + + + + + <li class="header">Part IV - Evaluation</li> + + + + <li class="chapter " data-level="4.1" data-path="stat_eval.html"> + + <a href="stat_eval.html"> + + + <b>4.1.</b> + + Statistical evaluation of a prediction model + + </a> + + + + <ul class="articles"> + + + <li class="chapter active" data-level="4.1.1" data-path="auc.html"> + + <a href="auc.html"> + + + <b>4.1.1.</b> + + Area Under the ROC Curve + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="4.2" data-path="rank.html"> + + <a href="rank.html"> + + + <b>4.2.</b> + + Ranking Measures + + </a> + + + + </li> + + <li class="chapter " data-level="4.3" data-path="datagen.html"> + + <a href="datagen.html"> + + + <b>4.3.</b> + + Data Generation + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="4.3.1" data-path="lr_datagen.html"> + + <a href="lr_datagen.html"> + + + <b>4.3.1.</b> + + Logistic Regression data generation + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part V - Binary classification</li> + + + + <li class="chapter " data-level="5.1" data-path="../binaryclass/a9a.html"> + + <a href="../binaryclass/a9a.html"> + + + <b>5.1.</b> + + a9a Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="5.1.1" data-path="../binaryclass/a9a_dataset.html"> + + <a href="../binaryclass/a9a_dataset.html"> + + + <b>5.1.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="5.1.2" data-path="../binaryclass/a9a_lr.html"> + + <a href="../binaryclass/a9a_lr.html"> + + + <b>5.1.2.</b> + + Logistic Regression + + </a> + + + + </li> + + <li class="chapter " data-level="5.1.3" data-path="../binaryclass/a9a_minibatch.html"> + + <a href="../binaryclass/a9a_minibatch.html"> + + + <b>5.1.3.</b> + + Mini-batch Gradient Descent + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="5.2" data-path="../binaryclass/news20.html"> + + <a href="../binaryclass/news20.html"> + + + <b>5.2.</b> + + News20 Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="5.2.1" data-path="../binaryclass/news20_dataset.html"> + + <a href="../binaryclass/news20_dataset.html"> + + + <b>5.2.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="5.2.2" data-path="../binaryclass/news20_pa.html"> + + <a href="../binaryclass/news20_pa.html"> + + + <b>5.2.2.</b> + + Perceptron, Passive Aggressive + + </a> + + + + </li> + + <li class="chapter " data-level="5.2.3" data-path="../binaryclass/news20_scw.html"> + + <a href="../binaryclass/news20_scw.html"> + + + <b>5.2.3.</b> + + CW, AROW, SCW + + </a> + + + + </li> + + <li class="chapter " data-level="5.2.4" data-path="../binaryclass/news20_adagrad.html"> + + <a href="../binaryclass/news20_adagrad.html"> + + + <b>5.2.4.</b> + + AdaGradRDA, AdaGrad, AdaDelta + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="5.3" data-path="../binaryclass/kdd2010a.html"> + + <a href="../binaryclass/kdd2010a.html"> + + + <b>5.3.</b> + + KDD2010a Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="5.3.1" data-path="../binaryclass/kdd2010a_dataset.html"> + + <a href="../binaryclass/kdd2010a_dataset.html"> + + + <b>5.3.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="5.3.2" data-path="../binaryclass/kdd2010a_scw.html"> + + <a href="../binaryclass/kdd2010a_scw.html"> + + + <b>5.3.2.</b> + + PA, CW, AROW, SCW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="5.4" data-path="../binaryclass/kdd2010b.html"> + + <a href="../binaryclass/kdd2010b.html"> + + + <b>5.4.</b> + + KDD2010b Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="5.4.1" data-path="../binaryclass/kdd2010b_dataset.html"> + + <a href="../binaryclass/kdd2010b_dataset.html"> + + + <b>5.4.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="5.4.2" data-path="../binaryclass/kdd2010b_arow.html"> + + <a href="../binaryclass/kdd2010b_arow.html"> + + + <b>5.4.2.</b> + + AROW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="5.5" data-path="../binaryclass/webspam.html"> + + <a href="../binaryclass/webspam.html"> + + + <b>5.5.</b> + + Webspam Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="5.5.1" data-path="../binaryclass/webspam_dataset.html"> + + <a href="../binaryclass/webspam_dataset.html"> + + + <b>5.5.1.