[08/23] incubator-hivemall-site git commit: Updated userguide for evaluation section

[my...@apache.org]

http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/blob/a98b42f8/userguide/recommend/movielens_cf.html
----------------------------------------------------------------------
diff --git a/userguide/recommend/movielens_cf.html b/userguide/recommend/movielens_cf.html
index 627c7c9..19abd6a 100644
--- a/userguide/recommend/movielens_cf.html
+++ b/userguide/recommend/movielens_cf.html
@@ -244,7 +244,7 @@
                     
                         <b>1.3.1.</b>
                     
-                    Explicit addBias() for better prediction
+                    Explicit add_bias() for better prediction
             
                 </a>
             
@@ -707,14 +707,14 @@
         
         
     
-        <li class="chapter " data-level="4.1" data-path="../eval/stat_eval.html">
+        <li class="chapter " data-level="4.1" data-path="../eval/binary_classification_measures.html">
             
-                <a href="../eval/stat_eval.html">
+                <a href="../eval/binary_classification_measures.html">
             
                     
                         <b>4.1.</b>
                     
-                    Statistical evaluation of a prediction model
+                    Binary Classification Metrics
             
                 </a>
             
@@ -743,13 +743,43 @@
             
         </li>
     
-        <li class="chapter " data-level="4.2" data-path="../eval/rank.html">
+        <li class="chapter " data-level="4.2" data-path="../eval/multilabel_classification_measures.html">
             
-                <a href="../eval/rank.html">
+                <a href="../eval/multilabel_classification_measures.html">
             
                     
                         <b>4.2.</b>
                     
+                    Multi-label Classification Metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.3" data-path="../eval/regression.html">
+            
+                <a href="../eval/regression.html">
+            
+                    
+                        <b>4.3.</b>
+                    
+                    Regression metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.4" data-path="../eval/rank.html">
+            
+                <a href="../eval/rank.html">
+            
+                    
+                        <b>4.4.</b>
+                    
                     Ranking Measures
             
                 </a>
@@ -758,12 +788,12 @@
             
         </li>
     
-        <li class="chapter " data-level="4.3" data-path="../eval/datagen.html">
+        <li class="chapter " data-level="4.5" data-path="../eval/datagen.html">
             
                 <a href="../eval/datagen.html">
             
                     
-                        <b>4.3.</b>
+                        <b>4.5.</b>
                     
                     Data Generation
             
@@ -774,12 +804,12 @@
             <ul class="articles">
                 
     
-        <li class="chapter " data-level="4.3.1" data-path="../eval/lr_datagen.html">
+        <li class="chapter " data-level="4.5.1" data-path="../eval/lr_datagen.html">
             
