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Posted to commits@madlib.apache.org by ok...@apache.org on 2017/12/28 22:51:51 UTC
[17/51] [abbrv] [partial] madlib-site git commit: Additional updates
for 1.13 release
http://git-wip-us.apache.org/repos/asf/madlib-site/blob/6c103d3e/docs/v1.13/group__grp__sssp.html
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+<title>MADlib: Single Source Shortest Path</title>
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+ <td style="padding-left: 0.5em;">
+ <div id="projectname">
+ <span id="projectnumber">1.13</span>
+ </div>
+ <div id="projectbrief">User Documentation for MADlib</div>
+ </td>
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+ <span class="left">
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+ <div class="headertitle">
+<div class="title">Single Source Shortest Path<div class="ingroups"><a class="el" href="group__grp__graph.html">Graph</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#sssp">SSSP</a> </li>
+<li>
+<a href="#notes">Notes</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+<li>
+<a href="#literature">Literature</a> </li>
+</ul>
+</div><p>Given a graph and a source vertex, the single source shortest path (SSSP) algorithm finds a path from the source vertex to every other vertex in the graph, such that the sum of the weights of the path edges is minimized.</p>
+<p><a class="anchor" id="sssp"></a></p><dl class="section user"><dt>SSSP</dt><dd><pre class="syntax">
+graph_sssp( vertex_table,
+ vertex_id,
+ edge_table,
+ edge_args,
+ source_vertex,
+ out_table,
+ grouping_cols
+ )
+</pre></dd></dl>
+<p><b>Arguments</b> </p><dl class="arglist">
+<dt>vertex_table </dt>
+<dd><p class="startdd">TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.</p>
+<p class="enddd"></p>
+</dd>
+<dt>vertex_id </dt>
+<dd><p class="startdd">TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids are of type INTEGER with no duplicates. They do not need to be contiguous.</p>
+<p class="enddd"></p>
+</dd>
+<dt>edge_table </dt>
+<dd><p class="startdd">TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex, destination vertex and edge weight. Column naming convention is described below in the 'edge_args' parameter.</p>
+<p class="enddd"></p>
+</dd>
+<dt>edge_args </dt>
+<dd><p class="startdd">TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:</p><ul>
+<li>src (INTEGER): Name of the column containing the source vertex ids in the edge table. Default column name is 'src'.</li>
+<li>dest (INTEGER): Name of the column containing the destination vertex ids in the edge table. Default column name is 'dest'.</li>
+<li>weight (FLOAT8): Name of the column containing the edge weights in the edge table. Default column name is 'weight'.</li>
+</ul>
+<p class="enddd"></p>
+</dd>
+<dt>source_vertex </dt>
+<dd><p class="startdd">INTEGER. The source vertex id for the algorithm to start. This vertex id must exist in the 'vertex_id' column of 'vertex_table'.</p>
+<p class="enddd"></p>
+</dd>
+<dt>out_table </dt>
+<dd><p class="startdd">TEXT. Name of the table to store the result of SSSP. It contains a row for every vertex of every group and have the following columns (in addition to the grouping columns):</p><ul>
+<li>vertex_id : The id for the destination. Will use the input parameter 'vertex_id' for column naming.</li>
+<li>weight : The total weight of the shortest path from the source vertex to this particular vertex. Will use the input parameter 'weight' for column naming.</li>
+<li>parent : The parent of this vertex in the shortest path from source. Will use 'parent' for column naming.</li>
+</ul>
+<p>A summary table named <out_table>_summary is also created. This is an internal table that keeps a record of the input parameters and is used by the path function described below. </p>
+<p class="enddd"></p>
+</dd>
+<dt>grouping_cols (optional) </dt>
+<dd>TEXT, default = NULL. List of columns used to group the input into discrete subgraphs. These columns must exist in the edge table. When this value is null, no grouping is used and a single SSSP result is generated. </dd>
+</dl>
+<dl class="section user"><dt>Path Retrieval</dt><dd></dd></dl>
+<p>The path retrieval function returns the shortest path from the source vertex to a specified desination vertex.</p>
+<pre class="syntax">
+graph_sssp_get_path( sssp_table,
+ dest_vertex,
+ path_table
+ )
+</pre><p><b>Arguments</b> </p><dl class="arglist">
+<dt>sssp_table </dt>
+<dd><p class="startdd">TEXT. Name of the table that contains the SSSP output.</p>
+<p class="enddd"></p>
+</dd>
+<dt>dest_vertex </dt>
+<dd><p class="startdd">INTEGER. The vertex that will be the destination of the desired path.</p>
+<p class="enddd"></p>
+</dd>
+<dt>path_table </dt>
+<dd><p class="startdd">TEXT. Name of the output table that contains the path. It contains a row for every group and has the following columns:</p><ul>
+<li>grouping_cols : The grouping columns given in the creation of the SSSP table. If there are no grouping columns, these columns will not exist and the table will have a single row.</li>
+<li>path (ARRAY) : The shortest path from the source vertex (as specified in the SSSP execution) to the destination vertex. </li>
