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| <a href="cross__validation_8sql__in.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/* ----------------------------------------------------------------------- */</span><span class="comment">/** </span> |
| <a name="l00002"></a>00002 <span class="comment"> *</span> |
| <a name="l00003"></a>00003 <span class="comment"> * @file cross_validation.sql_in</span> |
| <a name="l00004"></a>00004 <span class="comment"> *</span> |
| <a name="l00005"></a>00005 <span class="comment"> * @brief SQL functions for cross validation</span> |
| <a name="l00006"></a>00006 <span class="comment"> * @date January 2011</span> |
| <a name="l00007"></a>00007 <span class="comment"> *</span> |
| <a name="l00008"></a>00008 <span class="comment"> * @sa For a brief introduction to the usage of cross validation, see the</span> |
| <a name="l00009"></a>00009 <span class="comment"> * module description \ref grp_validation.</span> |
| <a name="l00010"></a>00010 <span class="comment"> *</span> |
| <a name="l00011"></a>00011 <span class="comment"> */</span><span class="comment">/* ----------------------------------------------------------------------- */</span> |
| <a name="l00012"></a>00012 |
| <a name="l00013"></a>00013 |
| <a name="l00014"></a>00014 m4_include(`SQLCommon.m4<span class="stringliteral">') --'</span> |
| <a name="l00015"></a>00015 <span class="comment"></span> |
| <a name="l00016"></a>00016 <span class="comment">/**</span> |
| <a name="l00017"></a>00017 <span class="comment">@addtogroup grp_validation</span> |
| <a name="l00018"></a>00018 <span class="comment"></span> |
| <a name="l00019"></a>00019 <span class="comment">@about</span> |
| <a name="l00020"></a>00020 <span class="comment"></span> |
| <a name="l00021"></a>00021 <span class="comment">Cross-validation, sometimes called rotation estimation, is a technique for assessing how the results of a statistical</span> |
| <a name="l00022"></a>00022 <span class="comment">analysis will generalize to an independent data set. It is mainly used in settings where the goal is prediction, and</span> |
| <a name="l00023"></a>00023 <span class="comment">one wants to estimate how accurately a predictive model will perform in practice. One round of cross-validation</span> |
| <a name="l00024"></a>00024 <span class="comment">involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called</span> |
| <a name="l00025"></a>00025 <span class="comment">the training set), and validating the analysis on the other subset (called the validation set or testing set). To</span> |
| <a name="l00026"></a>00026 <span class="comment">reduce variability, multiple rounds of cross-validation are performed using different partitions, and the validation</span> |
| <a name="l00027"></a>00027 <span class="comment">results are averaged over the rounds.</span> |
| <a name="l00028"></a>00028 <span class="comment"></span> |
| <a name="l00029"></a>00029 <span class="comment">In k-fold cross-validation, the original sample is randomly partitioned into k equal size subsamples. Of the k subsamples,</span> |
| <a name="l00030"></a>00030 <span class="comment">a single subsample is retained as the validation data for testing the model, and the remaining k − 1 subsamples are used</span> |
| <a name="l00031"></a>00031 <span class="comment">as training data. The cross-validation process is then repeated k times (the folds), with each of the k subsamples used</span> |
| <a name="l00032"></a>00032 <span class="comment">exactly once as the validation data. The k results from the folds then can be averaged (or otherwise combined) to produce</span> |
| <a name="l00033"></a>00033 <span class="comment">a single estimation. The advantage of this method over repeated random sub-sampling is that all observations are used for</span> |
| <a name="l00034"></a>00034 <span class="comment">both training and validation, and each observation is used for validation exactly once. 10-fold cross-validation is</span> |
| <a name="l00035"></a>00035 <span class="comment">commonly used, but in general k remains an unfixed parameter. </span> |
| <a name="l00036"></a>00036 <span class="comment"></span> |
| <a name="l00037"></a>00037 <span class="comment">@input</span> |
| <a name="l00038"></a>00038 <span class="comment"></span> |
| <a name="l00039"></a>00039 <span class="comment"><b>The flexible interface.</b></span> |
| <a name="l00040"></a>00040 <span class="comment"></span> |
| <a name="l00041"></a>00041 <span class="comment">The input includes the data set, a training function, a prediction function and an error metric function.</span> |
| <a name="l00042"></a>00042 <span class="comment"></span> |
| <a name="l00043"></a>00043 <span class="comment">The training function takes in a given data set with independent and dependent variables in it and produces</span> |
| <a name="l00044"></a>00044 <span class="comment">a model, which is stored in an output table.</span> |
| <a name="l00045"></a>00045 <span class="comment"></span> |
| <a name="l00046"></a>00046 <span class="comment">The prediction function takes in the model generated by the training function and a different data set with</span> |
| <a name="l00047"></a>00047 <span class="comment">independent variables in it, and it produces a prediction of the dependent variables bease on the model.</span> |
| <a name="l00048"></a>00048 <span class="comment">The prediction is stored in an output table. The prediction function should take a unique ID column name of</span> |
| <a name="l00049"></a>00049 <span class="comment">the data table as one of the inputs, otherwise the prediction result cannot be compared with the validation</span> |
