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For example, if you have a variable called race that is coded with 1=Hispanic, 2=Asian, 3=Black, 4=White, then entering race in your regression will look at the linear effect of the race variable, which is probably not what you intended. Instead, categorical variables like this need to be coded into a series of indicator variables which can then be entered into the regression model. There are a variety of coding systems that can be used for coding categorical variables, including one-hot, dummy, effects, orthogonal, and Helmert.</dd></dl> +<p>We currently support one-hot and dummy coding techniques.</p> +<p>Dummy coding is used when a researcher wants to compare other groups of the predictor variable with one specific group of the predictor variable. Often, the specific group to compare with is called the reference group.</p> +<p>One-hot encoding is similar to dummy coding except it builds indicator (0/1) columns (cast as numeric) for each value of each category. Only one of these columns could take on the value 1 for each row (data point). There is no reference category for this function.</p> +<pre class="syntax"> +encode_categorical_variables ( + source_table, + output_table, + categorical_cols, + categorical_cols_to_exclude, -- Optional + row_id, -- Optional + top, -- Optional + value_to_drop, -- Optional + encode_null, -- Optional + output_type, -- Optional + output_dictionary, -- Optional + distributed_by -- Optional + ) +</pre><p> <b>Arguments</b> </p><dl class="arglist"> +<dt>source_table </dt> +<dd><p class="startdd">VARCHAR. Name of the table containing the source categorical data to encode.</p> +<p class="enddd"></p> +</dd> +<dt>output_table </dt> +<dd><p class="startdd">VARCHAR. Name of the result table.</p> +<dl class="section note"><dt>Note</dt><dd>If there are index columns in the 'source_table' specified by the parameter 'row_id' (see below), then the output table will contain only the index columns 'row_id' and the encoded columns. If the parameter 'row_id' is not specified, then all columns from the 'source_table', with the exception of the original columns that have been encoded, will be included in the 'output_table'. </dd></dl> +</dd> +<dt>categorical_cols </dt> +<dd><p class="startdd">VARCHAR. Comma-separated string of column names of categorical variables to encode. Can also be '*' meaning all columns are to be encoded, except the ones specified in 'categorical_cols_to_exclude' and 'row_id'. Please note that all Boolean, integer and text columns are considered categorical columns and will be encoded when â*â is specified for this argument. </p> +<p class="enddd"></p> +</dd> +<dt>categorical_cols_to_exclude (optional) </dt> +<dd><p class="startdd">VARCHAR. Comma-separated string of column names to exclude from the categorical variables to encode. Applicable only if 'categorical_cols' = '*'. </p> +<p class="enddd"></p> +</dd> +<dt>row_id (optional) </dt> +<dd><p class="startdd">VARCHAR. Comma-separated column name(s) corresponding to the primary key(s) of the source table. This parameter determines the format of the 'output_table' as described above. If 'categorical_cols' = '*', these columns will be excluded from encoding (but will be included in the output table).</p> +<dl class="section note"><dt>Note</dt><dd>If you want to see both the raw categorical variable and its encoded form in the output_table, then include the categorical variable in the 'row_id' parameter. However, this will not work if you specify '*' for the parameter 'categorical_cols', because in this case 'row_id' columns will not be encoded at all. </dd></dl> +</dd> +<dt>top (optional) </dt> +<dd><p class="startdd">VARCHAR. default: NULL. If integer, encodes the top n values by frequency. If float in the range (0.0, 1.0), encodes the specified fraction of values by frequency (e.g., 0.1 means top 10%). Can be specified as a global for all categorical columns, or as a dictionary with separate 'top' values for each categorical variable. Set to NULL to encode all levels (values) for all categorical columns. </p> +<p class="enddd"></p> +</dd> +<dt>value_to_drop (optional) </dt> +<dd><p class="startdd">VARCHAR. Default: NULL.</p> +<ul> +<li>For dummy coding, indicate the desired value (reference) to drop for each categorical variable. Can be specified as a global for all categorical columns, or a comma-separated string containing items of the form 'name=value', where 'name' is the column name and 'value' is the reference value to be dropped.</li> +<li>Set to NULL for one-hot encoding (default)</li> +</ul> +<dl class="section note"><dt>Note</dt><dd>If you specify both 'value_to_drop' and 'top' parameters, the 'value_to_drop' will be applied first (takes priority), then 'top' will be applied to the remaining values. </dd></dl> +</dd> +<dt>encode_null (optional) </dt> +<dd><p class="startdd">BOOLEAN. default: FALSE. Whether NULL should be treated as one of the values of the categorical variable. If TRUE, then an indicator variable is created corresponding to the NULL value. If FALSE, then all encoded values for that variable will be set to 0. </p> +<p class="enddd"></p> +</dd> +<dt>output_type (optional) </dt> +<dd><p class="startdd">VARCHAR. default: 'column'. This parameter controls the output format of the indicator variables. If 'column', a column is created for each indicator variable. PostgreSQL limits the number of columns in a table. If the total number of indicator columns exceeds the limit, then make this parameter either 'array' to combine the indicator columns into an array or 'svec' to cast the array output to <em>'madlib.svec'</em> type.</p> +<p>Since the array output for any single tuple would be sparse (only one non-zero entry for each categorical column), the 'svec' output would be most efficient for storage. The 'array' output is useful if the array is used for post-processing, including concatenating with other non-categorical features.</p> +<p>The order of the array is the same as specified in 'categorical_cols'. A dictionary will be created when 'output_type' is 'array' or 'svec' to define an index into the array. The dictionary table will be given the name of the 'output_table' appended by '_dictionary'. </p> +<p class="enddd"></p> +</dd> +<dt>output_dictionary (optional) </dt> +<dd><p class="startdd">BOOLEAN. default: FALSE. This parameter is used to handle auto-generated column names that exceed the PostgreSQL limit of 63 bytes.</p> +<ul> +<li>If TRUE, column names will include numerical IDs and will create a dictionary table called 'output_table_dictionary' ('output_table' appended with '_dictionary').</li> +<li>If FALSE, will auto-generate column names in the usual way unless the limit of 63 bytes will be exceeded. In this case, a dictionary output file will be created and a message given to the user. </li> +</ul> +<p class="enddd"></p> +</dd> +<dt>distributed_by (optional) </dt> +<dd><p class="startdd">VARCHAR. default: NULL. Columns to use for the distribution policy of the output table. When NULL, either 'row_id' is used as distribution policy (when provided), or else the distribution policy of 'source_table' will be used. This argument does not apply to PostgreSQL platforms.