+</ul>
+<p class="enddd"></p>
+</dd>
+</dl>
+<p><a class="anchor" id="notes"></a></p><dl class="section user"><dt>Notes</dt><dd></dd></dl>
+<p>The Bellman-Ford algorithm [1] is used to implement SSSP. This algorithm allows negative edges but not negative cycles. In the case of graphs with negative cycles, an error will be given and no output table will be generated.</p>
+<p>Also see the Grail project [2] for more background on graph analytics processing in relational databases.</p>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<ol type="1">
+<li>Create vertex and edge tables to represent the graph: <pre class="syntax">
+DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+ id INTEGER
+ );
+CREATE TABLE edge(
+ src INTEGER,
+ dest INTEGER,
+ weight FLOAT8
+ );
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6),
+(7);
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+</pre></li>
+<li>Calculate the shortest paths from vertex 0: <pre class="syntax">
+DROP TABLE IF EXISTS out, out_summary;
+SELECT madlib.graph_sssp(
+ 'vertex', -- Vertex table
+ NULL, -- Vertix id column (NULL means use default naming)
+ 'edge', -- Edge table
+ NULL, -- Edge arguments (NULL means use default naming)
+ 0, -- Source vertex for path calculation
+ 'out'); -- Output table of shortest paths
+SELECT * FROM out ORDER BY id;
+</pre> <pre class="result">
+ id | weight | parent
+----+--------+--------
+ 0 | 0 | 0
+ 1 | 1 | 0
+ 2 | 1 | 0
+ 3 | 2 | 2
+ 4 | 10 | 0
+ 5 | 2 | 2
+ 6 | 3 | 5
+ 7 | 4 | 6
+(8 rows)
+</pre></li>
+<li>Get the shortest path to vertex 5: <pre class="syntax">
+DROP TABLE IF EXISTS out_path;
+SELECT madlib.graph_sssp_get_path('out',5,'out_path');
+SELECT * FROM out_path;
+</pre> <pre class="result">
+ path
+---------
+ {0,2,5}
+</pre></li>
+<li>Now let's do a similar example except using different column names in the tables (i.e., not the defaults). Create the vertex and edge tables: <pre class="syntax">
+DROP TABLE IF EXISTS vertex_alt, edge_alt;
+CREATE TABLE vertex_alt AS SELECT id AS v_id FROM vertex;
+CREATE TABLE edge_alt AS SELECT src AS e_src, dest, weight AS e_weight FROM edge;
+</pre></li>
+<li>Get the shortest path from vertex 1: <pre class="syntax">
+DROP TABLE IF EXISTS out_alt, out_alt_summary;
+SELECT madlib.graph_sssp(
+ 'vertex_alt', -- Vertex table
+ 'v_id', -- Vertex id column (NULL means use default naming)
+ 'edge_alt', -- Edge table
+ 'src=e_src, weight=e_weight', -- Edge arguments (NULL means use default naming)
+ 1, -- Source vertex for path calculation
+ 'out_alt'); -- Output table of shortest paths
+SELECT * FROM out_alt ORDER BY v_id;
+</pre> <pre class="result">
+ v_id | e_weight | parent
+------+----------+--------
+ 0 | 4 | 3
+ 1 | 0 | 1
+ 2 | 2 | 1
+ 3 | 3 | 2
+ 4 | 14 | 0
+ 5 | 3 | 2
+ 6 | 4 | 5
+ 7 | 5 | 6
+(8 rows)
+</pre></li>
+<li>Create a graph with 2 groups: <pre class="syntax">
+DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+ SELECT *, 0 AS grp FROM edge
+ UNION
+ SELECT *, 1 AS grp FROM edge WHERE src < 6 AND dest < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+</pre></li>
+<li>Find SSSP for all groups <pre class="syntax">
+DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_sssp(
+ 'vertex', -- Vertex table
+ NULL, -- Vertex id column (NULL means use default naming)
+ 'edge_gr', -- Edge table
+ NULL, -- Edge arguments (NULL means use default naming)
+ 0, -- Source vertex for path calculation
+ 'out_gr', -- Output table of shortest paths
+ 'grp' -- Grouping columns
+);
+SELECT * FROM out_gr ORDER BY grp,id;
+</pre> <pre class="result">
+ grp | id | weight | parent
+-----+----+--------+--------
+ 0 | 0 | 0 | 0
+ 0 | 1 | 1 | 0
+ 0 | 2 | 1 | 0
+ 0 | 3 | 2 | 2
+ 0 | 4 | 10 | 0
+ 0 | 5 | 2 | 2
+ 0 | 6 | 3 | 5
+ 0 | 7 | 4 | 6
+ 1 | 0 | 0 | 0
+ 1 | 1 | 1 | 0
+ 1 | 2 | 1 | 0
+ 1 | 3 | 2 | 2
+ 1 | 4 | 10 | 0
+ 1 | 5 | -10 | 4
+</pre></li>
+<li>Find the path to vertex 5 in every group <pre class="syntax">
+DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_sssp_get_path('out_gr',5,'out_gr_path');
+SELECT * FROM out_gr_path ORDER BY grp;
+</pre> <pre class="result">
+ grp | path
+-----+---------
+ 0 | {0,2,5}
+ 1 | {0,4,5}
+</pre></li>
+</ol>
+<p><a class="anchor" id="literature"></a></p><dl class="section user"><dt>Literature</dt><dd></dd></dl>
+<p>[1] Bellman–Ford algorithm. <a href="https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm">https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm</a></p>
+<p>[2] The case against specialized graph analytics engines, J. Fan, G. Soosai Raj, and J. M. Patel. CIDR 2015. <a href="http://cidrdb.org/cidr2015/Papers/CIDR15_Paper20.pdf">http://cidrdb.org/cidr2015/Papers/CIDR15_Paper20.pdf</a> </p>
+</div><!-- contents -->
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+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+ <ul>
+ <li class="footer">Generated on Wed Dec 27 2017 19:05:57 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
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+</html>
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+ <td style="padding-left: 0.5em;">
+ <div id="projectname">