| <a name="l00050"></a>00050 <span class="comment">values.</span> |
| <a name="l00051"></a>00051 <span class="comment"></span> |
| <a name="l00052"></a>00052 <span class="comment">The error metric function takes in the prediction made by the prediction function, and compare with the known</span> |
| <a name="l00053"></a>00053 <span class="comment">values of the dependent variables of the data set that was fed into the prediction function. It computes the</span> |
| <a name="l00054"></a>00054 <span class="comment">error metric defined by the function. The results are stored in a table</span> |
| <a name="l00055"></a>00055 <span class="comment"></span> |
| <a name="l00056"></a>00056 <span class="comment">Other inputs include the output table name, k value for the k-fold cross-validation, and how many folds the user</span> |
| <a name="l00057"></a>00057 <span class="comment">wants to try (for example, the user can choose to run a simple validation instead of a full cross-validation.)</span> |
| <a name="l00058"></a>00058 <span class="comment"></span> |
| <a name="l00059"></a>00059 <span class="comment">@usage</span> |
| <a name="l00060"></a>00060 <span class="comment"></span> |
| <a name="l00061"></a>00061 <span class="comment"><b>The flexible interface.</b></span> |
| <a name="l00062"></a>00062 <span class="comment"></span> |
| <a name="l00063"></a>00063 <span class="comment">In order to choose the optimum value for a parameter of the model, the user needs to provied the training function,</span> |
| <a name="l00064"></a>00064 <span class="comment">prediction function, error metric function, the parameter and its values to be studied and the data set.</span> |
| <a name="l00065"></a>00065 <span class="comment"></span> |
| <a name="l00066"></a>00066 <span class="comment">It would be better if the data set has a unique ID for each row, so that it is easier to cut the data set into the</span> |
| <a name="l00067"></a>00067 <span class="comment">training part and the validation part. The user also needs to inform the cross validation (CV) function about whether this</span> |
| <a name="l00068"></a>00068 <span class="comment">ID value is randomly assigned to each row. If it is not randomly assigned, the CV function will automatically generate</span> |
| <a name="l00069"></a>00069 <span class="comment">a random ID for each row.</span> |
| <a name="l00070"></a>00070 <span class="comment"></span> |
| <a name="l00071"></a>00071 <span class="comment">If the data set has no unique ID for each row, the CV function will copy the data set and create a randomly assigned ID</span> |
| <a name="l00072"></a>00072 <span class="comment">column for the newly created temp table. The new table will be dropped after the computation is finished. To minimize</span> |
| <a name="l00073"></a>00073 <span class="comment">the copying work load, the user needs to provide the data column names (for independent variables and dependent</span> |
| <a name="l00074"></a>00074 <span class="comment">variables) that are going to be used in the calculation, and only these columns will be copied.</span> |
| <a name="l00075"></a>00075 <span class="comment"></span> |
| <a name="l00076"></a>00076 <span class="comment"><pre>SELECT cross_validation_general(</span> |
| <a name="l00077"></a>00077 <span class="comment"> <em>modelling_func</em>, -- Name of function that trains the model</span> |
| <a name="l00078"></a>00078 <span class="comment"> <em>modelling_params</em>, -- Array of parameters for modelling function</span> |
| <a name="l00079"></a>00079 <span class="comment"> <em>modelling_params_type</em>, -- Types of each parameters for modelling function</span> |
| <a name="l00080"></a>00080 <span class="comment"> --</span> |
| <a name="l00081"></a>00081 <span class="comment"> <em>param_explored</em>, -- Name of parameter that will be checked to find the optimum value, the</span> |
| <a name="l00082"></a>00082 <span class="comment"> ---- same name must also appear in the array of modelling_params</span> |
| <a name="l00083"></a>00083 <span class="comment"> <em>explore_values</em>, -- Values of this parameter that will be studied</span> |
| <a name="l00084"></a>00084 <span class="comment"> --</span> |
| <a name="l00085"></a>00085 <span class="comment"> <em>predict_func</em>, -- Name of function for prediction</span> |
| <a name="l00086"></a>00086 <span class="comment"> <em>predict_params</em>, -- Array of parameters for prediction function</span> |
| <a name="l00087"></a>00087 <span class="comment"> <em>predict_params_type</em>, -- Types of each parameters for prediction function</span> |
| <a name="l00088"></a>00088 <span class="comment"> --</span> |
| <a name="l00089"></a>00089 <span class="comment"> <em>metric_func</em>, -- Name of function for measuring errors</span> |
| <a name="l00090"></a>00090 <span class="comment"> <em>metric_params</em>, -- Array of parameters for error metric function</span> |
| <a name="l00091"></a>00091 <span class="comment"> <em>metric_params_type</em>, -- Types of each parameters for metric function</span> |
| <a name="l00092"></a>00092 <span class="comment"> --</span> |
| <a name="l00093"></a>00093 <span class="comment"> <em>data_tbl</em>, -- Data table which will be split into training and validation parts</span> |
| <a name="l00094"></a>00094 <span class="comment"> <em>data_id</em>, -- Name of the unique ID associated with each row. Provide <em>NULL</em></span> |
| <a name="l00095"></a>00095 <span class="comment"> ---- if there is no such column in the data table</span> |
| <a name="l00096"></a>00096 <span class="comment"> <em>id_is_random</em>, -- Whether the provided ID is randomly assigned to each row</span> |
| <a name="l00097"></a>00097 <span class="comment"> --</span> |