</b> + + Data pareparation + + </a> + + + + </li> + + <li class="chapter " data-level="5.5.2" data-path="../binaryclass/webspam_scw.html"> + + <a href="../binaryclass/webspam_scw.html"> + + + <b>5.5.2.</b> + + PA1, AROW, SCW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="5.6" data-path="../binaryclass/titanic_rf.html"> + + <a href="../binaryclass/titanic_rf.html"> + + + <b>5.6.</b> + + Kaggle Titanic Tutorial + + </a> + + + + </li> + + + + + <li class="header">Part VI - Multiclass classification</li> + + + + <li class="chapter " data-level="6.1" data-path="../multiclass/news20.html"> + + <a href="../multiclass/news20.html"> + + + <b>6.1.</b> + + News20 Multiclass Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="6.1.1" data-path="../multiclass/news20_dataset.html"> + + <a href="../multiclass/news20_dataset.html"> + + + <b>6.1.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="6.1.2" data-path="../multiclass/news20_one-vs-the-rest_dataset.html"> + + <a href="../multiclass/news20_one-vs-the-rest_dataset.html"> + + + <b>6.1.2.</b> + + Data preparation for one-vs-the-rest classifiers + + </a> + + + + </li> + + <li class="chapter " data-level="6.1.3" data-path="../multiclass/news20_pa.html"> + + <a href="../multiclass/news20_pa.html"> + + + <b>6.1.3.</b> + + PA + + </a> + + + + </li> + + <li class="chapter " data-level="6.1.4" data-path="../multiclass/news20_scw.html"> + + <a href="../multiclass/news20_scw.html"> + + + <b>6.1.4.</b> + + CW, AROW, SCW + + </a> + + + + </li> + + <li class="chapter " data-level="6.1.5" data-path="../multiclass/news20_ensemble.html"> + + <a href="../multiclass/news20_ensemble.html"> + + + <b>6.1.5.</b> + + Ensemble learning + + </a> + + + + </li> + + <li class="chapter " data-level="6.1.6" data-path="../multiclass/news20_one-vs-the-rest.html"> + + <a href="../multiclass/news20_one-vs-the-rest.html"> + + + <b>6.1.6.</b> + + one-vs-the-rest classifier + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="6.2" data-path="../multiclass/iris.html"> + + <a href="../multiclass/iris.html"> + + + <b>6.2.</b> + + Iris Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="6.2.1" data-path="../multiclass/iris_dataset.html"> + + <a href="../multiclass/iris_dataset.html"> + + + <b>6.2.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="6.2.2" data-path="../multiclass/iris_scw.html"> + + <a href="../multiclass/iris_scw.html"> + + + <b>6.2.2.</b> + + SCW + + </a> + + + + </li> + + <li class="chapter " data-level="6.2.3" data-path="../multiclass/iris_randomforest.html"> + + <a href="../multiclass/iris_randomforest.html"> + + + <b>6.2.3.</b> + + RandomForest + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part VII - Regression</li> + + + + <li class="chapter " data-level="7.1" data-path="../regression/e2006.html"> + + <a href="../regression/e2006.html"> + + + <b>7.1.</b> + + E2006-tfidf regression Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="7.1.1" data-path="../regression/e2006_dataset.html"> + + <a href="../regression/e2006_dataset.html"> + + + <b>7.1.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="7.1.2" data-path="../regression/e2006_arow.html"> + + <a href="../regression/e2006_arow.html"> + + + <b>7.1.2.</b> + + Passive Aggressive, AROW + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="7.2" data-path="../regression/kddcup12tr2.html"> + + <a href="../regression/kddcup12tr2.html"> + + + <b>7.2.</b> + + KDDCup 2012 track 2 CTR prediction Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="7.2.1" data-path="../regression/kddcup12tr2_dataset.html"> + + <a href="../regression/kddcup12tr2_dataset.html"> + + + <b>7.2.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="7.2.2" data-path="../regression/kddcup12tr2_lr.html"> + + <a href="../regression/kddcup12tr2_lr.html"> + + + <b>7.2.2.</b> + + Logistic Regression, Passive Aggressive + + </a> + + + + </li> + + <li class="chapter " data-level="7.2.3" data-path="../regression/kddcup12tr2_lr_amplify.html"> + + <a href="../regression/kddcup12tr2_lr_amplify.html"> + + + <b>7.2.3.</b> + + Logistic Regression with Amplifier + + </a> + + + + </li> + + <li class="chapter " data-level="7.2.4" data-path="../regression/kddcup12tr2_adagrad.html"> + + <a href="../regression/kddcup12tr2_adagrad.html"> + + + <b>7.2.4.