</p> +<ul> +<li>NULL: By default, the distribution policy of the source_table will be used.</li> +<li>Comma-separated column names: Column(s) to be used for the distribution key.</li> +<li>RANDOMLY: Use random distribution policy (only if there does not exist a column named 'randomly').</li> +</ul> +<p class="enddd"></p> +</dd> +</dl> +<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd></dd></dl> +<ol type="1"> +<li>Use a subset of the abalone dataset [2]: <pre class="example"> +DROP TABLE IF EXISTS abalone; +CREATE TABLE abalone ( + id serial, + sex character varying, + length double precision, + diameter double precision, + height double precision, + rings int +); +INSERT INTO abalone (sex, length, diameter, height, rings) VALUES +('M', 0.455, 0.365, 0.095, 15), +('M', 0.35, 0.265, 0.09, 7), +('F', 0.53, 0.42, 0.135, 9), +('M', 0.44, 0.365, 0.125, 10), +('I', 0.33, 0.255, 0.08, 7), +('I', 0.425, 0.3, 0.095, 8), +('F', 0.53, 0.415, 0.15, 20), +('F', 0.545, 0.425, 0.125, 16), +('M', 0.475, 0.37, 0.125, 9), +(NULL, 0.55, 0.44, 0.15, 19), +('F', 0.525, 0.38, 0.14, 14), +('M', 0.43, 0.35, 0.11, 10), +('M', 0.49, 0.38, 0.135, 11), +('F', 0.535, 0.405, 0.145, 10), +('F', 0.47, 0.355, 0.1, 10), +('M', 0.5, 0.4, 0.13, 12), +('I', 0.355, 0.28, 0.085, 7), +('F', 0.44, 0.34, 0.1, 10), +('M', 0.365, 0.295, 0.08, 7), +(NULL, 0.45, 0.32, 0.1, 9); +</pre></li> +<li>Create new table with one-hot encoding. The column 'sex' is replaced by three columns encoding the values 'F', 'M' and 'I'. Null values are not encoded by default: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + 'sex' -- Categorical columns + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | length | diameter | height | rings | sex_F | sex_I | sex_M +----+--------+----------+--------+-------+-------+-------+------- + 1 | 0.455 | 0.365 | 0.095 | 15 | 0 | 0 | 1 + 2 | 0.35 | 0.265 | 0.09 | 7 | 0 | 0 | 1 + 3 | 0.53 | 0.42 | 0.135 | 9 | 1 | 0 | 0 + 4 | 0.44 | 0.365 | 0.125 | 10 | 0 | 0 | 1 + 5 | 0.33 | 0.255 | 0.08 | 7 | 0 | 1 | 0 + 6 | 0.425 | 0.3 | 0.095 | 8 | 0 | 1 | 0 + 7 | 0.53 | 0.415 | 0.15 | 20 | 1 | 0 | 0 + 8 | 0.545 | 0.425 | 0.125 | 16 | 1 | 0 | 0 + 9 | 0.475 | 0.37 | 0.125 | 9 | 0 | 0 | 1 + 10 | 0.55 | 0.44 | 0.15 | 19 | 0 | 0 | 0 + 11 | 0.525 | 0.38 | 0.14 | 14 | 1 | 0 | 0 + 12 | 0.43 | 0.35 | 0.11 | 10 | 0 | 0 | 1 + 13 | 0.49 | 0.38 | 0.135 | 11 | 0 | 0 | 1 + 14 | 0.535 | 0.405 | 0.145 | 10 | 1 | 0 | 0 + 15 | 0.47 | 0.355 | 0.1 | 10 | 1 | 0 | 0 + 16 | 0.5 | 0.4 | 0.13 | 12 | 0 | 0 | 1 + 17 | 0.355 | 0.28 | 0.085 | 7 | 0 | 1 | 0 + 18 | 0.44 | 0.34 | 0.1 | 10 | 1 | 0 | 0 + 19 | 0.365 | 0.295 | 0.08 | 7 | 0 | 0 | 1 + 20 | 0.45 | 0.32 | 0.1 | 9 | 0 | 0 | 0 +(20 rows) +</pre></li> +<li>Now include NULL values in encoding (note the additional column 'sex_NULL'): <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + 'sex', -- Categorical columns + NULL, -- Categorical columns to exclude + NULL, -- Index columns + NULL, -- Top values + NULL, -- Value to drop for dummy encoding + TRUE -- Encode nulls + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | length | diameter | height | rings | sex_F | sex_I | sex_M | sex_NULL +----+--------+----------+--------+-------+-------+-------+-------+---------- + 1 | 0.455 | 0.365 | 0.095 | 15 | 0 | 0 | 1 | 0 + 2 | 0.35 | 0.265 | 0.09 | 7 | 0 | 0 | 1 | 0 + 3 | 0.53 | 0.42 | 0.135 | 9 | 1 | 0 | 0 | 0 + 4 | 0.44 | 0.365 | 0.125 | 10 | 0 | 0 | 1 | 0 + 5 | 0.33 | 0.255 | 0.08 | 7 | 0 | 1 | 0 | 0 + 6 | 0.425 | 0.3 | 0.095 | 8 | 0 | 1 | 0 | 0 + 7 | 0.53 | 0.415 | 0.15 | 20 | 1 | 0 | 0 | 0 + 8 | 0.545 | 0.425 | 0.125 | 16 | 1 | 0 | 0 | 0 + 9 | 0.475 | 0.37 | 0.125 | 9 | 0 | 0 | 1 | 0 + 10 | 0.55 | 0.44 | 0.15 | 19 | 0 | 0 | 0 | 1 + 11 | 0.525 | 0.38 | 0.14 | 14 | 1 | 0 | 0 | 0 + 12 | 0.43 | 0.35 | 0.11 | 10 | 0 | 0 | 1 | 0 + 13 | 0.49 | 0.38 | 0.135 | 11 | 0 | 0 | 1 | 0 + 14 | 0.535 | 0.405 | 0.145 | 10 | 1 | 0 | 0 | 0 + 15 | 0.47 | 0.355 | 0.1 | 10 | 1 | 0 | 0 | 0 + 16 | 0.5 | 0.4 | 0.13 | 12 | 0 | 0 | 1 | 0 + 17 | 0.355 | 0.28 | 0.085 | 7 | 0 | 1 | 0 | 0 + 18 | 0.44 | 0.34 | 0.1 | 10 | 1 | 0 | 0 | 0 + 19 | 0.365 | 0.295 | 0.08 | 7 | 0 | 0 | 1 | 0 + 20 | 0.45 | 0.32 | 0.1 | 9 | 0 | 0 | 0 | 1 +(20 rows) +</pre></li> +<li>Encode all categorical variables in the source table. Also, specify the column 'id' as the index (primary key) which changes the output table to include only the index and the encoded variables: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + '*', -- Categorical columns + NULL, -- Categorical columns to exclude + 'id' -- Index columns + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | sex_F | sex_I | sex_M | rings_7 | rings_8 | rings_9 | rings_10 | rings_11 | rings_12 | rings_14 | rings_15 | rings_16 | rings_19 | rings_20 +----+-------+-------+-------+---------+---------+---------+----------+----------+----------+----------+----------+----------+----------+---------- + 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 + 2 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 3 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 4 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 5 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 6 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 + 8 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 + 9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 + 11 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 + 12 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 13 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 + 14 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 15 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 16 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 + 17 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 18 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 19 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 20 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 +(20 rows) +</pre></li> +<li>Now let's encode only the top values and group others into a miscellaneous bucket column. Top values can be global across all columns or specified by column. As an example of the latter, here are the top 2 'sex' values and the top 50% of 'rings' values: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + '*', -- Categorical columns + NULL, -- Categorical columns to exclude + 'id', -- Index columns + 'sex=2, rings=0.5' -- Top values + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | sex_M | sex_F | sex__MISC__ | rings_10 | rings_7 | rings_9 | rings__MISC__ +----+-------+-------+-------------+----------+---------+---------+--------------- + 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 + 2 | 1 | 0 | 0 | 0 | 1 | 0 | 0 + 3 | 0 | 1 | 0 | 0 | 0 | 1 | 0 + 4 | 1 | 0 | 0 | 1 | 0 | 0 | 0 + 5 | 0 | 0 | 1 | 0 | 1 | 0 | 0 + 6 | 0 | 0 | 1 | 0 | 0 | 0 | 1 + 7 | 0 | 1 | 0 | 0 | 0 | 0 | 1 + 8 | 0 | 1 | 0 | 0 | 0 | 0 | 1 + 9 | 1 | 0 | 0 | 0 | 0 | 1 | 0 + 10 | 0 | 0 | 0 | 0 | 0 | 0 | 1 + 11 | 0 | 1 | 0 | 0 | 0 | 0 | 1 + 12 | 1 | 0 | 0 | 1 | 0 | 0 | 0 + 13 | 1 | 0 | 0 | 0 | 0 | 0 | 1 + 14 | 0 | 1 | 0 | 1 | 0 | 0 | 0 + 15 | 0 | 1 | 0 | 1 | 0 | 0 | 0 + 16 | 1 | 0 | 0 | 0 | 0 | 0 | 1 + 17 | 0 | 0 | 1 | 0 | 1 | 0 | 0 + 18 | 0 | 1 | 0 | 1 | 0 | 0 | 0 + 19 | 1 | 0 | 0 | 0 | 1 | 0 | 0 + 20 | 0 | 0 | 0 | 0 | 0 | 1 | 0 +(20 rows) +</pre></li> +<li>If you want to see both the raw categorical variable and its encoded form in the output_table, then include the categorical variable(s) in the index parameter. (Remember that this will not work if you specify '*' for the parameter 'categorical_cols', because in this case 'row_id' columns will not be encoded at all.) <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + 'sex, rings', -- Categorical columns + NULL, -- Categorical columns to exclude + 'id, sex, rings' -- Index columns + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | sex | rings | sex_F | sex_I | sex_M | rings_7 | rings_8 | rings_9 | rings_10 | rings_11 | rings_12 | rings_14 | rings_15 | rings_16 | rings_19 | rings_20 +----+-----+-------+-------+-------+-------+---------+---------+---------+----------+----------+----------+----------+----------+----------+----------+---------- + 1 | M | 15 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 + 2 | M | 7 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 3 | F | 9 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 4 | M | 10 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 5 | I | 7 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 6 | I | 8 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 7 | F | 20 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 + 8 | F | 16 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 + 9 | M | 9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 10 | | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 + 11 | F | 14 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 + 12 | M | 10 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 13 | M | 11 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 + 14 | F | 10 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 15 | F | 10 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 16 | M | 12 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 + 17 | I | 7 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 18 | F | 10 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 19 | M | 7 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 20 | | 9 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 +(20 rows) +</pre></li> +<li>For dummy encoding, let's make the 'I' value from the 'sex' variable as the reference. Here we use the 'value_to_drop' parameter: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + '*', -- Categorical columns + 'rings', -- Categorical columns to exclude + 'id', -- Index columns + NULL, -- Top value + 'sex=I' -- Value to drop for dummy encoding + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | sex_F | sex_M +----+-------+------- + 1 | 0 | 1 + 2 | 0 | 1 + 3 | 1 | 0 + 4 | 0 | 1 + 5 | 0 | 0 + 6 | 0 | 0 + 7 | 1 | 0 + 8 | 1 | 0 + 9 | 0 | 1 + 10 | 0 | 0 + 11 | 1 | 0 + 12 | 0 | 1 + 13 | 0 | 1 + 14 | 1 | 0 + 15 | 1 | 0 + 16 | 0 | 1 + 17 | 0 | 0 + 18 | 1 | 0 + 19 | 0 | 1 + 20 | 0 | 0 +(20 rows) +</pre></li> +<li>Create an array output for the two categorical variables in the source table: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + '*', -- Categorical columns + NULL, -- Categorical columns to exclude + 'id', -- Index columns + NULL, -- Top values + NULL, -- Value to drop for dummy encoding + NULL, -- Encode nulls + 'array' -- Array output type + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | __encoded_variables__ +----+------------------------------- + 1 | {0,0,1,0,0,0,0,0,0,0,1,0,0,0} + 2 | {0,0,1,1,0,0,0,0,0,0,0,0,0,0} + 3 | {1,0,0,0,0,1,0,0,0,0,0,0,0,0} + 4 | {0,0,1,0,0,0,1,0,0,0,0,0,0,0} + 5 | {0,1,0,1,0,0,0,0,0,0,0,0,0,0} + 6 | {0,1,0,0,1,0,0,0,0,0,0,0,0,0} + 7 | {1,0,0,0,0,0,0,0,0,0,0,0,0,1} + 8 | {1,0,0,0,0,0,0,0,0,0,0,1,0,0} + 9 | {0,0,1,0,0,1,0,0,0,0,0,0,0,0} + 10 | {0,0,0,0,0,0,0,0,0,0,0,0,1,0} + 11 | {1,0,0,0,0,0,0,0,0,1,0,0,0,0} + 12 | {0,0,1,0,0,0,1,0,0,0,0,0,0,0} + 13 | {0,0,1,0,0,0,0,1,0,0,0,0,0,0} + 14 | {1,0,0,0,0,0,1,0,0,0,0,0,0,0} + 15 | {1,0,0,0,0,0,1,0,0,0,0,0,0,0} + 16 | {0,0,1,0,0,0,0,0,1,0,0,0,0,0} + 17 | {0,1,0,1,0,0,0,0,0,0,0,0,0,0} + 18 | {1,0,0,0,0,0,1,0,0,0,0,0,0,0} + 19 | {0,0,1,1,0,0,0,0,0,0,0,0,0,0} + 20 | {0,0,0,0,0,1,0,0,0,0,0,0,0,0} +(20 rows) +</pre> View the dictionary table that gives the index into the array: <pre class="example"> +SELECT * FROM abalone_out_dictionary; +</pre> <pre class="result"> + encoded_column_name | index | variable | value +-----------------------+-------+----------+------- + __encoded_variables__ | 1 | sex | F + __encoded_variables__ | 2 | sex | I + __encoded_variables__ | 3 | sex | M + __encoded_variables__ | 4 | rings | 7 + __encoded_variables__ | 5 | rings | 8 + __encoded_variables__ | 6 | rings | 9 + __encoded_variables__ | 7 | rings | 10 + __encoded_variables__ | 8 | rings | 11 + __encoded_variables__ | 9 | rings | 12 + __encoded_variables__ | 10 | rings | 14 + __encoded_variables__ | 11 | rings | 15 + __encoded_variables__ | 12 | rings | 16 + __encoded_variables__ | 13 | rings | 19 + __encoded_variables__ | 14 | rings | 20 +(14 rows) +</pre></li> +<li>Create a dictionary output: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + '*', -- Categorical columns + NULL, -- Categorical columns to exclude + 'id', -- Index columns + NULL, -- Top values + NULL, -- Value to drop for dummy encoding + NULL, -- Encode nulls + NULL, -- Output type + TRUE -- Dictionary output + ); +SELECT * FROM abalone_out ORDER BY id; +</pre> <pre class="result"> + id | sex_1 | sex_2 | sex_3 | rings_1 | rings_2 | rings_3 | rings_4 | rings_5 | rings_6 | rings_7 | rings_8 | rings_9 | rings_10 | rings_11 +----+-------+-------+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+----------+---------- + 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 + 2 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 3 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 4 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 5 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 6 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 7 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 + 8 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 + 9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 + 11 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 + 12 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 13 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 + 14 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 15 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 16 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 + 17 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 18 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 19 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 + 20 