| <a name="l00098"></a>00098 <span class="comment"> <em>validation_result</em>, -- Table name to store the output of CV function, see the Output for</span> |
| <a name="l00099"></a>00099 <span class="comment"> ---- format. It will be automatically created by CV function</span> |
| <a name="l00100"></a>00100 <span class="comment"> --</span> |
| <a name="l00101"></a>00101 <span class="comment"> <em>data_cols</em>, -- Names of data columns that are going to be used. It is only useful when</span> |
| <a name="l00102"></a>00102 <span class="comment"> ---- <em>data_id</em> is NULL, otherwise it is ignored.</span> |
| <a name="l00103"></a>00103 <span class="comment"> <em>fold_num</em> -- Value of k. How many folds validation? Each validation uses 1/fold_num</span> |
| <a name="l00104"></a>00104 <span class="comment"> ---- fraction of the data for validation. Deafult value: 10.</span> |
| <a name="l00105"></a>00105 <span class="comment">);</pre></span> |
| <a name="l00106"></a>00106 <span class="comment"></span> |
| <a name="l00107"></a>00107 <span class="comment">Special keywords in parameter arrays of modelling, prediction and metric functions:</span> |
| <a name="l00108"></a>00108 <span class="comment"></span> |
| <a name="l00109"></a>00109 <span class="comment"><em>\%data%</em> : The argument position for training/validation data </span> |
| <a name="l00110"></a>00110 <span class="comment"></span> |
| <a name="l00111"></a>00111 <span class="comment"><em>\%model%</em> : The argument position for the output/input of modelling/prediction function</span> |
| <a name="l00112"></a>00112 <span class="comment"></span> |
| <a name="l00113"></a>00113 <span class="comment"><em>\%id%</em> : The argument position of unique ID column (provided by user or generated by CV function as is mentioned above)</span> |
| <a name="l00114"></a>00114 <span class="comment"></span> |
| <a name="l00115"></a>00115 <span class="comment"><em>\%prediction%</em> : The argument position for the output/input of prediction/metric function</span> |
| <a name="l00116"></a>00116 <span class="comment"></span> |
| <a name="l00117"></a>00117 <span class="comment"><em>\%error%</em> : The argument position for the output of metric function</span> |
| <a name="l00118"></a>00118 <span class="comment"></span> |
| <a name="l00119"></a>00119 <span class="comment"><b>Note</b>: If the parameter <em>explore_values</em> is NULL or has zero length, then the cross validation function will only run a data folding.</span> |
| <a name="l00120"></a>00120 <span class="comment"></span> |
| <a name="l00121"></a>00121 <span class="comment">Output:</span> |
| <a name="l00122"></a>00122 <span class="comment"><pre> param_explored | average error | standard deviation of error</span> |
| <a name="l00123"></a>00123 <span class="comment">-------------------------|------------------|--------------------------------</span> |
| <a name="l00124"></a>00124 <span class="comment"> .......</span> |
| <a name="l00125"></a>00125 <span class="comment"></pre></span> |
| <a name="l00126"></a>00126 <span class="comment"></span> |
| <a name="l00127"></a>00127 <span class="comment"><b>Note:</b></span> |
| <a name="l00128"></a>00128 <span class="comment"></span> |
| <a name="l00129"></a>00129 <span class="comment"><em>max_locks_per_transaction</em>, which usually has the default value of 64, limits the number of tables that can be</span> |
| <a name="l00130"></a>00130 <span class="comment">dropped inside a single transaction (the CV function). Thus the number of different values of <em>param_explored</em></span> |
| <a name="l00131"></a>00131 <span class="comment">(or the length of array <em>explored_values</em>) cannot be too large. For 10-fold cross validation, the limit of</span> |
| <a name="l00132"></a>00132 <span class="comment">length(<em>explored_values</em>) is around 40. If this number is too large, the use might see "out of shared memory"</span> |
| <a name="l00133"></a>00133 <span class="comment">error because <em>max_locks_per_transaction</em> is used up.</span> |
| <a name="l00134"></a>00134 <span class="comment"></span> |
| <a name="l00135"></a>00135 <span class="comment">One way to overcome this limitation is to run CV function multiple times, and each run covers a different region of</span> |
| <a name="l00136"></a>00136 <span class="comment">values of the parameter.</span> |
| <a name="l00137"></a>00137 <span class="comment"></span> |
| <a name="l00138"></a>00138 <span class="comment">In the future, MADlib will implement cross-validation functions for each individual applicable module, where we can optimize the calculation to avoid table droppings and this max_locks_per_transaction limitation. However, such cross-validation functions need to know the implementation details of the modules to do the optimization and thus cannot be as flexible as the cross-validation function provided here.</span> |
| <a name="l00139"></a>00139 <span class="comment"></span> |
| <a name="l00140"></a>00140 <span class="comment">The cross-validation function provided here is very flexible, and can actually work with any algorithms that the user want to cross-validate including the algorithms written by the user. The price for this flexiblity is that the algorithms' details cannot be utilized to optimize the calculation and thus <em>max_locks_per_transaction</em> limitation cannot be avoided.</span> |
| <a name="l00141"></a>00141 <span class="comment"></span> |
| <a name="l00142"></a>00142 <span class="comment">@examp</span> |
| <a name="l00143"></a>00143 <span class="comment"></span> |
| <a name="l00144"></a>00144 <span class="comment">Cross validation is used on elastic net regression to find the best value of the regularization parameter.</span> |