</b> + + AdaGrad, AdaDelta + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part VIII - Recommendation</li> + + + + <li class="chapter " data-level="8.1" data-path="../recommend/cf.html"> + + <a href="../recommend/cf.html"> + + + <b>8.1.</b> + + Collaborative Filtering + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="8.1.1" data-path="../recommend/item_based_cf.html"> + + <a href="../recommend/item_based_cf.html"> + + + <b>8.1.1.</b> + + Item-based Collaborative Filtering + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="8.2" data-path="../recommend/news20.html"> + + <a href="../recommend/news20.html"> + + + <b>8.2.</b> + + News20 related article recommendation Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="8.2.1" data-path="../multiclass/news20_dataset.html"> + + <a href="../multiclass/news20_dataset.html"> + + + <b>8.2.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="8.2.2" data-path="../recommend/news20_jaccard.html"> + + <a href="../recommend/news20_jaccard.html"> + + + <b>8.2.2.</b> + + LSH/Minhash and Jaccard Similarity + + </a> + + + + </li> + + <li class="chapter " data-level="8.2.3" data-path="../recommend/news20_knn.html"> + + <a href="../recommend/news20_knn.html"> + + + <b>8.2.3.</b> + + LSH/Minhash and Brute-Force Search + + </a> + + + + </li> + + <li class="chapter " data-level="8.2.4" data-path="../recommend/news20_bbit_minhash.html"> + + <a href="../recommend/news20_bbit_minhash.html"> + + + <b>8.2.4.</b> + + kNN search using b-Bits Minhash + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="8.3" data-path="../recommend/movielens.html"> + + <a href="../recommend/movielens.html"> + + + <b>8.3.</b> + + MovieLens movie recommendation Tutorial + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="8.3.1" data-path="../recommend/movielens_dataset.html"> + + <a href="../recommend/movielens_dataset.html"> + + + <b>8.3.1.</b> + + Data preparation + + </a> + + + + </li> + + <li class="chapter " data-level="8.3.2" data-path="../recommend/movielens_mf.html"> + + <a href="../recommend/movielens_mf.html"> + + + <b>8.3.2.</b> + + Matrix Factorization + + </a> + + + + </li> + + <li class="chapter " data-level="8.3.3" data-path="../recommend/movielens_fm.html"> + + <a href="../recommend/movielens_fm.html"> + + + <b>8.3.3.</b> + + Factorization Machine + + </a> + + + + </li> + + <li class="chapter " data-level="8.3.4" data-path="../recommend/movielens_cv.html"> + + <a href="../recommend/movielens_cv.html"> + + + <b>8.3.4.</b> + + 10-fold Cross Validation (Matrix Factorization) + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part IX - Anomaly Detection</li> + + + + <li class="chapter " data-level="9.1" data-path="../anomaly/lof.html"> + + <a href="../anomaly/lof.html"> + + + <b>9.1.</b> + + Outlier Detection using Local Outlier Factor (LOF) + + </a> + + + + </li> + + <li class="chapter " data-level="9.2" data-path="../anomaly/sst.html"> + + <a href="../anomaly/sst.html"> + + + <b>9.2.</b> + + Change-Point Detection using Singular Spectrum Transformation (SST) + + </a> + + + + </li> + + <li class="chapter " data-level="9.3" data-path="../anomaly/changefinder.html"> + + <a href="../anomaly/changefinder.html"> + + + <b>9.3.</b> + + ChangeFinder: Detecting Outlier and Change-Point Simultaneously + + </a> + + + + </li> + + + + + <li class="header">Part X - Hivemall on Spark</li> + + + + <li class="chapter " data-level="10.1" data-path="../spark/binaryclass/"> + + <a href="../spark/binaryclass/"> + + + <b>10.1.</b> + + Binary Classification + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="10.1.1" data-path="../spark/binaryclass/a9a_df.html"> + + <a href="../spark/binaryclass/a9a_df.html"> + + + <b>10.1.1.</b> + + a9a Tutorial for DataFrame + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="10.2" data-path="../spark/binaryclass/"> + + <a href="../spark/binaryclass/"> + + + <b>10.2.</b> + + Regression + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="10.2.1" data-path="../spark/regression/e2006_df.html"> + + <a href="../spark/regression/e2006_df.html"> + + + <b>10.2.1.