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 +(20 rows) +</pre> View the dictionary table that defines the numerical columns in the output table: <pre class="example"> +SELECT * FROM abalone_out_dictionary ORDER BY encoded_column_name; +</pre> <pre class="result"> + encoded_column_name | index | variable | value +---------------------+-------+----------+------- + "rings_1" | 1 | rings | 7 + "rings_10" | 10 | rings | 19 + "rings_11" | 11 | rings | 20 + "rings_2" | 2 | rings | 8 + "rings_3" | 3 | rings | 9 + "rings_4" | 4 | rings | 10 + "rings_5" | 5 | rings | 11 + "rings_6" | 6 | rings | 12 + "rings_7" | 7 | rings | 14 + "rings_8" | 8 | rings | 15 + "rings_9" | 9 | rings | 16 + "sex_1" | 1 | sex | F + "sex_2" | 2 | sex | I + "sex_3" | 3 | sex | M +(14 rows) +</pre></li> +<li>We can chose from various distribution policies, for examply RANDOMLY: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + '*', -- Categorical columns + NULL, -- Categorical columns to exclude + 'id', -- Index columns + NULL, -- Top values + NULL, -- Value to drop for dummy encoding + NULL, -- Encode nulls + NULL, -- Output type + NULL, -- Dictionary output + 'RANDOMLY' -- Distribution policy + ); +</pre></li> +<li>If you have a reason to encode FLOAT variables, you can cast them in the following way within the function call: <pre class="example"> +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary; +SELECT madlib.encode_categorical_variables ( + 'abalone', -- Source table + 'abalone_out', -- Output table + 'height::TEXT' -- Categorical columns + ); +</pre></li> +</ol> +<p><a class="anchor" id="literature"></a></p><dl class="section user"><dt>Literature</dt><dd></dd></dl> +<p><a class="anchor" id="svm-lit-1"></a>[1] <a href="https://en.wikipedia.org/wiki/Categorical_variable";>https://en.wikipedia.org/wiki/Categorical_variable</a></p> +<p>[2] <a href="https://archive.ics.uci.edu/ml/datasets/Abalone";>https://archive.ics.uci.edu/ml/datasets/Abalone</a> </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 Tue May 16 2017 13:24:38 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/incubator-madlib-site/blob/b5b51c69/docs/v1.11/group__grp__fmsketch.html ---------------------------------------------------------------------- diff --git a/docs/v1.11/group__grp__fmsketch.html b/docs/v1.11/group__grp__fmsketch.html new file mode 100644 index 0000000..3a664c7 --- /dev/null +++ b/docs/v1.11/group__grp__fmsketch.html @@ -0,0 +1,161 @@ +<!-- HTML header for doxygen 1.8.4--> +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd";> +<html xmlns="http://www.w3.org/1999/xhtml";> +<head> +<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/> +<meta http-equiv="X-UA-Compatible" content="IE=9"/> +<meta name="generator" content="Doxygen 1.8.13"/> +<meta name="keywords" content="madlib,postgres,greenplum,machine learning,data mining,deep learning,ensemble methods,data science,market basket analysis,affinity analysis,pca,lda,regression,elastic net,huber white,proportional hazards,k-means,latent dirichlet allocation,bayes,support vector machines,svm"/> +<title>MADlib: FM (Flajolet-Martin)</title> +<link href="tabs.css" rel="stylesheet" type="text/css"/> +<script type="text/javascript" src="jquery.js"></script> +<script type="text/javascript" src="dynsections.js"></script> +<link href="navtree.css" rel="stylesheet" type="text/css"/> +<script type="text/javascript" src="resize.js"></script> +<script type="text/javascript" src="navtreedata.js"></script> +<script type="text/javascript" src="navtree.js"></script> +<script type="text/javascript"> + $(document).ready(initResizable); +</script> +<link href="search/search.css" rel="stylesheet" type="text/css"/> +<script type="text/javascript" src="search/searchdata.js"></script> +<script type="text/javascript" src="search/search.js"></script> +<script type="text/javascript"> + $(document).ready(function() { init_search(); }); +</script> +<!-- hack in the navigation tree --> +<script type="text/javascript" src="eigen_navtree_hacks.js"></script> +<link href="doxygen.css" rel="stylesheet" type="text/css" /> +<link href="madlib_extra.css" rel="stylesheet" type="text/css"/> +<!-- google analytics --> +<script> + (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ + (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), + m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) + })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); + ga('create', 'UA-45382226-1', 'madlib.incubator.apache.org'); + ga('send', 'pageview'); +</script> +</head> +<body> +<div id="top"><!-- do not remove this div, it is closed by doxygen! --> +<div id="titlearea"> +<table cellspacing="0" cellpadding="0"> + <tbody> + <tr style="height: 56px;"> + <td id="projectlogo"><a href="http://madlib.incubator.apache.org";><img alt="Logo" src="madlib.png" height="50" style="padding-left:0.5em;" border="0"/ ></a></td> + <td style="padding-left: 0.5em;"> + <div id="projectname"> + <span id="projectnumber">1.11</span> + </div> + <div id="projectbrief">User Documentation for MADlib</div> + </td> + <td> <div id="MSearchBox" class="MSearchBoxInactive"> + <span class="left"> + <img id="MSearchSelect" src="search/mag_sel.png" + onmouseover="return searchBox.OnSearchSelectShow()" + onmouseout="return searchBox.OnSearchSelectHide()" + alt=""/> + <input type="text" id="MSearchField" value="Search" accesskey="S" + onfocus="searchBox.OnSearchFieldFocus(true)" + onblur="searchBox.OnSearchFieldFocus(false)" + onkeyup="searchBox.OnSearchFieldChange(event)"/> + </span><span class="right"> + <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a> + </span> + </div> +</td> + </tr> + </tbody> +</table> +</div> +<!-- end header part --> +<!-- Generated by Doxygen 1.8.13 --> +<script type="text/javascript"> +var searchBox = new SearchBox("searchBox", "search",false,'Search'); +</script> +</div><!-- top --> +<div id="side-nav" class="ui-resizable side-nav-resizable"> + <div id="nav-tree"> + <div id="nav-tree-contents"> + <div id="nav-sync" class="sync"></div> + </div> + </div> + <div id="splitbar" style="-moz-user-select:none;" + class="ui-resizable-handle"> + </div> +</div> +<script type="text/javascript"> +$(document).ready(function(){initNavTree('group__grp__fmsketch.html','');}); +</script> +<div id="doc-content"> +<!-- window showing the filter options --> +<div id="MSearchSelectWindow" + onmouseover="return searchBox.OnSearchSelectShow()" + onmouseout="return searchBox.OnSearchSelectHide()" + onkeydown="return searchBox.OnSearchSelectKey(event)"> +</div> + +<!-- iframe showing the search results (closed by default) --> +<div id="MSearchResultsWindow"> +<iframe src="javascript:void(0)" frameborder="0" + name="MSearchResults" id="MSearchResults"> +</iframe> +</div> + +<div class="header"> + <div class="headertitle"> +<div class="title">FM (Flajolet-Martin)<div class="ingroups"><a class="el" href="group__grp__early__stage.html">Early Stage Development</a> » <a class="el" href="group__grp__sketches.html">Cardinality Estimators</a></div></div> </div> +</div><!