                 <a href="../eval/lr_datagen.html">
             
                     
-                        <b>4.3.1.</b>
+                        <b>4.5.1.</b>
                     
                     Logistic Regression data generation
             
@@ -2166,6 +2196,7 @@
 </ul>
 
 </div><!-- tocstop -->
+<div class="panel panel-warning"><div class="panel-heading"><h3 class="panel-title" id="caution"><i class="fa fa-exclamation-triangle"></i> Caution</h3></div><div class="panel-body"><p>In order to obtain ranked list of items, this page introduces queries using <code>to_ordered_map()</code> such as <code>map_values(to_ordered_map(rating, movieid, true))</code>. However, this kind of usage has a potential issue that multiple <code>movieid</code>-s (i.e., values) which have the exactly same <code>rating</code> (i.e., key) will be aggregated to single arbitrary <code>movieid</code>, because <code>to_ordered_map()</code> creates a key-value map which uses duplicated <code>rating</code> as key.</p><p>Hence, if map key could duplicate on more then one map values, we recommend you to use <code>to_ordered_list(value, key, &apos;-reverse&apos;)</code> instead of <code>map_values(to_ordered_map(key, value, true))</code>. The alternative approach is available from Hivemall v0.5-rc.1 or later.</
 p></div></div>
 <h1 id="compute-movie-movie-similarity">Compute movie-movie similarity</h1>
 <p><a href="item_based_cf.html#dimsum-approximated-all-pairs-cosine-similarity-computation.md">As we explained in the general introduction of item-based CF</a>, following query finds top-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span></span> nearest-neighborhood movies for each movie:</p>
 <pre><code class="lang-sql"><span class="hljs-keyword">drop</span> <span class="hljs-keyword">table</span> <span class="hljs-keyword">if</span> <span class="hljs-keyword">exists</span> dimsum_movie_similarity;
@@ -2353,8 +2384,8 @@ topk <span class="hljs-keyword">as</span> (
 <p>Theoretically, for the <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.61508em;"></span><span class="strut bottom" style="height:0.61508em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">t</span></span></span></span>-th nearest-neighborhood item <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>&#x3C4;</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">\tau(t)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.1132em;">&#x3C4;</span><span class=
 "mopen">(</span><span class="mord mathit">t</span><span class="mclose">)</span></span></span></span>, prediction can be done by top-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span></span> weighted sum of target user&apos;s historical ratings:
 <span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>r</mi><mrow><mi>u</mi><mo separator="true">,</mo><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msubsup><mo>&#x2211;</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></msubsup><msub><mi>s</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>&#x3C4;</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub><mo>&#x22C5;</mo><msub><mi>r</mi><mrow><mi>u</mi><mo separator="true">,</mo><mi>&#x3C4;</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub></mrow><mrow><msubsup><mo>&#x2211;</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></msubsup><msub><mi>s</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>&#x3C4;</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msub></mrow></mfrac><mo separator="true">,</mo></mrow><annotation encoding="application/x-tex">
 r_{u,i} = \frac{\sum^k_{t=1} s_{i,\tau(t)} \cdot r_{u,\tau(t)} }{ \sum^k_{t=1} s_{i,\tau(t)} },
-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.5953079999999997em;"></span><span class="strut bottom" style="height:2.6906159999999995em;vertical-align:-1.0953079999999997em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">u</span><span class="mpunct">,</span><span class="mord mathit">i</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mrel">=</span><span class="mord reset-te
 xtstyle displaystyle textstyle uncramped"><span class="sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.7401079999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mop"><span class="op-symbol small-op mop" style="top:-0.0000050000000000050004em;">&#x2211;</span><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">t</span><span class="mrel">=</span><span class="mord mathrm">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 siz
 e5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mord"><span class="mord mathit">s</span><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">i</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.1132em;">&#x3C4;</span><span class="mopen">(</span><span class="mord mathit">t</span><span class="mclose">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 si
 ze5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.7451999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mop"><span class="op-symbol small-op mop" style="top:-0.0000050000000000050004em;">&#x2211;</span><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">t</span><span class="mrel">=</span
 ><span class="mord mathrm">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mord"><span class="mord mathit">s</span><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">i</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.1132em;">&#x3C4;</span><span class="mopen">(</span><spa
 n class="mord mathit">t</span><span class="mclose">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mbin">&#x22C5;</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">u</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.1132em;">&#x3C4;</span><span class="mopen">(</span><span class="mord mathit">t</span><span class="mclose">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;
 ">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mpunct">,</span></span></span></span></span>
-where <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>r</mi><mrow><mi>u</mi><mo separator="true">,</mo><mi>i</mi></mrow></msub></mrow><annotation encoding="application/x-tex">r_{u,i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">u</span><span class="mpunct">,</span><span class="mord mathit">i</span></span></span></span><span class="baseline-fix"><span class=
 "fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span> is user <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">u</span></span></span></span>&apos;s rating for item (movie) <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;vertical-align:0em;"></span><span class="base textstyle uncrampe
 d"><span class="mord mathit">i</span></span></span></span>, and <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>s</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">s_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">s</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit">i</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.05724em;">j</span></span></
 span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span> is similarity of <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span></span></span></span>-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.85396em;vertical-align:-0.19444em;"></span>
 <span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.05724em;">j</span></span></span></span> (<code>movieid</code>-<code>other</code>) pair.</p>