+ <span id="projectnumber">1.13</span>
+ </div>
+ <div id="projectbrief">User Documentation for MADlib</div>
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+<a href="#groups">Modules</a> </div>
+ <div class="headertitle">
+<div class="title">Statistics</div> </div>
+</div><!--header-->
+<div class="contents">
+<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
+<p>Contains statistics modules </p>
+<table class="memberdecls">
+<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="groups"></a>
+Modules</h2></td></tr>
+<tr class="memitem:group__grp__desc__stats"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__desc__stats.html">Descriptive Statistics</a></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__inf__stats"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__inf__stats.html">Inferential Statistics</a></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+<tr class="memitem:group__grp__prob"><td class="memItemLeft" align="right" valign="top"> </td><td class="memItemRight" valign="bottom"><a class="el" href="group__grp__prob.html">Probability Functions</a></td></tr>
+<tr class="memdesc:group__grp__prob"><td class="mdescLeft"> </td><td class="mdescRight">Provides cumulative distribution, density/mass, and quantile functions for a wide range of probability distributions. <br /></td></tr>
+<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
+</table>
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+[
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+<div class="title">Hypothesis Tests<div class="ingroups"><a class="el" href="group__grp__stats.html">Statistics</a> » <a class="el" href="group__grp__inf__stats.html">Inferential Statistics</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#input">Input</a> </li>
+<li>
+<a href="#usage">Usage</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+<li>
+<a href="#literature">Literature</a> </li>
+<li>
+<a href="#related">Related Topics</a> </li>
+</ul>
+</div><p>Hypothesis tests are used to confirm or reject a <em>null hypothesis</em> \( H_0 \) about the distribution of random variables, given realizations of these random variables. Since in general it is not possible to make statements with certainty, one is interested in the probability \( p \) of seeing random variates at least as extreme as the ones observed, assuming that \( H_0 \) is true. If this probability \( p \) is small, \( H_0 \) will be rejected by the test with <em>significance level</em> \( p \). Falsifying \( H_0 \) is the canonic goal when employing a hypothesis test. That is, hypothesis tests are typically used in order to substantiate that instead the <em>alternative hypothesis</em> \( H_1 \) is true.</p>
+<p>Hypothesis tests may be divided into parametric and non-parametric tests. A parametric test assumes certain distributions and makes inferences about parameters of the distributions (e.g., the mean of a normal distribution). Formally, there is a given domain of possible parameters \( \Gamma \) and the null hypothesis \( H_0 \) is the event that the true parameter \( \gamma_0 \in \Gamma_0 \), where \( \Gamma_0 \subsetneq \Gamma \). Non-parametric tests, on the other hand, do not assume any particular distribution of the sample (e.g., a non-parametric test may simply test if two distributions are similar).</p>
+<p>The first step of a hypothesis test is to compute a <em>test statistic</em>, which is a function of the random variates, i.e., a random variate itself. A hypothesis test relies on the distribution of the test statistic being (approximately) known. Now, the \( p \)-value is the probability of seeing a test statistic at least as extreme as the one observed, assuming that \( H_0 \) is true. In a case where the null hypothesis corresponds to a family of distributions (e.g., in a parametric test where \( \Gamma_0 \) is not a singleton set), the \( p \)-value is the supremum, over all possible distributions according to the null hypothesis, of these probabilities.</p>
+<dl class="section note"><dt>Note</dt><dd>Please refer to <a class="el" href="hypothesis__tests_8sql__in.html">hypothesis_tests.sql_in</a> for additional technical information on the MADlib implementation of hypothesis tests, and for detailed function signatures for all tests.</dd></dl>
+<p><a class="anchor" id="input"></a></p><dl class="section user"><dt>Input</dt><dd></dd></dl>
+<p>Input data is assumed to be normalized with all values stored row-wise. In general, the following inputs are expected.</p>
+<p><b>One-sample tests</b> expect the following form: </p><pre>{TABLE|VIEW} <em>source</em> (
+ ...
+ <em>value</em> DOUBLE PRECISION
+ ...
+)</pre><p><b>Two-sample tests</b> expect the following form: </p><pre>{TABLE|VIEW} <em>source</em> (
+ ...
+ <em>first</em> BOOLEAN,
+ <em>value</em> DOUBLE PRECISION
+ ...
+)</pre><p> The <code>first</code> column indicates whether a value is from the first sample (if <code>TRUE</code>) or the second sample (if <code>FALSE</code>).</p>
+<p><b>Many-sample tests</b> expect the following form: </p><pre>{TABLE|VIEW} <em>source</em> (
+ ...
+ <em>group</em> INTEGER,
+ <em>value</em> DOUBLE PRECISION
+ ...