</b> + + E2006-tfidf regression Tutorial for DataFrame + + </a> + + + + </li> + + + </ul> + + </li> + + <li class="chapter " data-level="10.3" data-path="../spark/misc/misc.html"> + + <a href="../spark/misc/misc.html"> + + + <b>10.3.</b> + + Generic features + + </a> + + + + <ul class="articles"> + + + <li class="chapter " data-level="10.3.1" data-path="../spark/misc/topk_join.html"> + + <a href="../spark/misc/topk_join.html"> + + + <b>10.3.1.</b> + + Top-k Join processing + + </a> + + + + </li> + + + </ul> + + </li> + + + + + <li class="header">Part X - External References</li> + + + + <li class="chapter " data-level="11.1" > + + <a target="_blank" href="https://github.com/maropu/hivemall-spark";> + + + <b>11.1.</b> + + Hivemall on Apache Spark + + </a> + + + + </li> + + <li class="chapter " data-level="11.2" > + + <a target="_blank" href="https://github.com/daijyc/hivemall/wiki/PigHome";> + + + <b>11.2.</b> + + Hivemall on Apache Pig + + </a> + + + + </li> + + + + + <li class="divider"></li> + + <li> + <a href="https://www.gitbook.com"; target="blank" class="gitbook-link"> + Published with GitBook + </a> + </li> +</ul> + + + </nav> + + + </div> + + <div class="book-body"> + + <div class="body-inner"> + + + +<div class="book-header" role="navigation"> + + + <!-- Title --> + <h1> + <i class="fa fa-circle-o-notch fa-spin"></i> + <a href=".." >Area Under the ROC Curve</a> + </h1> +</div> + + + + + <div class="page-wrapper" tabindex="-1" role="main"> + <div class="page-inner"> + +<div id="book-search-results"> + <div class="search-noresults"> + + <section class="normal markdown-section"> + + <!-- + Licensed to the Apache Software Foundation (ASF) under one + or more contributor license agreements. See the NOTICE file + distributed with this work for additional information + regarding copyright ownership. The ASF licenses this file + to you under the Apache License, Version 2.0 (the + "License"); you may not use this file except in compliance + with the License. You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, + software distributed under the License is distributed on an + "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + KIND, either express or implied. See the License for the + specific language governing permissions and limitations + under the License. +--> +<!-- toc --><div id="toc" class="toc"> + +<ul> +<li><a href="#area-under-the-roc-curve">Area Under the ROC Curve</a></li> +<li><a href="#compute-auc-on-hivemall">Compute AUC on Hivemall</a></li> +<li><a href="#difference-between-auc-and-logarithmic-loss">Difference between AUC and Logarithmic Loss</a></li> +</ul> + +</div><!-- tocstop --> +<h1 id="area-under-the-roc-curve">Area Under the ROC Curve</h1> +<p><a href="https://en.wikipedia.org/wiki/Receiver_operating_characteristic"; target="_blank">ROC curve</a> and Area Under the ROC Curve (AUC) are widely-used metric for binary (i.e., positive or negative) classification problems such as <a href="../binaryclass/a9a_lr.html">Logistic Regression</a>.</p> +<p>Binary classifiers generally predict how likely a sample is to be positive by computing probability. Ultimately, we can evaluate the classifiers by comparing the probabilities with truth positive/negative labels.</p> +<p>Now we assume that there is a table which contains predicted scores (i.e., probabilities) and truth labels as follows:</p> +<table> +<thead> +<tr> +<th style="text-align:center">probability<br>(predicted score)</th> +<th style="text-align:center">truth label</th> +</tr> +</thead> +<tbody> +<tr> +<td style="text-align:center">0.5</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">0.3</td> +<td style="text-align:center">1</td> +</tr> +<tr> +<td style="text-align:center">0.2</td> +<td style="text-align:center">0</td> +</tr> +<tr> +<td style="text-align:center">0.8</td> +<td style="text-align:center">1</td> +</tr> +<tr> +<td style="text-align:center">0.7</td> +<td style="text-align:center">1</td> +</tr> +</tbody> +</table> +<p>Once the rows are sorted by the probabilities in a descending order, AUC gives a metric based on how many positive (<code>label=1</code>) samples are ranked higher than negative (<code>label=0</code>) samples. If many positive rows get larger scores than negative rows, AUC would be large, and hence our classifier would perform well.