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:1.5953079999999997em;"></span><span class="strut bottom" style="height:2.6906159999999995em;vertical-align:-1.0953079999999997em;"></span><span class="base displaystyle textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">u</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">i</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></s
 pan></span><span class="mrel">=</span><span class="mord reset-textstyle displaystyle textstyle uncramped"><span class="mopen sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span><span class="mfrac"><span class="vlist"><span style="top:0.7401079999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">&#x2211;</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">t</span><span class="mrel mtight">=</span><span class="mord mathrm mti
 ght">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">s</span><span class="msupsub"><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.1
 132em;">&#x3C4;</span><span class="mopen mtight">(</span><span class="mord mathit mtight">t</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.7451999999999999em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">&#x2211;</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.0
 5em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">t</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mord"><span class="mord mathit">s</span><span class="msupsub"><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-
 ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="mopen mtight">(</span><span class="mord mathit mtight">t</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mbin">&#x22C5;</span><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist"><span style="top:0.18019999999999992em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-t
 extstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">u</span><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.1132em;">&#x3C4;</span><span class="mopen mtight">(</span><span class="mord mathit mtight">t</span><span class="mclose mtight">)</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span><span class="mclose sizing reset-size5 size5 reset-textstyle textstyle uncramped nulldelimiter"></span></span><span class="mpunct">,</span></span></span></span></span>
+where <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>r</mi><mrow><mi>u</mi><mo separator="true">,</mo><mi>i</mi></mrow></msub></mrow><annotation encoding="application/x-tex">r_{u,i}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.02778em;">r</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.02778em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">u</span><span class="mpunct mtight">,</span><span class="mord mathit mtight">i</span></s
 pan></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> is user <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>u</mi></mrow><annotation encoding="application/x-tex">u</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.43056em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">u</span></span></span></span>&apos;s rating for item (movie) <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;
 vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span></span></span></span>, and <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>s</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">s_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">s</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</sp
 an><span class="mpunct mtight">,</span><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span></span></span></span> is similarity of <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span></span></span></span>-<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class
 ="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.05724em;">j</span></span></span></span> (<code>movieid</code>-<code>other</code>) pair.</p>
 <div class="panel panel-warning"><div class="panel-heading"><h3 class="panel-title" id="caution"><i class="fa fa-exclamation-triangle"></i> Caution</h3></div><div class="panel-body"><p>Since the number of similarities and users&apos; past ratings are limited, we cannot say this output <strong>always</strong> contains prediction for <strong>every</strong> unforeseen user-item pairs; sometimes prediction for a specific user-item pair might be missing (i.e., <code>NULL</code>).</p></div></div>
 <p>In fact, our goal is to make recommendation, but we can evaluate the intermediate result as a rating prediction problem:</p>
 <pre><code class="lang-sql"><span class="hljs-keyword">select</span>
@@ -2445,8 +2476,8 @@ where <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msu
     userid
 )
 <span class="hljs-keyword">select</span> 
-  recall(t1.rec_movies, t2.truth, <span class="hljs-number">10</span>) <span class="hljs-keyword">as</span> recall,
-  <span class="hljs-keyword">precision</span>(t1.rec_movies, t2.truth, <span class="hljs-number">10</span>) <span class="hljs-keyword">as</span> <span class="hljs-keyword">precision</span>,
+  recall_at(t1.rec_movies, t2.truth, <span class="hljs-number">10</span>) <span class="hljs-keyword">as</span> recall,
+  precision_at(t1.rec_movies, t2.truth, <span class="hljs-number">10</span>) <span class="hljs-keyword">as</span> <span class="hljs-keyword">precision</span>,
   average_precision(t1.rec_movies, t2.truth) <span class="hljs-keyword">as</span> average_precision,
   auc(t1.rec_movies, t2.truth) <span class="hljs-keyword">as</span> auc,
   mrr(t1.rec_movies, t2.truth) <span class="hljs-keyword">as</span> mrr,
@@ -2493,8 +2524,9 @@ where <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msu
 </tr>
 </tbody>
 </table>
-<p>If you set larger value to the DIMSUM&apos;s <code>-threshold</code> option, similarity will be more aggressively approximated. Consequently, while efficiency is improved, the accuracy is likely to be decreased.
-<div id="page-footer" class="localized-footer"><hr><!--
+<p>If you set larger value to the DIMSUM&apos;s <code>-threshold</code> option, similarity will be more aggressively approximated. Consequently, while efficiency is improved, the accuracy is likely to be decreased.</p>
+<div class="panel panel-warning"><div class="panel-heading"><h3 class="panel-title" id="caution"><i class="fa fa-exclamation-triangle"></i> Caution</h3></div><div class="panel-body"><p>Before Hivemall v0.5-rc.1, <code>recall_at()</code> and <code>precision_at()</code> are respectively registered as <code>recall()</code> and <code>precision()</code>. However, since <code>precision</code> is a reserved keyword from Hive v2.2.0, <a href="https://issues.apache.org/jira/browse/HIVEMALL-140" target="_blank">we renamed the function names</a>. If you are still using <code>recall()</code> and/or <code>precision()</code>, we strongly recommend you to use the latest version of Hivemall and replace them with the newer function names.</p></div></div>
+<p><div id="page-footer" class="localized-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
@@ -2549,7 +2581,7 @@ Apache Hivemall is an effort undergoing incubation at The Apache Software Founda
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http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/blob/a98b42f8/userguide/recommend/movielens_cv.html
----------------------------------------------------------------------
diff --git a/userguide/recommend/movielens_cv.html b/userguide/recommend/movielens_cv.html
index d54823f..5d84ebe 100644
--- a/userguide/recommend/movielens_cv.html
+++ b/userguide/recommend/movielens_cv.html
@@ -244,7 +244,7 @@
                     