+)</pre><p><a class="anchor" id="usage"></a></p><dl class="section user"><dt>Usage</dt><dd></dd></dl>
+<p>All tests are implemented as aggregate functions. The non-parametric (rank-based) tests are implemented as ordered aggregate functions and thus necessitate an <code>ORDER BY</code> clause. In the following, the most simple forms of usage are given. Specific function signatures, as described in <a class="el" href="hypothesis__tests_8sql__in.html">hypothesis_tests.sql_in</a>, may require more arguments or a different <code>ORDER BY</code> clause.</p>
+<ul>
+<li>Run a parametric one-sample test: <pre>SELECT <em>test</em>(<em>value</em>) FROM <em>source</em></pre> where '<em>test</em>' can be one of<ul>
+<li><code>t_test_one</code> (one-sample or dependent paired Student's t-test)</li>
+<li><code>chi2_gof_test</code> (Pearson's chi-squared goodness of fit test, also used for chi-squared independence test as shown in example section below)</li>
+</ul>
+</li>
+<li>Run a parametric two-sample/multi-sample test: <pre>SELECT <em>test</em>(<em>first/group</em>, <em>value</em>) FROM <em>source</em></pre> where '<em>test</em>' can be one of<ul>
+<li><code>f_test</code> (Fisher F-test)</li>
+<li><code>t_test_two_pooled</code> (two-sample pooled Student’s t-test, i.e. equal variances)</li>
+<li><code>t_test_two_unpooled</code> (two-sample unpooled t-test, i.e., unequal variances, also known as Welch's t-test)</li>
+<li><code>one_way_anova</code> (one-way analysis of variance, multi-sample)</li>
+</ul>
+</li>
+<li><p class="startli">Run a non-parametric two-sample/multi-sample test: </p><pre>SELECT <em>test</em>(<em>first/group</em>, <em>value</em> ORDER BY <em>value</em>) FROM <em>source</em></pre><p> where '<em>test</em>' can be one of</p><ul>
+<li><code>ks_test</code> (Kolmogorov-Smirnov test)</li>
+<li><code>mw_test</code> (Mann-Whitney test)</li>
+<li><code>wsr_test</code> (Wilcoxon signed-rank test, multi-sample)</li>
+</ul>
+<p class="startli"><b>Note on non-parametric tests:</b> Kolomogov-Smirnov two-sample test is based on the asymptotic theory. The p-value is given by comparing the test statistics with the Kolomogov distribution. The p-value is also adjusted for data with heavy tail distribution, which may give different results than those given by R function's ks.test. See [3] for a detailed explanation. The literature is not unanimous about the definitions of the Wilcoxon rank sum and Mann-Whitney tests. There are two possible definitions for the statistic; MADlib outputs the minimum of the two and uses it for significance testing. This might give different results for both mw_test and wsr_test compared to statistical functions in other popular packages (like R's wilcox.test function). See [4] for a detailed explanation.</p>
+</li>
+</ul>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<ul>
+<li><b>One-sample and two-sample t-test</b> (data is subset of mpg data from <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm">NIST/SEMATECH</a>)</li>
+</ul>
+<pre class="example">
+-- Load data
+DROP TABLE IF EXISTS auto83b;
+CREATE TABLE auto83b (
+ id SERIAL,
+ mpg_us DOUBLE PRECISION,
+ mpg_j DOUBLE PRECISION
+);
+COPY auto83b (mpg_us, mpg_j) FROM stdin DELIMITER '|';
+18|24
+15|27
+18|27
+16|25
+17|31
+15|35
+14|24
+14|19
+21|31
+10|32
+10|24
+11|26
+9| 9
+\N|32
+\N|37
+\N|38
+\N|34
+\N|34
+\N|32
+\N|33
+\N|32
+\N|25
+\N|24
+\N|37
+13|\N
+12|\N
+18|\N
+21|\N
+19|\N
+21|\N
+15|\N
+16|\N
+15|\N
+11|\N
+20|\N
+21|\N
+19|\N
+15|\N
+\.
+</pre><pre class="example">
+-- Create table for one sample tests
+DROP TABLE IF EXISTS auto83b_one_sample;
+CREATE TABLE auto83b_one_sample AS
+ SELECT mpg_us AS mpg
+ FROM auto83b
+ WHERE mpg_us is not NULL;
+-- Print table
+SELECT * FROM auto83b_one_sample;
+</pre><pre class="result">
+mpg
+ 18
+ 15
+ 18
+ 16
+ 17
+ 15
+ 14
+ 14
+ 21
+ 10
+ 10
+ 11
+ 9
+ 13
+ 12
+ 18
+ 21
+ 19
+ 21
+ 15
+ 16
+ 15
+ 11
+ 20
+ 21
+ 19
+ 15
+(27 rows)
+</pre> <pre class="example">
+-- Create table for two sample tests
+DROP TABLE IF EXISTS auto83b_two_sample;
+CREATE TABLE auto83b_two_sample AS
+SELECT TRUE AS is_us, mpg_us AS mpg
+ FROM auto83b
+ WHERE mpg_us is not NULL
+ UNION ALL
+ SELECT FALSE, mpg_j
+ FROM auto83b
+ WHERE mpg_j is not NULL;
+-- Print table
+SELECT * FROM auto83b_two_sample;
+</pre> <pre class="result">
+ is_us | mpg
+-------+-----
+ t | 18
+ t | 15
+ t | 18
+ t | 16
+ t | 17
+ t | 15
+ t | 14
+ t | 14
+ t | 21
+ t | 10
+ t | 10
+ t | 11
+ t | 9
+ t | 13
+ t | 12
+ t | 18
+ t | 21
+ t | 19
+ t | 21
+ t | 15
+ t | 16
+ t | 15
+ t | 11
+ t | 20
+ t | 21
+ t | 19
+ t | 15
+ f | 24
+ f | 27
+ f | 27
+ f | 25
+ f | 31
+ f | 35
+ f | 24
+ f | 19
+ f | 31
+ f | 32
+ f | 24
+ f | 26
+ f | 9
+ f | 32
+ f | 37
+ f | 38
+ f | 34
+ f | 34
+ f | 32
+ f | 33
+ f | 32
+ f | 25
+ f | 24
+ f | 37
+(51 rows)
+</pre> <pre class="example">
+-- One sample tests
+SELECT (madlib.t_test_one(mpg - 20)).* FROM auto83b_one_sample; -- test rejected for mean = 20