</p> +<h1 id="compute-auc-on-hivemall">Compute AUC on Hivemall</h1> +<p>In Hivemall, a function <code>auc(double score, int label)</code> provides a way to compute AUC for pairs of probability and truth label.</p> +<p>For instance, following query computes AUC of the table which was shown above:</p> +<pre><code class="lang-sql">with data as ( + <span class="hljs-keyword">select</span> <span class="hljs-number">0.5</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">0</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.3</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">1</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.2</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">0</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.8</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">1</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.7</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">1</span> <span class="hljs-keyword">as</span> label +) +<span class="hljs-keyword">select</span> + auc(prob, label) <span class="hljs-keyword">as</span> auc +<span class="hljs-keyword">from</span> ( + <span class="hljs-keyword">select</span> prob, label + <span class="hljs-keyword">from</span> <span class="hljs-keyword">data</span> + <span class="hljs-keyword">ORDER</span> <span class="hljs-keyword">BY</span> prob <span class="hljs-keyword">DESC</span> +) t; +</code></pre> +<p>This query returns <code>0.83333</code> as AUC.</p> +<p>Since AUC is a metric based on ranked probability-label pairs as mentioned above, input data (rows) needs to be ordered by scores in a descending order.</p> +<p>Meanwhile, Hive's <code>distribute by</code> clause allows you to compute AUC in parallel: </p> +<pre><code class="lang-sql">with data as ( + <span class="hljs-keyword">select</span> <span class="hljs-number">0.5</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">0</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.3</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">1</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.2</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">0</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.8</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">1</span> <span class="hljs-keyword">as</span> label + <span class="hljs-keyword">union</span> all + <span class="hljs-keyword">select</span> <span class="hljs-number">0.7</span> <span class="hljs-keyword">as</span> prob, <span class="hljs-number">1</span> <span class="hljs-keyword">as</span> label +) +<span class="hljs-keyword">select</span> auc(prob, label) <span class="hljs-keyword">as</span> auc +<span class="hljs-keyword">from</span> ( + <span class="hljs-keyword">select</span> prob, label + <span class="hljs-keyword">from</span> <span class="hljs-keyword">data</span> + <span class="hljs-keyword">DISTRIBUTE</span> <span class="hljs-keyword">BY</span> <span class="hljs-keyword">floor</span>(prob / <span class="hljs-number">0.2</span>) + <span class="hljs-keyword">SORT</span> <span class="hljs-keyword">BY</span> prob <span class="hljs-keyword">DESC</span> +) t; +</code></pre> +<p>Note that <code>floor(prob / 0.2)</code> means that the rows are distributed to 5 bins for the AUC computation because the column <code>prob</code> is in a [0, 1] range.</p> +<h1 id="difference-between-auc-and-logarithmic-loss">Difference between AUC and Logarithmic Loss</h1> +<p>Hivemall has another metric called <a href="stat_eval.html#logarithmic-loss">Logarithmic Loss</a> for binary classification. Both AUC and Logarithmic Loss compute scores for probability-label pairs. </p> +<p>Score produced by AUC is a relative metric based on sorted pairs. On the other hand, Logarithmic Loss simply gives a metric by comparing probability with its truth label one-by-one.</p> +<p>To give an example, <code>auc(prob, label)</code> and <code>logloss(prob, label)</code> respectively returns <code>0.83333</code> and <code>0.54001</code> in the above case. Note that larger AUC and smaller Logarithmic Loss are better.</p> +<p><div id="page-footer"><hr><!