                         <b>1.3.1.</b>
                     
-                    Explicit addBias() for better prediction
+                    Explicit add_bias() for better prediction
             
                 </a>
             
@@ -707,14 +707,14 @@
         
         
     
-        <li class="chapter " data-level="4.1" data-path="../eval/stat_eval.html">
+        <li class="chapter " data-level="4.1" data-path="../eval/binary_classification_measures.html">
             
-                <a href="../eval/stat_eval.html">
+                <a href="../eval/binary_classification_measures.html">
             
                     
                         <b>4.1.</b>
                     
-                    Statistical evaluation of a prediction model
+                    Binary Classification Metrics
             
                 </a>
             
@@ -743,13 +743,43 @@
             
         </li>
     
-        <li class="chapter " data-level="4.2" data-path="../eval/rank.html">
+        <li class="chapter " data-level="4.2" data-path="../eval/multilabel_classification_measures.html">
             
-                <a href="../eval/rank.html">
+                <a href="../eval/multilabel_classification_measures.html">
             
                     
                         <b>4.2.</b>
                     
+                    Multi-label Classification Metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.3" data-path="../eval/regression.html">
+            
+                <a href="../eval/regression.html">
+            
+                    
+                        <b>4.3.</b>
+                    
+                    Regression metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.4" data-path="../eval/rank.html">
+            
+                <a href="../eval/rank.html">
+            
+                    
+                        <b>4.4.</b>
+                    
                     Ranking Measures
             
                 </a>
@@ -758,12 +788,12 @@
             
         </li>
     
-        <li class="chapter " data-level="4.3" data-path="../eval/datagen.html">
+        <li class="chapter " data-level="4.5" data-path="../eval/datagen.html">
             