+</pre><pre class="result">
+ statistic | df | p_value_one_sided | p_value_two_sided
+ ------------------+----+-------------------+----------------------
+ -6.0532478722666 | 26 | 0.999998926789141 | 2.14642171769697e-06
+ </pre><pre class="example">
+SELECT (madlib.t_test_one(mpg - 15.7)).* FROM auto83b_one_sample; -- test not rejected
+</pre><pre class="result">
+ statistic | df | p_value_one_sided | p_value_two_sided
+ ---------------------+----+-------------------+-------------------
+ 0.00521831713126531 | 26 | 0.497938118950661 | 0.995876237901321
+</pre><pre class="example">
+-- Two sample tests
+SELECT (madlib.t_test_two_pooled(is_us, mpg)).* FROM auto83b_two_sample;
+</pre> <pre class="result">
+ statistic | df | p_value_one_sided | p_value_two_sided
+ -------------------+----+-------------------+----------------------
+ -8.89342267075968 | 49 | 0.999999999995748 | 8.50408632402377e-12
+ </pre><pre class="example">
+SELECT (madlib.t_test_two_unpooled(is_us, mpg)).* FROM auto83b_two_sample;
+</pre><pre class="result">
+ statistic | df | p_value_one_sided | p_value_two_sided
+ -------------------+------------------+-------------------+----------------------
+ -8.61746388524314 | 35.1283818346179 | 0.999999999821218 | 3.57563867403599e-10
+</pre><ul>
+<li><b>F-Test</b> (Uses same data as above t-test)</li>
+</ul>
+<pre class="example">
+SELECT (madlib.f_test(is_us, mpg)).* FROM auto83b_two_sample;
+-- Test result indicates that the two distributions have different variances
+</pre> <pre class="result">
+ statistic | df1 | df2 | p_value_one_sided | p_value_two_sided
+ -------------------+-----+-----+-------------------+---------------------
+ 0.311786921089247 | 26 | 23 | 0.997559863672441 | 0.00488027265511803
+</pre><ul>
+<li><b>Chi-squared goodness-of-fit test</b> (<a href="http://www.statsdirect.com/help/default.htm#nonparametric_methods/chisq_goodness_fit.htm">Data source</a>)</li>
+</ul>
+<pre class="example">
+CREATE TABLE chi2_test_blood_group (
+ id SERIAL,
+ blood_group VARCHAR,
+ observed BIGINT,
+ expected DOUBLE PRECISION
+);
+INSERT INTO chi2_test_blood_group(blood_group, observed, expected) VALUES
+ ('O', 67, 82.28),
+ ('A', 83, 84.15),
+ ('B', 29, 14.96),
+ ('AB', 8, 5.61);
+SELECT (madlib.chi2_gof_test(observed, expected)).* FROM chi2_test_blood_group;
+</pre> <pre class="result">
+ statistic | p_value | df | phi | contingency_coef
+ ------------------+----------------------+----+------------------+-------------------
+ 17.0481013341976 | 0.000690824622923826 | 3 | 2.06446732440826 | 0.899977280680593
+ </pre><ul>
+<li><b>Chi-squared independence test</b> (<a href="http://itl.nist.gov/div898/software/dataplot/refman1/auxillar/chistest.htm">Data source</a>)</li>
+</ul>
+<p>The Chi-squared independence test uses the Chi-squared goodness-of-fit function, as shown in the example below. The expected value needs to be computed and passed to the goodness-of-fit function. The expected value for MADlib is computed as <em>sum of rows * sum of columns</em>, for each element of the input matrix. For e.g., expected value for element (2,1) would be <em>sum of row 2 * sum of column 1</em>.</p>
+<pre class="example">
+CREATE TABLE chi2_test_friendly (
+ id_x SERIAL,
+ values INTEGER[]
+);
+INSERT INTO chi2_test_friendly(values) VALUES
+ (array[5, 29, 14, 16]),
+ (array[15, 54, 14, 10]),
+ (array[20, 84, 17, 94]),
+ (array[68, 119, 26, 7]);</pre><pre class="example">-- Input table is expected to be unpivoted, so need to pivot it
+CREATE TABLE chi2_test_friendly_unpivoted AS
+SELECT id_x, id_y, values[id_y] AS observed
+FROM
+ chi2_test_friendly,
+ generate_series(1,4) AS id_y;</pre><pre class="example">-- Compute Chi-squared independence statistic, by calculating expected value in the SQL and calling the goodness-of-fit function
+SELECT (madlib.chi2_gof_test(observed, expected, deg_freedom)).*
+FROM (
+ -- Compute expected values and degrees of freedom
+ SELECT
+ observed,
+ sum(observed) OVER (PARTITION BY id_x)::DOUBLE PRECISION *
+ sum(observed) OVER (PARTITION BY id_y) AS expected
+ FROM chi2_test_friendly_unpivoted
+) p, (
+ SELECT
+ (count(DISTINCT id_x) - 1) * (count(DISTINCT id_y) - 1) AS deg_freedom
+ FROM chi2_test_friendly_unpivoted
+) q;
+</pre> <pre class="result">
+ statistic | p_value | df | phi | contingency_coef
+ ------------------+----------------------+----+------------------+-------------------
+ 138.289841626008 | 2.32528678709871e-25 | 9 | 2.93991753313346 | 0.946730727519112
+ </pre><ul>
+<li><b>ANOVA test</b> (<a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc433.htm">Data source</a>)</li>
+</ul>
+<pre class="example">
+CREATE TABLE nist_anova_test (
+ id SERIAL,
+ resistance FLOAT8[]
+);
+INSERT INTO nist_anova_test(resistance) VALUES
+ (array[6.9,8.3,8.0]),
+ (array[5.4,6.8,10.5]),
+ (array[5.8,7.8,8.1]),
+ (array[4.6,9.2,6.9]),