--header--> +<div class="contents"> +<div class="toc"><b>Contents</b> <ul> +<li> +<a href="#syntax">Syntax</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><dl class="section warning"><dt>Warning</dt><dd><em> This MADlib method is still in early stage development. There may be some issues that will be addressed in a future version. Interface and implementation is subject to change. </em></dd></dl> +<p><a class="el" href="sketch_8sql__in.html#ae27d5aaa5e4b426bcfe55e05a89c8e0b">fmsketch_dcount</a> can be run on a column of any type. It returns an approximation to the number of distinct values (a la <code>COUNT(DISTINCT x)</code>), but faster and approximate. Like any aggregate, it can be combined with a GROUP BY clause to do distinct counts per group.</p> +<p><a class="anchor" id="syntax"></a></p><dl class="section user"><dt>Syntax</dt><dd></dd></dl> +<p>Get the number of distinct values in a designated column. </p><pre class="syntax"> +fmsketch_dcount( col_name ) +</pre><p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd><ol type="1"> +<li>Generate some data. <pre class="example"> +CREATE TABLE data(class INT, a1 INT); +INSERT INTO data SELECT 1,1 FROM generate_series(1,10000); +INSERT INTO data SELECT 1,2 FROM generate_series(1,15000); +INSERT INTO data SELECT 1,3 FROM generate_series(1,10000); +INSERT INTO data SELECT 2,5 FROM generate_series(1,1000); +INSERT INTO data SELECT 2,6 FROM generate_series(1,1000); +</pre></li> +<li>Find the distinct number of values for each class. <pre class="example"> +SELECT class, fmsketch_dcount(a1) +FROM data +GROUP BY data.class; +</pre> Result: <pre class="result"> +class | fmsketch_dcount + ------+----------------- + 2 | 2 + 1 | 3 +(2 rows) +</pre></li> +</ol> +</dd></dl> +<p><a class="anchor" id="literature"></a></p><dl class="section user"><dt>Literature</dt><dd>[1] P. Flajolet and N.G. Martin. Probabilistic counting algorithms for data base applications, Journal of Computer and System Sciences 31(2), pp 182-209, 1985. <a href="http://algo.inria.fr/flajolet/Publications/FlMa85.pdf";>http://algo.inria.fr/flajolet/Publications/FlMa85.pdf</a></dd></dl> +<p><a class="anchor" id="related"></a></p><dl class="section user"><dt>Related Topics</dt><dd>File <a class="el" href="sketch_8sql__in.html" title="SQL functions for sketch-based approximations of descriptive statistics. ">sketch.sql_in</a> documenting the SQL function. </dd></dl> +</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 Tue May 16 2017 13:24:39 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/incubator-madlib-site/blob/b5b51c69/docs/v1.11/group__grp__glm.html ---------------------------------------------------------------------- diff --git a/docs/v1.11/group__grp__glm.html b/docs/v1.11/group__grp__glm.html new file mode 100644 index 0000000..aec02ac --- /dev/null +++ b/docs/v1.11/group__grp__glm.html @@ -0,0 +1,572 @@ +<!-- HTML header for doxygen 1.8.4--> +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd";> +<html xmlns="http://www.w3.org/1999/xhtml";> +<head> +<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/> +<meta http-equiv="X-UA-Compatible" content="IE=9"/> +<meta name="generator" content="Doxygen 1.8.13"/> +<meta name="keywords" content="madlib,postgres,greenplum,machine learning,data mining,deep learning,ensemble methods,data science,market basket analysis,affinity analysis,pca,lda,regression,elastic net,huber white,proportional hazards,k-means,latent dirichlet allocation,bayes,support vector machines,svm"/> +<title>MADlib: Generalized Linear Models</title> +<link href="tabs.css" rel="stylesheet" type="text/css"/> +<script type="text/javascript" src="jquery.js"></script> +<script type="text/javascript" src="dynsections.js"></script> +<link href="navtree.css" rel="stylesheet" type="text/css"/> +<script type="text/javascript" src="resize.js"></script> +<script type="text/javascript" src="navtreedata.js"></script> +<script type="text/javascript" src="navtree.js"></script> +<script type="text/javascript"> + $(document).ready(initResizable); +</script> +<link href="search/search.css" rel="stylesheet" type="text/css"/> +<script type="text/javascript" src="search/searchdata.js"></script> +<script type="text/javascript" src="search/search.js"></script> +<script type="text/javascript"> + $(document).ready(function() { init_search(); }); +</script> +<!-- hack in the navigation tree --> +<script type="text/javascript" src="eigen_navtree_hacks.js"></script> +<link href="doxygen.css" rel="stylesheet" type="text/css" /> +<link href="madlib_extra.css" rel="stylesheet" type="text/css"/> +<!-- google analytics --> +<script> + (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ + (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), + m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) + })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); + ga('create', 'UA-45382226-1', 'madlib.incubator.apache.org'); + ga('send', 'pageview'); +</script> +</head> +<body> +<div id="top"><!-- do not remove this div, it is closed by doxygen! --> +<div id="titlearea"> +<table cellspacing="0" cellpadding="0"> + <tbody> + <tr style="height: 56px;"> + <td id="projectlogo"><a href="http://madlib.incubator.apache.org";><img alt="Logo" src="madlib.png" height="50" style="padding-left:0.5em;" border="0"/ ></a></td> + <td style="padding-left: 0.5em;"> + <div id="projectname"> + <span id="projectnumber">1.11</span> + </div> + <div id="projectbrief">User Documentation for MADlib</div> + </td> + <td> <div id="MSearchBox" class="MSearchBoxInactive"> + <span class="left"> + <img id="MSearchSelect" src="search/mag_sel.png" + onmouseover="return searchBox.OnSearchSelectShow()" + onmouseout="return searchBox.OnSearchSelectHide()" + alt=""/> + <input type="text" id="MSearchField" value="Search" accesskey="S" + onfocus="searchBox.OnSearchFieldFocus(true)" + onblur="searchBox.OnSearchFieldFocus(false)" + onkeyup="searchBox.OnSearchFieldChange(event)"/> + </span><span class="right"> + <a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a> + </span> + </div> +</td> + </tr> + </tbody> +</table> +</div> +<!-- end header part --> +<!-- Generated by Doxygen 1.8.13 --> +<script type="text/javascript"> +var searchBox = new SearchBox("searchBox", "search",false,'Search'); +</script> +</div><!-- top --> +<div id="side-nav" class="ui-resizable side-nav-resizable"> + <div id="nav-tree"> + <div id="nav-tree-contents"> + <div id="nav-sync" class="sync"></div> + </div> + </div> + <div id="splitbar" style="-moz-user-select:none;" + class="ui-resizable-handle"> + </div> +</div> +<script type="text/javascript"> +$(document).ready(function(){initNavTree('group__grp__glm.html','');}); +</script> +<div id="doc-content"> +<!-- window showing the filter options --> +<div id="MSearchSelectWindow" + onmouseover="return searchBox.OnSearchSelectShow()" + onmouseout="return searchBox.OnSearchSelectHide()" + onkeydown="return searchBox.OnSearchSelectKey(event)"> +</div> + +<!