| <a name="l00145"></a>00145 <span class="comment"></span> |
| <a name="l00146"></a>00146 <span class="comment">(1) Populate the table 'cvtest' with 101 dimensional independent variable 'val', and dependent</span> |
| <a name="l00147"></a>00147 <span class="comment">variable 'dep'.</span> |
| <a name="l00148"></a>00148 <span class="comment"></span> |
| <a name="l00149"></a>00149 <span class="comment">(2) Run the general CV function</span> |
| <a name="l00150"></a>00150 <span class="comment"><pre></span> |
| <a name="l00151"></a>00151 <span class="comment">select madlib.cross_validation_general (</span> |
| <a name="l00152"></a>00152 <span class="comment"> 'madlib.elastic_net_train',</span> |
| <a name="l00153"></a>00153 <span class="comment"> '{\%data%, \%model%, dep, val, gaussian, 1, lambda, True, Null, fista, "{eta = 2, max_stepsize = 2, use_active_set = t}", Null, 2000, 1e-6}'::varchar[],</span> |
| <a name="l00154"></a>00154 <span class="comment"> '{varchar, varchar, varchar, varchar, varchar, double precision, double precision, boolean, varchar, varchar, varchar[], varchar, integer, double precision}'::varchar[],</span> |
| <a name="l00155"></a>00155 <span class="comment"> --</span> |
| <a name="l00156"></a>00156 <span class="comment"> 'lambda',</span> |
| <a name="l00157"></a>00157 <span class="comment"> '{0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, 0.20, 0.22, 0.24, 0.26, 0.28, 0.30, 0.32, 0.34, 0.36}'::varchar[],</span> |
| <a name="l00158"></a>00158 <span class="comment"> --</span> |
| <a name="l00159"></a>00159 <span class="comment"> 'madlib.elastic_net_predict',</span> |
| <a name="l00160"></a>00160 <span class="comment"> '{\%model%, \%data%, \%id%, \%prediction%}'::varchar[],</span> |
| <a name="l00161"></a>00161 <span class="comment"> '{text, text, text, text}'::varchar[],</span> |
| <a name="l00162"></a>00162 <span class="comment"> --</span> |
| <a name="l00163"></a>00163 <span class="comment"> 'madlib.mse_error', </span> |
| <a name="l00164"></a>00164 <span class="comment"> '{\%prediction%, \%data%, \%id%, dep, \%error%}'::varchar[],</span> |
| <a name="l00165"></a>00165 <span class="comment"> '{varchar, varchar, varchar, varchar, varchar}'::varchar[],</span> |
| <a name="l00166"></a>00166 <span class="comment"> --</span> |
| <a name="l00167"></a>00167 <span class="comment"> 'cvtest',</span> |
| <a name="l00168"></a>00168 <span class="comment"> NULL::varchar,</span> |
| <a name="l00169"></a>00169 <span class="comment"> False,</span> |
| <a name="l00170"></a>00170 <span class="comment"> --</span> |
| <a name="l00171"></a>00171 <span class="comment"> 'valid_rst_tbl',</span> |
| <a name="l00172"></a>00172 <span class="comment"> '{val, dep}'::varchar[],</span> |
| <a name="l00173"></a>00173 <span class="comment"> 10</span> |
| <a name="l00174"></a>00174 <span class="comment">);</span> |
| <a name="l00175"></a>00175 <span class="comment"></span> |
| <a name="l00176"></a>00176 <span class="comment"></pre></span> |
| <a name="l00177"></a>00177 <span class="comment"></span> |
| <a name="l00178"></a>00178 <span class="comment">@sa File cross_validation.sql_in documenting the SQL functions.</span> |
| <a name="l00179"></a>00179 <span class="comment"></span> |
| <a name="l00180"></a>00180 <span class="comment">*/</span> |
| <a name="l00181"></a>00181 |
| <a name="l00182"></a>00182 ------------------------------------------------------------------------ |
| <a name="l00183"></a>00183 <span class="comment">/*</span> |
| <a name="l00184"></a>00184 <span class="comment"> * @brief Perform cross validation for modules that conforms with a fixed SQL API</span> |
| <a name="l00185"></a>00185 <span class="comment"> * Note: There is a lock number limitation of this function. It is flexible to use, so that the user can</span> |
| <a name="l00186"></a>00186 <span class="comment"> * try CV method on their own functions. On the other hand, cross_validation function does not have the</span> |
| <a name="l00187"></a>00187 <span class="comment"> * lock number limitation.</span> |
| <a name="l00188"></a>00188 <span class="comment"> *</span> |
| <a name="l00189"></a>00189 <span class="comment"> * @param modelling_func Name of function that trains the model</span> |
| <a name="l00190"></a>00190 <span class="comment"> * @param modelling_params Array of parameters for modelling function</span> |
| <a name="l00191"></a>00191 <span class="comment"> * @param modelling_params_type Types of each parameters for modelling function</span> |
| <a name="l00192"></a>00192 <span class="comment"> * @param param_explored Name of parameter that will be checked to find the optimum value, the same name must also appear in the array of modelling_params</span> |
| <a name="l00193"></a>00193 <span class="comment"> * @param explore_values Values of this parameter that will be studied</span> |
| <a name="l00194"></a>00194 <span class="comment"> * @param predict_func Name of function for prediction</span> |
| <a name="l00195"></a>00195 <span class="comment"> * @param predict_params Array of parameters for prediction function</span> |
| <a name="l00196"></a>00196 <span class="comment"> * @param predict_params_type Types of each parameters for prediction function</span> |
| <a name="l00197"></a>00197 <span class="comment"> * @param metric_func Name of function for measuring errors</span> |
| <a name="l00198"></a>00198 <span class="comment"> * @param metric_params Array of parameters for error metric function</span> |
| <a name="l00199"></a>00199 <span class="comment"> * @param metric_params_type Types of each parameters for metric function</span> |
| <a name="l00200"></a>00200 <span class="comment"> * @param data_tbl Data table which will be split into training and validation parts</span> |