+ (array[4.0,6.5,9.3]);</pre><pre class="example">SELECT (madlib.one_way_anova(level, value)).* FROM (
+ SELECT level, resistance[level] AS value
+ FROM
+ nist_anova_test, (SELECT * FROM generate_series(1,3) level) q1
+) q2;
+</pre> <pre class="result">
+ sum_squares_between | sum_squares_within | df_between | df_within | mean_squares_between | mean_squares_within | statistic | p_value
+ ---------------------+--------------------+------------+-----------+----------------------+---------------------+------------------+--------------------
+ 27.8973333333333 | 17.452 | 2 | 12 | 13.9486666666667 | 1.45433333333333 | 9.59110703644281 | 0.0032482226008593
+</pre><ul>
+<li><b>Kolmogorov-Smirnov test</b> (<a href="http://www.physics.csbsju.edu/stats/KS-test.html">Data source</a>)</li>
+</ul>
+<pre class="example">
+CREATE TABLE ks_sample_1 AS
+SELECT
+ TRUE AS first,
+ unnest(ARRAY[0.22, -0.87, -2.39, -1.79, 0.37, -1.54, 1.28, -0.31, -0.74, 1.72, 0.38, -0.17, -0.62, -1.10, 0.30, 0.15, 2.30, 0.19, -0.50, -0.09]) AS value
+UNION ALL
+SELECT
+ FALSE,
+ unnest(ARRAY[-5.13, -2.19, -2.43, -3.83, 0.50, -3.25, 4.32, 1.63, 5.18, -0.43, 7.11, 4.87, -3.10, -5.81, 3.76, 6.31, 2.58, 0.07, 5.76, 3.50]);</pre><pre class="example">SELECT (madlib.ks_test(first, value,
+ (SELECT count(value) FROM ks_sample_1 WHERE first),
+ (SELECT count(value) FROM ks_sample_1 WHERE NOT first)
+ ORDER BY value)).*
+FROM ks_sample_1;
+</pre> <pre class="result">
+ statistic | k_statistic | p_value
+ -----------+-----------------+--------------------
+ 0.45 | 1.4926782214936 | 0.0232132758544496
+</pre><ul>
+<li><b>Mann-Whitney test</b> (use same data as t-test)</li>
+</ul>
+<pre class="example">
+SELECT (madlib.mw_test(is_us, mpg ORDER BY mpg)).* from auto83b_two_sample;
+-- Note first parameter above is BOOLEAN
+</pre> <pre class="result">
+ statistic | u_statistic | p_value_one_sided | p_value_two_sided
+ -------------------+-------------+-------------------+----------------------
+ -5.50097925755249 | 32.5 | 0.999999981115618 | 3.77687645883758e-08
+</pre><ul>
+<li><b>Wilcoxon signed-rank test</b></li>
+</ul>
+<pre class="example">
+DROP TABLE IF EXISTS test_wsr;
+CREATE TABLE test_wsr (
+ x DOUBLE PRECISION,
+ y DOUBLE PRECISION
+);
+COPY test_wsr (x, y) FROM stdin DELIMITER '|';
+0.32|0.39
+0.4|0.47
+0.11|0.11
+0.47|0.43
+0.32|0.42
+0.35|0.3
+0.32|0.43
+0.63|0.98
+0.5|0.86
+0.6|0.79
+0.38|0.33
+0.46|0.45
+0.2|0.22
+0.31|0.3
+0.62|0.6
+0.52|0.53
+0.77|0.85
+0.23|0.21
+0.3|0.33
+0.7|0.57
+0.41|0.43
+0.53|0.49
+0.19|0.2
+0.31|0.35
+0.48|0.4
+\.
+
+SELECT (madlib.wsr_test(
+ x - y,
+ 2 * 2^(-52) * greatest(x,y)
+ ORDER BY abs(x - y)
+)).*
+FROM test_wsr;
+</pre> <pre class="result">
+ statistic | rank_sum_pos | rank_sum_neg | num | z_statistic | p_value_one_sided | p_value_two_sided
+ -----------+--------------+--------------+-----+-------------------+-------------------+-------------------
+ 105.5 | 105.5 | 194.5 | 24 | -1.27318365656729 | 0.898523560667509 | 0.202952878664983
+</pre><p><a class="anchor" id="literature"></a></p><dl class="section user"><dt>Literature</dt><dd></dd></dl>
+<p>[1] M. Hollander, D. Wolfe: <em>Nonparametric Statistical Methods</em>, 2nd edition, Wiley, 1999</p>
+<p>[2] E. Lehmann, J. Romano: <em>Testing Statistical Hypotheses</em>, 3rd edition, Springer, 2005</p>
+<p>[3] M. Stephens: <em>Use of the Kolmogorov-Smirnov, Cramer-Von Mises and related statistics without extensive tables</em>, Journal of the Royal Statistical Society. Series B (Methodological) (1970): 115-122.</p>
+<p>[4] Wikipedia: Mann–Whitney U test calculation, <a href="http://en.wikipedia.org/wiki/Mann-Whitney_test#Calculations">http://en.wikipedia.org/wiki/Mann-Whitney_test#Calculations</a></p>
+<p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl>
+<p>File <a class="el" href="hypothesis__tests_8sql__in.html" title="SQL functions for statistical hypothesis tests. ">hypothesis_tests.sql_in</a> documenting the SQL functions. </p>
+</div><!-- contents -->
+</div><!-- doc-content -->
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+ <li class="footer">Generated on Wed Dec 27 2017 19:05:57 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
+ </ul>
+</div>
+</body>
+</html>
http://git-wip-us.apache.org/repos/asf/madlib-site/blob/6c103d3e/docs/v1.13/group__grp__stemmer.html
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+<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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+<title>MADlib: Stemming</title>
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+ <span id="projectnumber">1.13</span>
+ </div>
+ <div id="projectbrief">User Documentation for MADlib</div>
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+ <span class="left">
+ <img id="MSearchSelect" src="search/mag_sel.png"
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+<!-- window showing the filter options -->