-- iframe showing the search results (closed by default) --> +<div id="MSearchResultsWindow"> +<iframe src="javascript:void(0)" frameborder="0" + name="MSearchResults" id="MSearchResults"> +</iframe> +</div> + +<div class="header"> + <div class="headertitle"> +<div class="title">Generalized Linear Models<div class="ingroups"><a class="el" href="group__grp__super.html">Supervised Learning</a> » <a class="el" href="group__grp__regml.html">Regression Models</a></div></div> </div> +</div><!--header--> +<div class="contents"> +<div class="toc"><b>Contents</b><ul> +<li class="level1"> +<a href="#train">Training Function</a> </li> +<li class="level1"> +<a href="#predict">Prediction Function</a> </li> +<li class="level1"> +<a href="#examples">Examples</a> </li> +<li class="level1"> +<a href="#related">Related Topics</a> </li> +</ul> +</div><p>Generalized linear models extends ordinary linear regression by allowing the response variable to follow a more general set of distributions (rather than simply Gaussian distributions), and for a general family of functions of the response variable (the link function) to vary linearly with the predicted values (rather than assuming that the response itself must vary linearly).</p> +<p>For example, data of counts would typically be modeled with a Poisson distribution and a log link, while binary outcomes would typically be modeled with a Bernoulli distribution (or binomial distribution, depending on exactly how the problem is phrased) and a log-odds (or logit) link function.</p> +<p>Currently, the implemented distribution families are </p><center> <table class="doxtable"> +<tr> +<th>Distribution Family </th><th>Link Functions </th></tr> +<tr> +<td>Binomial </td><td>logit, probit </td></tr> +<tr> +<td>Gamma </td><td>inverse, identity, log </td></tr> +<tr> +<td>Gaussian </td><td>identity, inverse, log </td></tr> +<tr> +<td>Inverse Gaussian </td><td>inverse of square, inverse, identity, log </td></tr> +<tr> +<td>Poisson </td><td>log, identity, square-root<br /> + </td></tr> +</table> +</center><p><a class="anchor" id="train"></a></p><dl class="section user"><dt>Training Function</dt><dd>GLM training function has the following format: <pre class="syntax"> +glm(source_table, + model_table, + dependent_varname, + independent_varname, + family_params, + grouping_col, + optim_params, + verbose + ) +</pre> <b>Arguments</b> <dl class="arglist"> +<dt>source_table </dt> +<dd><p class="startdd">TEXT. The name of the table containing the training data.</p> +<p class="enddd"></p> +</dd> +<dt>model_table </dt> +<dd><p class="startdd">TEXT. Name of the generated table containing the model.</p> +<p>The model table produced by glm contains the following columns:</p> +<table class="output"> +<tr> +<th><...> </th><td><p class="starttd">Text. Grouping columns, if provided in input. This could be multiple columns depending on the <code>grouping_col</code> input. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>coef </th><td><p class="starttd">FLOAT8. Vector of the coefficients in linear predictor. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>log_likelihood </th><td><p class="starttd">FLOAT8. The log-likelihood <img class="formulaInl" alt="$ l(\boldsymbol \beta) $" src="form_93.png"/>. We use the maximum likelihood estimate of dispersion parameter to calculate the log-likelihood while R and Python use deviance estimate and Pearson estimate respectively. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>std_err </th><td><p class="starttd">FLOAT8[]. Vector of the standard error of the coefficients. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>z_stats or t_stats </th><td><p class="starttd">FLOAT8[]. Vector of the z-statistics (in Poisson distribtuion and Binomial distribution) or the t-statistics (in all other distributions) of the coefficients. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>p_values </th><td><p class="starttd">FLOAT8[]. Vector of the p-values of the coefficients. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>dispersion </th><td><p class="starttd">FLOAT8. The dispersion value (Pearson estimate). When family=poisson or family=binomial, the dispersion is always 1. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>num_rows_processed </th><td><p class="starttd">BIGINT. Numbers of rows processed. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>num_rows_skipped </th><td><p class="starttd">BIGINT. Numbers of rows skipped due to missing values or failures. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>num_iterations </th><td>INTEGER. The number of iterations actually completed. This would be different from the <code>nIterations</code> argument if a <code>tolerance</code> parameter is provided and the algorithm converges before all iterations are completed. </td></tr> +</table> +<p>A summary table named <model_table>_summary is also created at the same time, which has the following columns: </p><table class="output"> +<tr> +<th>method </th><td><p class="starttd">'glm' </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>source_table </th><td><p class="starttd">The data source table name. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>model_table </th><td><p class="starttd">The model table name. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>dependent_varname </th><td><p class="starttd">The dependent variable. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>independent_varname </th><td><p class="starttd">The independent variables </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>family_params </th><td><p class="starttd">A string that contains family parameters, and has the form of 'family=..., link=...' </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>grouping_col </th><td><p class="starttd">Name of grouping columns. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>optimizer_params </th><td><p class="starttd">A string that contains optimizer parameters, and has the form of 'optimizer=..., max_iter=..., tolerance=...' </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>num_all_groups </th><td><p class="starttd">Number of groups in glm training. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>num_failed_groups </th><td><p class="starttd">Number of failed groups in glm training. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>total_rows_processed </th><td><p class="starttd">BIGINT. Total numbers of rows processed in all groups. </p> +<p class="endtd"></p> +</td></tr> +<tr> +<th>total_rows_skipped </th><td><p class="starttd">BIGINT. Total numbers of rows skipped in all groups due to missing values or failures. </p> +<p class="endtd"></p> +</td></tr> +</table> +<p class="enddd"></p> +</dd> +<dt>dependent_varname </dt> +<dd><p class="startdd">TEXT. Name of the dependent variable column.</p> +<p class="enddd"></p> +</dd> +<dt>independent_varname </dt> +<dd><p class="startdd">TEXT. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant <code>1</code> term in the independent variable list.</p> +<p class="enddd"></p> +</dd> +<dt>family_params (optional) </dt> +<dd><p class="startdd">TEXT, Parameters for distribution family. Currently, we support</p> +<p>(1) family=poisson and link=[log or identity or sqrt].