| <a name="l00201"></a>00201 <span class="comment"> * @param data_id Name of the unique ID associated with each row. Provide <em>NULL</em> if there is no such column in the data table</span> |
| <a name="l00202"></a>00202 <span class="comment"> * @param id_is_random Whether the provided ID is randomly assigned to each row</span> |
| <a name="l00203"></a>00203 <span class="comment"> * @param validation_result Table name to store the output of CV function, see the Output for format. It will be automatically created by CV function</span> |
| <a name="l00204"></a>00204 <span class="comment"> * @param fold_num Value of k. How many folds validation? Each validation uses 1/fold_num fraction of the data for validation. Deafult value: 10.</span> |
| <a name="l00205"></a>00205 <span class="comment"> * @param data_cols Names of data columns that are going to be used. It is only useful when <em>data_id</em> is NULL, otherwise it is ignored.</span> |
| <a name="l00206"></a>00206 <span class="comment"> */</span> |
| <a name="l00207"></a>00207 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cross_validation_general( |
| <a name="l00208"></a>00208 modelling_func VARCHAR, -- <span class="keyword">function</span> <span class="keywordflow">for</span> setting up the model |
| <a name="l00209"></a>00209 modelling_params VARCHAR[], -- parameters <span class="keywordflow">for</span> modelling |
| <a name="l00210"></a>00210 modelling_params_type VARCHAR[], -- parameter types <span class="keywordflow">for</span> modelling |
| <a name="l00211"></a>00211 -- |
| <a name="l00212"></a>00212 param_explored VARCHAR, -- which parameter will be studied <span class="keyword">using</span> validation |
| <a name="l00213"></a>00213 explore_values VARCHAR[], -- values that will be explored <span class="keywordflow">for</span> <span class="keyword">this</span> parameter |
| <a name="l00214"></a>00214 -- |
| <a name="l00215"></a>00215 predict_func VARCHAR, -- <span class="keyword">function</span> <span class="keywordflow">for</span> predicting <span class="keyword">using</span> the model |
| <a name="l00216"></a>00216 predict_params VARCHAR[], -- parameters <span class="keywordflow">for</span> prediction |
| <a name="l00217"></a>00217 predict_params_type VARCHAR[], -- parameter types <span class="keywordflow">for</span> prediction |
| <a name="l00218"></a>00218 -- |
| <a name="l00219"></a>00219 metric_func VARCHAR, -- <span class="keyword">function</span> that computes the error metric |
| <a name="l00220"></a>00220 metric_params VARCHAR[], -- parameters <span class="keywordflow">for</span> metric |
| <a name="l00221"></a>00221 metric_params_type VARCHAR[], -- parameter types <span class="keywordflow">for</span> metric |
| <a name="l00222"></a>00222 -- |
| <a name="l00223"></a>00223 data_tbl VARCHAR, -- table containing the data, which will be split into training and validation parts |
| <a name="l00224"></a>00224 data_id VARCHAR, -- user provide a unique ID <span class="keywordflow">for each</span> row |
| <a name="l00225"></a>00225 id_is_random BOOLEAN, -- the ID provided by user is random |
| <a name="l00226"></a>00226 -- |
| <a name="l00227"></a>00227 validation_result VARCHAR, -- store the result: param values, error, +/- |
| <a name="l00228"></a>00228 -- |
| <a name="l00229"></a>00229 data_cols VARCHAR[], -- names of data columns that are going to be used |
| <a name="l00230"></a>00230 fold_num INTEGER -- how many fold validation, <span class="keywordflow">default</span>: 10 |
| <a name="l00231"></a>00231 ) RETURNS VOID AS $$ |
| <a name="l00232"></a>00232 PythonFunction(validation, cross_validation, cross_validation_general) |
| <a name="l00233"></a>00233 $$ LANGUAGE plpythonu; |
| <a name="l00234"></a>00234 |
| <a name="l00235"></a>00235 ------------------------------------------------------------------------ |
| <a name="l00236"></a>00236 |
| <a name="l00237"></a>00237 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cross_validation_general( |
| <a name="l00238"></a>00238 modelling_func VARCHAR, -- <span class="keyword">function</span> <span class="keywordflow">for</span> setting up the model |
| <a name="l00239"></a>00239 modelling_params VARCHAR[], -- parameters <span class="keywordflow">for</span> modelling |
| <a name="l00240"></a>00240 modelling_params_type VARCHAR[], -- parameter types <span class="keywordflow">for</span> modelling |
| <a name="l00241"></a>00241 -- |
| <a name="l00242"></a>00242 param_explored VARCHAR, -- which parameter will be studied <span class="keyword">using</span> validation |
| <a name="l00243"></a>00243 explore_values VARCHAR[], -- values that will be explored <span class="keywordflow">for</span> <span class="keyword">this</span> parameter |
| <a name="l00244"></a>00244 -- |
| <a name="l00245"></a>00245 predict_func VARCHAR, -- <span class="keyword">function</span> <span class="keywordflow">for</span> predicting <span class="keyword">using</span> the model |
| <a name="l00246"></a>00246 predict_params VARCHAR[], -- parameters <span class="keywordflow">for</span> prediction |
| <a name="l00247"></a>00247 predict_params_type VARCHAR[], -- parameter types <span class="keywordflow">for</span> prediction |
| <a name="l00248"></a>00248 -- |
| <a name="l00249"></a>00249 metric_func VARCHAR, -- <span class="keyword">function</span> that computes the error metric |
| <a name="l00250"></a>00250 metric_params VARCHAR[], -- parameters <span class="keywordflow">for</span> prediction |
| <a name="l00251"></a>00251 metric_params_type VARCHAR[], -- parameter types <span class="keywordflow">for</span> prediction |
| <a name="l00252"></a>00252 -- |