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+ onmouseover="return searchBox.OnSearchSelectShow()"
+ onmouseout="return searchBox.OnSearchSelectHide()"
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+
+<div class="header">
+ <div class="headertitle">
+<div class="title">Stemming<div class="ingroups"><a class="el" href="group__grp__datatrans.html">Data Types and Transformations</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#notes">Implementation Notes</a> </li>
+<li>
+<a href="#list">List of Stemmer Operations</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+<li>
+<a href="#related">Related Topics</a> </li>
+</ul>
+</div><p>This module provides a basic stemming operation for text input. It is a support module for several machine learning algorithms that require a stemmer. Currently, it only supports English words.</p>
+<p>This function is a SQL interface to the implementation of the <a href="http://tartarus.org/~martin/PorterStemmer/">Porter Stemming Algorithm</a>. The original stemming algorithm is written and maintained by Martin Porter</p>
+<p><a class="anchor" id="notes"></a></p><dl class="section user"><dt>Implementation Notes</dt><dd></dd></dl>
+<p>All functions described in this module work with text OR text array.</p>
+<p>Several of the function require TEXT VALUES, and returns NULL for a NULL input. See details in description of individual functions.</p>
+<p><a class="anchor" id="list"></a></p><dl class="section user"><dt>Stemmer Operations</dt><dd><table class="output">
+<tr>
+<th><a class="el" href="porter__stemmer_8sql__in.html#aca5bc24a9a8f5c33470b9f0bf0b3c515" title="Returns stem of input token. Returns NULL if input token is NULL. ">stem_token()</a></th><td><p class="starttd">Returns the stem of the token. Returns NULL if input is NULL.</p>
+<p class="endtd"></p>
+</td></tr>
+<tr>
+<th><a class="el" href="porter__stemmer_8sql__in.html#a1ac3a2fd645ddf807b36a1328134a4ea" title="Returns stems in an array of input token array. Returns NULL element for corresponding input NULL tok...">stem_token_arr()</a></th><td><p class="starttd">Returns the stems in an array of input token array. The stem would be NULL for corresponding NULL token.</p>
+<p class="endtd"><a class="anchor" id="examples"></a></p>
+</td></tr>
+</table>
+</dd></dl>
+<dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<ol type="1">
+<li>Create a table with some words to be stemmed. <pre class="example">
+CREATE TABLE token_tbl ( id integer,
+ word text
+ );
+INSERT INTO token_tbl VALUES
+ (1, 'kneel'),
+ (2, 'kneeled'),
+ (3, 'kneeling'),
+ (4, 'kneels'),
+ (5, 'knees'),
+ (6, 'knell'),
+ (7, 'knelt'),
+ (8, 'knew'),
+ (9, 'knick'),
+ (10, 'knif'),
+ (11, 'knife'),
+ (12, 'knight'),
+ (13, 'knightly'),
+ (14, 'knights'),
+ (15, 'knit'),
+ (16, 'knits'),
+ (17, 'knitted'),
+ (18, 'knitting'),
+ (19, 'knives'),
+ (20, 'knob'),
+ (21, 'knobs'),
+ (22, 'knock'),
+ (23, 'knocked'),
+ (24, 'knocker'),
+ (25, 'knockers'),
+ (26, 'knocking'),
+ (27, 'knocks'),
+ (28, 'knopp'),
+ (29, 'knot'),
+ (30, 'knots');
+</pre></li>
+<li>Return the stem words <pre class="example">
+SELECT madlib.stem_token(word) FROM token_tbl;
+</pre> <pre class="result">
+ stem_token
+ ------------
+ kneel
+ kneel
+ kneel
+ kneel
+ knee
+ knell
+ knelt
+ knew
+ knick
+ knif
+ knife
+ knight
+ knight
+ knight
+ knit
+ knit
+ knit
+ knit
+ knive
+ knob
+ knob
+ knock
+ knock
+ knocker
+ knocker
+ knock
+ knock
+ knopp
+ knot
+ knot
+(30 rows)
+</pre></li>
+<li>The input can be processed as an array <pre class="example">
+SELECT madlib.stem_token_arr(array_agg(word order by word)) FROM token_tbl;
+</pre> <pre class="result">
+ stem_token_arr
+ -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+ {kneel,kneel,kneel,kneel,knee,knell,knelt,knew,knick,knif,knife,knight,knight,knight,knit,knit,knit,knit,knive,knob,knob,knock,knock,knocker,knocker,knock,knock,knopp,knot,knot}
+(1 row)
+</pre></li>
+</ol>
+<p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd></dd></dl>
+<p>File <a class="el" href="porter__stemmer_8sql__in.html" title="implementation of porter stemmer operations in SQL ">porter_stemmer.sql_in</a> for list of functions and usage. </p>
+</div><!-- contents -->
+</div><!-- doc-content -->
+<!-- start footer part -->
+<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
+ <ul>
+ <li class="footer">Generated on Wed Dec 27 2017 19:05:57 for MADlib by
+ <a href="http://www.doxygen.org/index.html">
+ <img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.8.13 </li>
+ </ul>
+</div>
+</body>
+</html>
http://git-wip-us.apache.org/repos/asf/madlib-site/blob/6c103d3e/docs/v1.13/group__grp__strs.html
----------------------------------------------------------------------
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new file mode 100644
index 0000000..7a311d9
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+<!-- HTML header for doxygen 1.8.4-->