                 <a href="../eval/datagen.html">
             
                     
-                        <b>4.3.</b>
+                        <b>4.5.</b>
                     
                     Data Generation
             
@@ -774,12 +804,12 @@
             <ul class="articles">
                 
     
-        <li class="chapter " data-level="4.3.1" data-path="../eval/lr_datagen.html">
+        <li class="chapter " data-level="4.5.1" data-path="../eval/lr_datagen.html">
             
                 <a href="../eval/lr_datagen.html">
             
                     
-                        <b>4.3.1.</b>
+                        <b>4.5.1.</b>
                     
                     Logistic Regression data generation
             
@@ -2205,8 +2235,8 @@ cluster <span class="hljs-keyword">by</span> gid, <span class="hljs-keyword">ran
 <p>0.6695442192077673 (MAE)</p>
 <p>0.8502739040257945 (RMSE)</p>
 </blockquote>
-<p><em>We recommend to use <a href="http://tez.apache.org/" target="_blank">Tez</a> for running queries having many stages.</em>
-<div id="page-footer" class="localized-footer"><hr><!--
+<p><em>We recommend to use <a href="http://tez.apache.org/" target="_blank">Tez</a> for running queries having many stages.</em></p>
+<p><div id="page-footer" class="localized-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
@@ -2261,7 +2291,7 @@ Apache Hivemall is an effort undergoing incubation at The Apache Software Founda
     <script>
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diff --git a/userguide/recommend/movielens_dataset.html b/userguide/recommend/movielens_dataset.html
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                         <b>1.3.1.</b>
                     
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                 </a>
             
@@ -707,14 +707,14 @@
         
         
     
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                         <b>4.2.</b>
                     
+                    Multi-label Classification Metrics
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+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.3" data-path="../eval/regression.html">
+            
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+            
+                    
+                        <b>4.3.</b>
+                    
+                    Regression metrics
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+            
+
+            
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+        <li class="chapter " data-level="4.4" data-path="../eval/rank.html">
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-                        <b>4.3.1.</b>
+                        <b>4.5.1.</b>
                     
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diff --git a/userguide/recommend/movielens_fm.html b/userguide/recommend/movielens_fm.html
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@@ -707,14 +707,14 @@
         
         
     
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                         <b>4.2.</b>
                     
+                    Multi-label Classification Metrics
+            
+                </a>
+            
+
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+            
+                    
+                        <b>4.3.</b>
+                    
+                    Regression metrics
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+            
+
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+                        <b>4.4.</b>
+                    
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diff --git a/userguide/recommend/movielens_mf.html b/userguide/recommend/movielens_mf.html
index cb0f354..4007263 100644
--- a/userguide/recommend/movielens_mf.html
+++ b/userguide/recommend/movielens_mf.html
@@ -244,7 +244,7 @@
                     
                         <b>1.3.1.</b>
                     
-                    Explicit addBias() for better prediction
+                    Explicit add_bias() for better prediction
             
                 </a>
             
@@ -707,14 +707,14 @@
         
         
     
-        <li class="chapter " data-level="4.1" data-path="../eval/stat_eval.html">
+        <li class="chapter " data-level="4.1" data-path="../eval/binary_classification_measures.html">
             
-                <a href="../eval/stat_eval.html">
+                <a href="../eval/binary_classification_measures.html">
             
                     
                         <b>4.1.</b>
                     
-                    Statistical evaluation of a prediction model
+                    Binary Classification Metrics
             
                 </a>
             
@@ -743,13 +743,43 @@
             
         </li>
     
-        <li class="chapter " data-level="4.2" data-path="../eval/rank.html">
+        <li class="chapter " data-level="4.2" data-path="../eval/multilabel_classification_measures.html">
             
-                <a href="../eval/rank.html">
+                <a href="../eval/multilabel_classification_measures.html">
             