| <a name="l00253"></a>00253 data_tbl VARCHAR, -- table containing the data, which will be split into training and validation parts |
| <a name="l00254"></a>00254 data_id VARCHAR, -- user provide a unique ID <span class="keywordflow">for each</span> row |
| <a name="l00255"></a>00255 id_is_random BOOLEAN, -- the ID provided by user is random |
| <a name="l00256"></a>00256 -- |
| <a name="l00257"></a>00257 validation_result VARCHAR, -- store the result: param values, error, +/- |
| <a name="l00258"></a>00258 -- |
| <a name="l00259"></a>00259 data_cols VARCHAR[] -- names of data columns that are going to be used |
| <a name="l00260"></a>00260 ) RETURNS VOID AS $$ |
| <a name="l00261"></a>00261 BEGIN |
| <a name="l00262"></a>00262 PERFORM MADLIB_SCHEMA.cross_validation_general($1,$2,$3,$4,$5,$6,$7,$8,$9,$10,$11,$12,$13,$14,$15,$16,10); |
| <a name="l00263"></a>00263 END; |
| <a name="l00264"></a>00264 $$ LANGUAGE plpgsql VOLATILE; |
| <a name="l00265"></a>00265 |
| <a name="l00266"></a>00266 ------------------------------------------------------------------------ |
| <a name="l00267"></a>00267 ------------------------------------------------------------------------ |
| <a name="l00268"></a>00268 ------------------------------------------------------------------------ |
| <a name="l00269"></a>00269 <span class="comment"></span> |
| <a name="l00270"></a>00270 <span class="comment">/**</span> |
| <a name="l00271"></a>00271 <span class="comment"> * @brief Simple interface of cross-validation, which has no limitation on lock number</span> |
| <a name="l00272"></a>00272 <span class="comment"> *</span> |
| <a name="l00273"></a>00273 <span class="comment"> * @param module_name Module to be cross validated</span> |
| <a name="l00274"></a>00274 <span class="comment"> * @param func_args Arguments of modelling function of the module, including the table name of data</span> |
| <a name="l00275"></a>00275 <span class="comment"> * @param param_to_try The name of the paramter that CV runs through</span> |
| <a name="l00276"></a>00276 <span class="comment"> * @param param_values The values of the parameter that CV will try</span> |
| <a name="l00277"></a>00277 <span class="comment"> * @param data_id Name of the unique ID associated with each row. Provide <em>NULL</em> if there is no such column in the data table</span> |
| <a name="l00278"></a>00278 <span class="comment"> * @param id_is_random Whether the provided ID is randomly assigned to each row</span> |
| <a name="l00279"></a>00279 <span class="comment"> * @param validation_result Table name to store the output of CV function, see the Output for format. It will be automatically created by CV function</span> |
| <a name="l00280"></a>00280 <span class="comment"> * @param fold_num How many fold cross-validation</span> |
| <a name="l00281"></a>00281 <span class="comment"> */</span> |
| <a name="l00282"></a>00282 <span class="comment">/*</span> |
| <a name="l00283"></a>00283 <span class="comment">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cross_validation(</span> |
| <a name="l00284"></a>00284 <span class="comment"> module_name VARCHAR, -- module to be cross validated</span> |
| <a name="l00285"></a>00285 <span class="comment"> func_args VARCHAR[],</span> |
| <a name="l00286"></a>00286 <span class="comment"> param_to_try VARCHAR,</span> |
| <a name="l00287"></a>00287 <span class="comment"> param_values DOUBLE PRECISION[],</span> |
| <a name="l00288"></a>00288 <span class="comment"> data_id VARCHAR,</span> |
| <a name="l00289"></a>00289 <span class="comment"> id_is_random BOOLEAN,</span> |
| <a name="l00290"></a>00290 <span class="comment"> validation_result VARCHAR,</span> |
| <a name="l00291"></a>00291 <span class="comment"> fold_num INTEGER</span> |
| <a name="l00292"></a>00292 <span class="comment">) RETURNS VOID AS $$</span> |
| <a name="l00293"></a>00293 <span class="comment">PythonFunction(validation, cross_validation, cross_validation)</span> |
| <a name="l00294"></a>00294 <span class="comment">$$ LANGUAGE plpythonu;</span> |
| <a name="l00295"></a>00295 <span class="comment">*/</span> |
| <a name="l00296"></a>00296 -- ------------------------------------------------------------------------ |
| <a name="l00297"></a>00297 <span class="comment">/*</span> |
| <a name="l00298"></a>00298 <span class="comment">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cross_validation(</span> |
| <a name="l00299"></a>00299 <span class="comment"> module_name VARCHAR,</span> |
| <a name="l00300"></a>00300 <span class="comment"> func_args VARCHAR[],</span> |
| <a name="l00301"></a>00301 <span class="comment"> param_to_try VARCHAR,</span> |
| <a name="l00302"></a>00302 <span class="comment"> param_values DOUBLE PRECISION[],</span> |
| <a name="l00303"></a>00303 <span class="comment"> data_id VARCHAR,</span> |
| <a name="l00304"></a>00304 <span class="comment"> id_is_random BOOLEAN,</span> |
| <a name="l00305"></a>00305 <span class="comment"> validation_result VARCHAR</span> |
| <a name="l00306"></a>00306 <span class="comment">) RETURNS VOID AS $$</span> |
| <a name="l00307"></a>00307 <span class="comment">BEGIN</span> |
| <a name="l00308"></a>00308 <span class="comment"> PERFORM MADLIB_SCHEMA.cross_validation($1, $2, $3, $4, $5, $6, $7, 10);</span> |
| <a name="l00309"></a>00309 <span class="comment">END;</span> |
| <a name="l00310"></a>00310 <span class="comment">$$ LANGUAGE plpgsql VOLATILE;</span> |
| <a name="l00311"></a>00311 <span class="comment">*/</span> |
| <a name="l00312"></a>00312 -- ------------------------------------------------------------------------ |
| <a name="l00313"></a>00313 <span class="comment"></span> |
| <a name="l00314"></a>00314 <span class="comment">/**</span> |