</p> +<p>(2) family=gaussian and link=[identity or log or inverse]. And when family=gaussian and link=identity, the GLM model is exactly the same as the linear regression.</p> +<p>(3) family=gamma and link=[inverse or identity or log].</p> +<p>(4) family=inverse_gaussian and link=[sqr_inverse or log or identity or inverse].</p> +<p>(5) family=binomial and link=[probit or logit]. </p> +<p class="enddd"></p> +</dd> +<dt>grouping_col (optional) </dt> +<dd><p class="startdd">TEXT, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single model is generated.</p> +<p class="enddd"></p> +</dd> +<dt>optim_params (optional) </dt> +<dd><p class="startdd">TEXT, default: 'max_iter=100,optimizer=irls,tolerance=1e-6'. Parameters for optimizer. Currently, we support tolerance=[tolerance for relative error between log-likelihoods], max_iter=[maximum iterations to run], optimizer=irls.</p> +<p class="enddd"></p> +</dd> +<dt>verbose (optional) </dt> +<dd>BOOLEAN, default: FALSE. Provides verbose output of the results of training. </dd> +</dl> +</dd></dl> +<dl class="section note"><dt>Note</dt><dd>For p-values, we just return the computation result directly. Other statistical packages, like 'R', produce the same result, but on printing the result to screen, another format function is used and any p-value that is smaller than the machine epsilon (the smallest positive floating-point number 'x' such that '1 + x != 1') will be printed on screen as "< xxx" (xxx is the value of the machine epsilon). Although the results may look different, they are in fact the same. </dd></dl> +<p><a class="anchor" id="predict"></a></p><dl class="section user"><dt>Prediction Function</dt><dd>The prediction function is provided to estimate the conditional mean given a new predictor. It has the following syntax: <pre class="syntax"> +glm_predict(coef, + col_ind_var + link) +</pre></dd></dl> +<p><b>Arguments</b> </p><dl class="arglist"> +<dt>coef </dt> +<dd><p class="startdd">DOUBLE PRECISION[]. Model coefficients obtained from <a class="el" href="glm_8sql__in.html#a3f8eb219013e05675626acb8cf4612cc">glm()</a>.</p> +<p class="enddd"></p> +</dd> +<dt>col_ind_var </dt> +<dd><p class="startdd">New predictor, as a DOUBLE array. This should be the same length as the array obtained by evaluation of the 'independent_varname' argument in <a class="el" href="glm_8sql__in.html#a3f8eb219013e05675626acb8cf4612cc">glm()</a>.</p> +<p class="enddd"></p> +</dd> +<dt>link </dt> +<dd>link function, as a string. This should match the link function the user inputted in <a class="el" href="glm_8sql__in.html#a3f8eb219013e05675626acb8cf4612cc">glm()</a>. </dd> +</dl> +<p><a class="anchor" id="examples"></a></p><dl class="section user"><dt>Examples</dt><dd><ol type="1"> +<li>Create the training data table. <pre class="example"> +CREATE TABLE warpbreaks( + id serial, + breaks integer, + wool char(1), + tension char(1) +); +INSERT INTO warpbreaks(breaks, wool, tension) VALUES +(26, 'A', 'L'), +(30, 'A', 'L'), +(54, 'A', 'L'), +(25, 'A', 'L'), +(70, 'A', 'L'), +(52, 'A', 'L'), +(51, 'A', 'L'), +(26, 'A', 'L'), +(67, 'A', 'L'), +(18, 'A', 'M'), +(21, 'A', 'M'), +(29, 'A', 'M'), +(17, 'A', 'M'), +(12, 'A', 'M'), +(18, 'A', 'M'), +(35, 'A', 'M'), +(30, 'A', 'M'), +(36, 'A', 'M'), +(36, 'A', 'H'), +(21, 'A', 'H'), +(24, 'A', 'H'), +(18, 'A', 'H'), +(10, 'A', 'H'), +(43, 'A', 'H'), +(28, 'A', 'H'), +(15, 'A', 'H'), +(26, 'A', 'H'), +(27, 'B', 'L'), +(14, 'B', 'L'), +(29, 'B', 'L'), +(19, 'B', 'L'), +(29, 'B', 'L'), +(31, 'B', 'L'), +(41, 'B', 'L'), +(20, 'B', 'L'), +(44, 'B', 'L'), +(42, 'B', 'M'), +(26, 'B', 'M'), +(19, 'B', 'M'), +(16, 'B', 'M'), +(39, 'B', 'M'), +(28, 'B', 'M'), +(21, 'B', 'M'), +(39, 'B', 'M'), +(29, 'B', 'M'), +(20, 'B', 'H'), +(21, 'B', 'H'), +(24, 'B', 'H'), +(17, 'B', 'H'), +(13, 'B', 'H'), +(15, 'B', 'H'), +(15, 'B', 'H'), +(16, 'B', 'H'), +(28, 'B', 'H'); +SELECT create_indicator_variables('warpbreaks', 'warpbreaks_dummy', 'wool,tension'); +</pre></li> +<li>Train a GLM model. <pre class="example"> +SELECT glm('warpbreaks_dummy', + 'glm_model', + 'breaks', + 'ARRAY[1.0,"wool_B","tension_M", "tension_H"]', + 'family=poisson, link=log'); +</pre></li> +<li>View the regression results. <pre class="example"> +-- Set extended display on for easier reading of output +\x on +SELECT * FROM glm_model; +</pre> Result: <pre class="result"> +coef | {3.69196314494079,-0.205988442638621,-0.321320431600611,-0.51848849651156} +log_likelihood | -242.527983208979 +std_err | {0.04541079434248,0.0515712427835191,0.0602659166951256,0.0639595193956924} +z_stats | {81.3014438174473,-3.99425011926316,-5.3317106786264,-8.10651020224019} +p_values | {0,6.48993254938271e-05,9.72918600322907e-08,5.20943463005751e-16} +num_rows_processed | 54 +num_rows_skipped | 0 +iteration | 5 +</pre> Alternatively, unnest the arrays in the results for easier reading of output: <pre class="example"> +\x off +SELECT unnest(coef) as coefficient, + unnest(std_err) as standard_error, + unnest(z_stats) as z_stat, + unnest(p_values) as pvalue +FROM glm_model; +</pre></li> +<li>Predicting dependent variable using GLM model. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used for prediction.) <pre class="example"> +\x off +-- Display predicted mean value on the original dataset +SELECT + w.id, + madlib.glm_predict( + coef, + ARRAY[1, "wool_B", "tension_M", "tension_H"]::float8[], + 'log') AS mu +FROM warpbreaks_dummy w, glm_model m +ORDER BY w.id; +</pre> <pre class="example"> +-- Display predicted counts (which are predicted mean values rounded to the nearest integral value) on the original dataset +SELECT + w.id, + madlib.glm_predict_poisson( + coef, + ARRAY[1, "wool_B", "tension_M", "tension_H"]::float8[], + 'log') AS poisson_count +FROM warpbreaks_dummy w, glm_model m +ORDER BY w.id; +</pre></li> +</ol> +</dd></dl> +<p><b>Example for Gaussian family:</b></p> +<ol type="1"> +<li>Create a testing data table <pre class="example"> +CREATE TABLE abalone ( + id integer, + sex text, + length double precision, + diameter double precision, + height double precision, + whole double precision, + shucked double precision, + viscera double precision, + shell double precision, + rings integer +); +INSERT INTO abalone VALUES +(3151, 'F', 0.655000000000000027, 0.505000000000000004, 0.165000000000000008, 1.36699999999999999, 0.583500000000000019, 0.351499999999999979, 0.396000000000000019, 10), +(2026, 'F', 0.550000000000000044, 0.469999999999999973, 0.149999999999999994, 0.920499999999999985, 0.381000000000000005, 0.243499999999999994, 0.267500000000000016, 10), +(3751, 'I', 0.434999999999999998, 0.375, 0.110000000000000001, 0.41549999999999998, 0.170000000000000012, 0.0759999999999999981, 0.14499999999999999, 8), +(720, 'I', 0.149999999999999994, 0.100000000000000006, 0.0250000000000000014, 0.0149999999999999994, 0.00449999999999999966, 0.00400000000000000008, 0.0050000000000000001, 2), +(1635, 'F', 0.574999999999999956, 0.469999999999999973, 0.154999999999999999, 1.1160000000000001, 0.509000000000000008, 0.237999999999999989, 