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+<title>MADlib: Stratified Sampling</title>
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+ </div>
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+ <div class="headertitle">
+<div class="title">Stratified Sampling<div class="ingroups"><a class="el" href="group__grp__utility__functions.html">Utility Functions</a> » <a class="el" href="group__grp__sampling.html">Sampling</a></div></div> </div>
+</div><!--header-->
+<div class="contents">
+<div class="toc"><b>Contents</b> <ul>
+<li>
+<a href="#strs">Stratified Sampling</a> </li>
+<li>
+<a href="#examples">Examples</a> </li>
+</ul>
+</div><p>Stratified sampling is a method for independently sampling subpopulations (strata). It is commonly used to reduce sampling error by ensuring that subgroups are adequately represented in the sample.</p>
+<p><a class="anchor" id="strs"></a></p><dl class="section user"><dt>Stratified Sampling</dt><dd></dd></dl>
+<pre class="syntax">
+stratified_sample( source_table,
+ output_table,
+ proportion,
+ grouping_cols,
+ target_cols,
+ with_replacement
+ )
+</pre><p><b>Arguments</b> </p><dl class="arglist">
+<dt>source_table </dt>
+<dd><p class="startdd">TEXT. Name of the table containing the input data.</p>
+<p class="enddd"></p>
+</dd>
+<dt>output_table </dt>
+<dd><p class="startdd">TEXT. Name of output table that contains the sampled data. The output table contains all columns present in the source table unless otherwise specified in the 'target_cols' parameter below.</p>
+<p class="enddd"></p>
+</dd>
+<dt>proportion </dt>
+<dd><p class="startdd">FLOAT8 in the range (0,1). Each stratum is sampled independently.</p>
+<p class="enddd"></p>
+</dd>
+<dt>grouping_cols (optional) </dt>
+<dd><p class="startdd">TEXT, default: NULL. A single column or a list of comma-separated columns that defines the strata. When this parameter is NULL, no grouping is used so the sampling is non-stratified, that is, the whole table is treated as a single group.</p>
+<p class="enddd"></p>
+</dd>
+<dt>target_cols (optional) </dt>
+<dd><p class="startdd">TEXT, default NULL. A comma-separated list of columns to appear in the 'output_table'. If NULL or '*', all columns from the 'source_table' will appear in the 'output_table'.</p>
+<p class="enddd"><a class="anchor" id="note"></a></p><dl class="section note"><dt>Note</dt><dd>Do not include 'grouping_cols' in the parameter 'target_cols', because they are always included in the 'output_table'.</dd></dl>
+</dd>
+<dt>with_replacement (optional) </dt>
+<dd>BOOLEAN, default FALSE. Determines whether to sample with replacement or without replacement (default). With replacement means that it is possible that the same row may appear in the sample set more than once. Without replacement means a given row can be selected only once. </dd>
+</dl>
+<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl>
+<p>Please note that due to the random nature of sampling, your results may look different from those below.</p>
+<ol type="1">
+<li>Create an input table: <pre class="syntax">
+DROP TABLE IF EXISTS test;
+CREATE TABLE test(
+ id1 INTEGER,
+ id2 INTEGER,
+ gr1 INTEGER,
+ gr2 INTEGER
+);
+INSERT INTO test VALUES
+(1,0,1,1),
+(2,0,1,1),
+(3,0,1,1),
+(4,0,1,1),
+(5,0,1,1),
+(6,0,1,1),
+(7,0,1,1),
+(8,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(0,1,1,2),
+(0,2,1,2),
+(0,3,1,2),
+(0,4,1,2),
+(0,5,1,2),
+(0,6,1,2),
+(10,10,2,2),
+(20,20,2,2),
+(30,30,2,2),
+(40,40,2,2),
+(50,50,2,2),
+(60,60,2,2),
+(70,70,2,2);
+</pre></li>
+<li>Sample without replacement: <pre class="syntax">
+DROP TABLE IF EXISTS out;
+SELECT madlib.stratified_sample(
+ 'test', -- Source table
+ 'out', -- Output table
+ 0.5, -- Sample proportion
+ 'gr1,gr2', -- Strata definition
+ 'id1,id2', -- Columns to output
+ FALSE); -- Sample without replacement
+SELECT * FROM out ORDER BY gr1,gr2,id1,id2;
+</pre> <pre class="result">
+ gr1 | gr2 | id1 | id2
+-----+-----+-----+-----
+ 1 | 1 | 2 | 0
+ 1 | 1 | 4 | 0
+ 1 | 1 | 7 | 0
+ 1 | 1 | 8 | 0
+ 1 | 1 | 9 | 0
+ 1 | 1 | 9 | 0
+ 1 | 2 | 0 | 2
+ 1 | 2 | 0 | 3
+ 1 | 2 | 0 | 4
+ 2 | 2 | 20 | 20
+ 2 | 2 | 30 | 30
+ 2 | 2 | 40 | 40
+ 2 | 2 | 60 | 60
+(13 rows)
+</pre></li>
+<li>Sample with replacement: <pre class="syntax">
+DROP TABLE IF EXISTS out;
+SELECT madlib.stratified_sample(
+ 'test', -- Source table
+ 'out', -- Output table
+ 0.5, -- Sample proportion
+ 'gr1,gr2', -- Strata definition
+ 'id1,id2', -- Columns to output
+ TRUE); -- Sample with replacement
+SELECT * FROM out ORDER BY gr1,gr2,id1,id2;
+</pre> <pre class="result">
+ gr1 | gr2 | id1 | id2
+----—+----—+----—+----—
+ 1 | 1 | 3 | 0
+ 1 | 1 | 6 | 0
+ 1 | 1 | 6 | 0
+ 1 | 1 | 7 | 0
+ 1 | 1 | 7 | 0
+ 1 | 1 | 9 | 0
+ 1 | 2 | 0 | 1
+ 1 | 2 | 0 | 2
+ 1 | 2 | 0 | 6
+ 2 | 2 | 20 | 20
+ 2 | 2 | 30 | 30
+ 2 | 2 | 50 | 50
+ 2 | 2 | 50 | 50
+</pre> </li>
+</ol>
+</div><!-- contents -->
+</div><!-- doc-content -->
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