| <a name="l00315"></a>00315 <span class="comment"> * @brief Print the help message for a given module's cross-validation.</span> |
| <a name="l00316"></a>00316 <span class="comment"> */</span> |
| <a name="l00317"></a>00317 <span class="comment">/*</span> |
| <a name="l00318"></a>00318 <span class="comment">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cross_validation(module_name VARCHAR)</span> |
| <a name="l00319"></a>00319 <span class="comment">RETURNS VARCHAR AS $$</span> |
| <a name="l00320"></a>00320 <span class="comment">PythonFunction(validation, cross_validation, cross_validation_help)</span> |
| <a name="l00321"></a>00321 <span class="comment">$$ LANGUAGE plpythonu;</span> |
| <a name="l00322"></a>00322 <span class="comment">*/</span> |
| <a name="l00323"></a>00323 -- ------------------------------------------------------------------------ |
| <a name="l00324"></a>00324 <span class="comment"></span> |
| <a name="l00325"></a>00325 <span class="comment">/**</span> |
| <a name="l00326"></a>00326 <span class="comment"> * @brief Print the supported module names for cross_validation</span> |
| <a name="l00327"></a>00327 <span class="comment"> */</span> |
| <a name="l00328"></a>00328 <span class="comment">/*</span> |
| <a name="l00329"></a>00329 <span class="comment">CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cross_validation()</span> |
| <a name="l00330"></a>00330 <span class="comment">RETURNS VARCHAR AS $$</span> |
| <a name="l00331"></a>00331 <span class="comment">DECLARE</span> |
| <a name="l00332"></a>00332 <span class="comment"> msg VARCHAR;</span> |
| <a name="l00333"></a>00333 <span class="comment">BEGIN</span> |
| <a name="l00334"></a>00334 <span class="comment"> msg := 'cross_validation function now supports Ridge linear regression';</span> |
| <a name="l00335"></a>00335 <span class="comment"> return msg;</span> |
| <a name="l00336"></a>00336 <span class="comment">END;</span> |
| <a name="l00337"></a>00337 <span class="comment">$$ LANGUAGE plpgsql STRICT;</span> |
| <a name="l00338"></a>00338 <span class="comment">*/</span> |
| <a name="l00339"></a>00339 ------------------------------------------------------------------------ |
| <a name="l00340"></a>00340 <span class="comment"></span> |
| <a name="l00341"></a>00341 <span class="comment">/**</span> |
| <a name="l00342"></a>00342 <span class="comment"> * @brief A wrapper for linear regression</span> |
| <a name="l00343"></a>00343 <span class="comment"> */</span> |
| <a name="l00344"></a>00344 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cv_linregr_train( |
| <a name="l00345"></a>00345 tbl_source VARCHAR, |
| <a name="l00346"></a>00346 col_ind_var VARCHAR, |
| <a name="l00347"></a>00347 col_dep_var VARCHAR, |
| <a name="l00348"></a>00348 tbl_result VARCHAR |
| <a name="l00349"></a>00349 ) RETURNS VOID AS $$ |
| <a name="l00350"></a>00350 PythonFunction(validation, cross_validation, <a class="code" href="cross__validation_8sql__in.html#aa151eb3fa9acc7f4cc33236e22ad4362" title="Simple interface of cross-validation, which has no limitation on lock number.">cv_linregr_train</a>) |
| <a name="l00351"></a>00351 $$ LANGUAGE plpythonu; |
| <a name="l00352"></a>00352 |
| <a name="l00353"></a>00353 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.linregr_predict( |
| <a name="l00354"></a>00354 coef DOUBLE PRECISION[], |
| <a name="l00355"></a>00355 col_ind DOUBLE PRECISION[] |
| <a name="l00356"></a>00356 ) RETURNS DOUBLE PRECISION AS $$ |
| <a name="l00357"></a>00357 PythonFunction(validation, cross_validation, linregr_predict) |
| <a name="l00358"></a>00358 $$ LANGUAGE plpythonu; |
| <a name="l00359"></a>00359 <span class="comment"></span> |
| <a name="l00360"></a>00360 <span class="comment">/**</span> |
| <a name="l00361"></a>00361 <span class="comment"> * @brief A wrapper for linear regression prediction</span> |
| <a name="l00362"></a>00362 <span class="comment"> */</span> |
| <a name="l00363"></a>00363 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cv_linregr_predict( |
| <a name="l00364"></a>00364 tbl_model VARCHAR, |
| <a name="l00365"></a>00365 tbl_newdata VARCHAR, |
| <a name="l00366"></a><a class="code" href="cross__validation_8sql__in.html#aa151eb3fa9acc7f4cc33236e22ad4362">00366</a> col_ind_var VARCHAR, |
| <a name="l00367"></a>00367 col_id VARCHAR, -- ID column |
| <a name="l00368"></a>00368 tbl_predict VARCHAR |
| <a name="l00369"></a>00369 ) RETURNS VOID AS $$ |
| <a name="l00370"></a>00370 PythonFunction(validation, cross_validation, <a class="code" href="cross__validation_8sql__in.html#aa572f1f57c0dd106b30948928161d8cc" title="A wrapper for linear regression prediction.">cv_linregr_predict</a>) |
| <a name="l00371"></a>00371 $$ LANGUAGE plpythonu; |
| <a name="l00372"></a>00372 |
| <a name="l00373"></a>00373 -- compare the prediction and actual values |
| <a name="l00374"></a>00374 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.mse_error( |
| <a name="l00375"></a>00375 tbl_prediction VARCHAR, -- predicted values |
| <a name="l00376"></a>00376 tbl_actual VARCHAR, |
| <a name="l00377"></a>00377 id_actual VARCHAR, |
| <a name="l00378"></a>00378 values_actual VARCHAR, |
| <a name="l00379"></a>00379 tbl_error VARCHAR |
| <a name="l00380"></a>00380 ) RETURNS VOID AS $$ |
| <a name="l00381"></a>00381 DECLARE |
| <a name="l00382"></a>00382 error DOUBLE PRECISION; |
| <a name="l00383"></a>00383 old_messages VARCHAR; |
| <a name="l00384"></a>00384 BEGIN |
| <a name="l00385"></a><a class="code" href="cross__validation_8sql__in.html#aa572f1f57c0dd106b30948928161d8cc">00385</a> old_messages := (SELECT setting FROM pg_settings WHERE name = <span class="stringliteral">'client_min_messages'</span>); |
| <a name="l00386"></a>00386 EXECUTE <span class="stringliteral">'SET client_min_messages TO warning'</span>; |