0.340000000000000024, 10), +(2648, 'I', 0.5, 0.390000000000000013, 0.125, 0.582999999999999963, 0.293999999999999984, 0.132000000000000006, 0.160500000000000004, 8), +(1796, 'F', 0.57999999999999996, 0.429999999999999993, 0.170000000000000012, 1.47999999999999998, 0.65349999999999997, 0.32400000000000001, 0.41549999999999998, 10), +(209, 'F', 0.525000000000000022, 0.41499999999999998, 0.170000000000000012, 0.832500000000000018, 0.275500000000000023, 0.168500000000000011, 0.309999999999999998, 13), +(1451, 'I', 0.455000000000000016, 0.33500000000000002, 0.135000000000000009, 0.501000000000000001, 0.274000000000000021, 0.0995000000000000051, 0.106499999999999997, 7), +(1108, 'I', 0.510000000000000009, 0.380000000000000004, 0.115000000000000005, 0.515499999999999958, 0.214999999999999997, 0.113500000000000004, 0.166000000000000009, 8), +(3675, 'F', 0.594999999999999973, 0.450000000000000011, 0.165000000000000008, 1.08099999999999996, 0.489999999999999991, 0.252500000000000002, 0.279000000000000026, 12), +(2108, 'F', 0.675000000000000044, 0.550000000000000044, 0.179999999999999993, 1.68849999999999989, 0.562000000000000055, 0.370499999999999996, 0.599999999999999978, 15), +(3312, 'F', 0.479999999999999982, 0.380000000000000004, 0.135000000000000009, 0.507000000000000006, 0.191500000000000004, 0.13650000000000001, 0.154999999999999999, 12), +(882, 'M', 0.655000000000000027, 0.520000000000000018, 0.165000000000000008, 1.40949999999999998, 0.585999999999999965, 0.290999999999999981, 0.405000000000000027, 9), +(3402, 'M', 0.479999999999999982, 0.395000000000000018, 0.149999999999999994, 0.681499999999999995, 0.214499999999999996, 0.140500000000000014, 0.2495, 18), +(829, 'I', 0.409999999999999976, 0.325000000000000011, 0.100000000000000006, 0.394000000000000017, 0.20799999999999999, 0.0655000000000000027, 0.105999999999999997, 6), +(1305, 'M', 0.535000000000000031, 0.434999999999999998, 0.149999999999999994, 0.716999999999999971, 0.347499999999999976, 0.14449999999999999, 0.194000000000000006, 9), +(3613, 'M', 0.599999999999999978, 0.46000000000000002, 0.179999999999999993, 1.1399999999999999, 0.422999999999999987, 0.257500000000000007, 0.364999999999999991, 10), +(1068, 'I', 0.340000000000000024, 0.265000000000000013, 0.0800000000000000017, 0.201500000000000012, 0.0899999999999999967, 0.0475000000000000006, 0.0550000000000000003, 5), +(2446, 'M', 0.5, 0.380000000000000004, 0.135000000000000009, 0.583500000000000019, 0.22950000000000001, 0.126500000000000001, 0.179999999999999993, 12), +(1393, 'M', 0.635000000000000009, 0.474999999999999978, 0.170000000000000012, 1.19350000000000001, 0.520499999999999963, 0.269500000000000017, 0.366499999999999992, 10), +(359, 'M', 0.744999999999999996, 0.584999999999999964, 0.214999999999999997, 2.49900000000000011, 0.92649999999999999, 0.471999999999999975, 0.699999999999999956, 17), +(549, 'F', 0.564999999999999947, 0.450000000000000011, 0.160000000000000003, 0.79500000000000004, 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0.474999999999999978, 0.170000000000000012, 1.02649999999999997, 0.434999999999999998, 0.233500000000000013, 0.303499999999999992, 10), +(3759, 'I', 0.525000000000000022, 0.400000000000000022, 0.140000000000000013, 0.605500000000000038, 0.260500000000000009, 0.107999999999999999, 0.209999999999999992, 9); +</pre></li> +<li>Train a model with family=gaussian and link=identity <pre class="example"> +SELECT madlib.glm( + 'abalone', + 'abalone_out', + 'rings', + 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]', + 'family=gaussian, link=identity'); +</pre></li> +</ol> +<p><b>Example for Gamma family:</b> (reuse the dataset in Gaussian case)</p> +<ol type="1"> +<li>Reuse the test data set in Gaussian</li> +<li>Train a model with family=gamma and link=inverse <pre class="example"> +SELECT madlib.glm( + 'abalone', + 'abalone_out', + 'rings', + 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]', + 'family=gamma, link=inverse'); +</pre></li> +</ol> +<p><b>Example for Inverse Gaussian family:</b> (reuse the dataset in Gaussian case)</p> +<ol type="1"> +<li>Reuse the test data set in Gaussian</li> +<li>Train a model with family=inverse_gaussian and link=sqr_inverse <pre class="example"> +SELECT madlib.glm( + 'abalone', + 'abalone_out', + 'rings', + 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]', + 'family=inverse_gaussian, link=sqr_inverse'); +</pre></li> +</ol> +<p><b>Example for Binomial family:</b> (reuse the dataset in Gaussian case)</p> +<ol type="1"> +<li>Reuse the test data set in Gaussian</li> +<li>Train a model with family=binomial and link=probit <pre class="example"> +SELECT madlib.glm( + 'abalone', + 'abalone_out', + 'rings < 10', + 'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]', + 'family=binomial, link=probit'); +</pre></li> +<li>Predict output probabilities <pre class="example"> +SELECT madlib.glm_predict( + coef, + ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]::float8[], + 'probit') +FROM abalone_out, abalone; +</pre></li> +<li>Predict output categories <pre class="example"> +SELECT madlib.glm_predict( +SELECT madlib.glm_predict_binomial( + coef, + ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]::float8[], + 'probit') +FROM abalone_out, abalone; +</pre></li> +</ol> +<p><a class="anchor" id="notes"></a></p><dl class="section user"><dt>Notes</dt><dd>All table names can be optionally schema qualified (current_schemas() would be searched if a schema name is not provided) and all table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').</dd></dl> +<p>Currently implementation uses Newton's method and, according to performance tests, when number of features are over 1000, this GLM function could be running slowly.</p> +<p>Functions in <a class="el" href="group__grp__linreg.html">Linear Regression</a> is prefered to GLM with family=gaussian,link=identity, as the former require only a single pass over the training data. In addition, if user expects to use robust variance, clustered variance, or marginal effects on top of the trained model, functions in <a class="el" href="group__grp__linreg.html">Linear Regression</a> and <a class="el" href="group__grp__logreg.html">Logistic Regression</a> should be used.</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="glm_8sql__in.html" title="SQL functions for GLM (Poisson) ">glm.sql_in</a> documenting the training function</p> +<p><a class="el" href="group__grp__linreg.html">Linear Regression</a></p> +<p><a class="el" href="group__grp__logreg.html">Logistic Regression</a></p> +<p><a class="el" href="group__grp__mlogreg.html">Multinomial Logistic Regression</a></p> +<p><a class="el" href="group__grp__robust.html">Robust Variance</a></p> +<p><a class="el" href="group__grp__clustered__errors.html">Clustered Variance</a></p> +<p><a class="el" href="group__grp__validation.html">Cross Validation</a></p> +<p><a class="el" href="group__grp__marginal.html">Marginal Effects</a></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 Tue May 16 2017 13:24:38 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>