-- + Licensed to the Apache Software Foundation (ASF) under one + or more contributor license agreements. See the NOTICE file + distributed with this work for additional information + regarding copyright ownership. The ASF licenses this file + to you under the Apache License, Version 2.0 (the + "License"); you may not use this file except in compliance + with the License. You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, + software distributed under the License is distributed on an + "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + KIND, either express or implied. See the License for the + specific language governing permissions and limitations + under the License. +--> +<p><sub><font color="gray"> +Apache Hivemall is an effort undergoing incubation at The Apache Software Foundation (ASF), sponsored by the Apache Incubator. +</font></sub></p> +</div></p> + + + </section> + + </div> + <div class="search-results"> + <div class="has-results"> + + <h1 class="search-results-title"><span class='search-results-count'></span> results matching "<span class='search-query'></span>"</h1> + <ul class="search-results-list"></ul> + + </div> + <div class="no-results"> + + <h1 class="search-results-title">No results matching "<span class='search-query'></span>"</h1> + + </div> + </div> +</div> + + </div> + </div> + + </div> + + + + + </div> + + <script> + var gitbook = gitbook || []; + gitbook.push(function() { + gitbook.page.hasChanged({"page":{"title":"Area Under the ROC Curve","level":"4.1.1","depth":2,"next":{"title":"Ranking Measures","level":"4.2","depth":1,"path":"eval/rank.md","ref":"eval/rank.md","articles":[]},"previous":{"title":"Statistical evaluation of a prediction model","level":"4.1","depth":1,"path":"eval/stat_eval.md","ref":"eval/stat_eval.md","articles":[{"title":"Area Under the ROC Curve","level":"4.1.1","depth":2,"path":"eval/auc.md","ref":"eval/auc.md","articles":[]}]},"dir":"ltr"},"config":{"plugins":["theme-api","edit-link","github","splitter","sitemap","etoc","callouts","toggle-chapters","anchorjs","codeblock-filename","expandable-chapters","multipart","codeblock-filename","katex","emphasize","localized-footer"],"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/ebook.css","print":"styles/print.css"},"pluginsConfig":{"emphasize":{},"callouts":{},"etoc":{"maxdepth":3,"mindepth": 1,"notoc":true},"github":{"url":"https://github.com/apache/incubator-hivemall/"},"splitter":{},"search":{},"downloadpdf":{"base":"https://github.com/apache/incubator-hivemall/docs/gitbook","label":"PDF","multilingual":false},"multipart":{},"localized-footer":{"filename":"FOOTER.md"},"lunr":{"maxIndexSize":1000000,"ignoreSpecialCharacters":false},"katex":{},"fontsettings":{"theme":"white","family":"sans","size":2,"font":"sans"},"highlight":{},"codeblock-filename":{},"sitemap":{"hostname":"http://hivemall.incubator.apache.org/"},"theme-api":{"languages":[],"split":false,"theme":"dark"},"sharing":{"facebook":true,"twitter":true,"google":false,"weibo":false,"instapaper":false,"vk":false,"all":["facebook","google","twitter","weibo","instapaper"]},"edit-link":{"label":"Edit","base":"https://github.com/apache/incubator-hivemall/docs/gitbook"},"theme-default":{"styles":{"website":"styles/website.css","pdf":"styles/pdf.css","epub":"styles/epub.css","mobi":"styles/mobi.css","ebook":"styles/eb ook.css","print":"styles/print.css"},"showLevel":true},"anchorjs":{"selector":"h1,h2,h3,*:not(.callout) > h4,h5"},"toggle-chapters":{},"expandable-chapters":{}},"theme":"default","pdf":{"pageNumbers":true,"fontSize":12,"fontFamily":"Arial","paperSize":"a4","chapterMark":"pagebreak","pageBreaksBefore":"/","margin":{"right":62,"left":62,"top":56,"bottom":56}},"structure":{"langs":"LANGS.md","readme":"README.md","glossary":"GLOSSARY.md","summary":"SUMMARY.md"},"variables":{},"title":"Hivemall User Manual","links":{"sidebar":{"<i class=\"fa fa-home\"></i> Home":"http://hivemall.incubator.apache.org/"}},"gitbook":"3.x.x","description":"User Manual for Apache Hivemall"},"file":{"path":"eval/auc.md","mtime":"2017-02-28T11:04:12.000Z","type":"markdown"},"gitbook":{"version":"3.2.2","time":"2017-03-02T07:07:17.486Z"},"basePath":"..","book":{"language":""}}); 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