                     
                         <b>4.2.</b>
                     
+                    Multi-label Classification Metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.3" data-path="../eval/regression.html">
+            
+                <a href="../eval/regression.html">
+            
+                    
+                        <b>4.3.</b>
+                    
+                    Regression metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.4" data-path="../eval/rank.html">
+            
+                <a href="../eval/rank.html">
+            
+                    
+                        <b>4.4.</b>
+                    
                     Ranking Measures
             
                 </a>
@@ -758,12 +788,12 @@
             
         </li>
     
-        <li class="chapter " data-level="4.3" data-path="../eval/datagen.html">
+        <li class="chapter " data-level="4.5" data-path="../eval/datagen.html">
             
                 <a href="../eval/datagen.html">
             
                     
-                        <b>4.3.</b>
+                        <b>4.5.</b>
                     
                     Data Generation
             
@@ -774,12 +804,12 @@
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-        <li class="chapter " data-level="4.3.1" data-path="../eval/lr_datagen.html">
+        <li class="chapter " data-level="4.5.1" data-path="../eval/lr_datagen.html">
             
                 <a href="../eval/lr_datagen.html">
             
                     
-                        <b>4.3.1.</b>
+                        <b>4.5.1.</b>
                     
                     Logistic Regression data generation
             
@@ -2378,7 +2408,7 @@ Apache Hivemall is an effort undergoing incubation at The Apache Software Founda
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http://git-wip-us.apache.org/repos/asf/incubator-hivemall-site/blob/a98b42f8/userguide/recommend/news20.html
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diff --git a/userguide/recommend/news20.html b/userguide/recommend/news20.html
index 567afd5..fafce31 100644
--- a/userguide/recommend/news20.html
+++ b/userguide/recommend/news20.html
@@ -244,7 +244,7 @@
                     
                         <b>1.3.1.</b>
                     
-                    Explicit addBias() for better prediction
+                    Explicit add_bias() for better prediction
             
                 </a>
             
@@ -707,14 +707,14 @@
         
         
     
-        <li class="chapter " data-level="4.1" data-path="../eval/stat_eval.html">
+        <li class="chapter " data-level="4.1" data-path="../eval/binary_classification_measures.html">
             
-                <a href="../eval/stat_eval.html">
+                <a href="../eval/binary_classification_measures.html">
             
                     
                         <b>4.1.</b>
                     
-                    Statistical evaluation of a prediction model
+                    Binary Classification Metrics
             
                 </a>
             
@@ -743,13 +743,43 @@
             
         </li>
     
-        <li class="chapter " data-level="4.2" data-path="../eval/rank.html">
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-                <a href="../eval/rank.html">
+                <a href="../eval/multilabel_classification_measures.html">
             
                     
                         <b>4.2.</b>
                     
+                    Multi-label Classification Metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.3" data-path="../eval/regression.html">
+            
+                <a href="../eval/regression.html">
+            
+                    
+                        <b>4.3.</b>
+                    
+                    Regression metrics
+            
+                </a>
+            
+
+            
+        </li>
+    
+        <li class="chapter " data-level="4.4" data-path="../eval/rank.html">
+            
+                <a href="../eval/rank.html">
+            
+                    
+                        <b>4.4.</b>
+                    
                     Ranking Measures
             
                 </a>
@@ -758,12 +788,12 @@
             
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-        <li class="chapter " data-level="4.3" data-path="../eval/datagen.html">
+        <li class="chapter " data-level="4.5" data-path="../eval/datagen.html">
             
                 <a href="../eval/datagen.html">
             
                     
-                        <b>4.3.</b>
+                        <b>4.5.</b>
                     
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@@ -774,12 +804,12 @@
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                 <a href="../eval/lr_datagen.html">
             
                     
-                        <b>4.3.1.</b>
+                        <b>4.5.1.</b>
                     
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@@ -2210,7 +2240,7 @@ Apache Hivemall is an effort undergoing incubation at The Apache Software Founda
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