| <a name="l00387"></a>00387 |
| <a name="l00388"></a>00388 EXECUTE <span class="stringliteral">'</span> |
| <a name="l00389"></a>00389 <span class="stringliteral"> CREATE TABLE '</span>|| tbl_error ||<span class="stringliteral">' AS</span> |
| <a name="l00390"></a>00390 <span class="stringliteral"> SELECT</span> |
| <a name="l00391"></a>00391 <span class="stringliteral"> avg(('</span>|| tbl_prediction ||<span class="stringliteral">'.prediction - '</span>|| tbl_actual ||<span class="charliteral">'.'</span>|| values_actual ||<span class="stringliteral">')^2) as mean_squared_error</span> |
| <a name="l00392"></a>00392 <span class="stringliteral"> FROM</span> |
| <a name="l00393"></a>00393 <span class="stringliteral"> '</span>|| tbl_prediction ||<span class="stringliteral">',</span> |
| <a name="l00394"></a>00394 <span class="stringliteral"> '</span>|| tbl_actual ||<span class="stringliteral">'</span> |
| <a name="l00395"></a>00395 <span class="stringliteral"> WHERE</span> |
| <a name="l00396"></a>00396 <span class="stringliteral"> '</span>|| tbl_prediction ||<span class="stringliteral">'.id = '</span>|| tbl_actual ||<span class="charliteral">'.'</span>|| id_actual; |
| <a name="l00397"></a>00397 |
| <a name="l00398"></a>00398 EXECUTE <span class="stringliteral">'SET client_min_messages TO '</span> || old_messages; |
| <a name="l00399"></a>00399 END; |
| <a name="l00400"></a>00400 $$ LANGUAGE plpgsql VOLATILE; |
| <a name="l00401"></a>00401 |
| <a name="l00402"></a>00402 ------------------------------------------------------------------------ |
| <a name="l00403"></a>00403 <span class="comment"></span> |
| <a name="l00404"></a>00404 <span class="comment">/**</span> |
| <a name="l00405"></a>00405 <span class="comment"> * @brief A prediction function for logistic regression</span> |
| <a name="l00406"></a>00406 <span class="comment"> *</span> |
| <a name="l00407"></a>00407 <span class="comment"> * @param coef Coefficients. Note: MADlib logregr_train function does not produce a seperate intercept term</span> |
| <a name="l00408"></a>00408 <span class="comment"> * as elastic_net_train function.</span> |
| <a name="l00409"></a>00409 <span class="comment"> * @param col_ind Independent variable, which must be an array</span> |
| <a name="l00410"></a>00410 <span class="comment"> *</span> |
| <a name="l00411"></a>00411 <span class="comment"> */</span> |
| <a name="l00412"></a>00412 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.logregr_predict( |
| <a name="l00413"></a>00413 coef DOUBLE PRECISION[], |
| <a name="l00414"></a>00414 col_ind DOUBLE PRECISION[] |
| <a name="l00415"></a>00415 ) RETURNS BOOLEAN AS $$ |
| <a name="l00416"></a>00416 PythonFunction(validation, cross_validation, <a class="code" href="cross__validation_8sql__in.html#a66b3cb92a758ed6ea3b8da7c6dfa516c" title="A prediction function for logistic regression.">logregr_predict</a>) |
| <a name="l00417"></a>00417 $$ LANGUAGE plpythonu; |
| <a name="l00418"></a>00418 <span class="comment"></span> |
| <a name="l00419"></a>00419 <span class="comment">/**</span> |
| <a name="l00420"></a>00420 <span class="comment"> * @brief A prediction function for logistic regression</span> |
| <a name="l00421"></a>00421 <span class="comment"> * The result is stored in the table of tbl_predict</span> |
| <a name="l00422"></a>00422 <span class="comment"> *</span> |
| <a name="l00423"></a>00423 <span class="comment"> * This function can be used together with cross-validation</span> |
| <a name="l00424"></a>00424 <span class="comment"> */</span> |
| <a name="l00425"></a>00425 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cv_logregr_predict( |
| <a name="l00426"></a>00426 tbl_model VARCHAR, |
| <a name="l00427"></a>00427 tbl_newdata VARCHAR, |
| <a name="l00428"></a>00428 col_ind_var VARCHAR, |
| <a name="l00429"></a>00429 col_id VARCHAR, |
| <a name="l00430"></a>00430 tbl_predict VARCHAR |
| <a name="l00431"></a>00431 ) RETURNS VOID AS $$ |
| <a name="l00432"></a>00432 PythonFunction(validation, cross_validation, <a class="code" href="cross__validation_8sql__in.html#ac7dbc115f0c4624ccbf62b2d5494388d" title="A prediction function for logistic regression The result is stored in the table of tbl_predict...">cv_logregr_predict</a>) |
| <a name="l00433"></a>00433 $$ LANGUAGE plpythonu; |
| <a name="l00434"></a><a class="code" href="cross__validation_8sql__in.html#a66b3cb92a758ed6ea3b8da7c6dfa516c">00434</a> <span class="comment"></span> |
| <a name="l00435"></a>00435 <span class="comment">/**</span> |
| <a name="l00436"></a>00436 <span class="comment"> * @brief Metric function for logistic regression</span> |
| <a name="l00437"></a>00437 <span class="comment"> *</span> |
| <a name="l00438"></a>00438 <span class="comment"> * @param coef Logistic fitting coefficients. Note: MADlib logregr_train function does not produce a seperate intercept term</span> |
| <a name="l00439"></a>00439 <span class="comment"> * as elastic_net_train function.</span> |
| <a name="l00440"></a>00440 <span class="comment"> * @param col_ind Independent variable, an array</span> |
| <a name="l00441"></a>00441 <span class="comment"> * @param col_dep Dependent variable</span> |
| <a name="l00442"></a>00442 <span class="comment"> *</span> |
| <a name="l00443"></a>00443 <span class="comment"> * returns 1 if the prediction is the same as col_dep, otherwise 0</span> |
| <a name="l00444"></a>00444 <span class="comment"> */</span> |
| <a name="l00445"></a>00445 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.logregr_accuracy( |
| <a name="l00446"></a>00446 coef DOUBLE PRECISION[], |
| <a name="l00447"></a><a class="code" href="cross__validation_8sql__in.html#ac7dbc115f0c4624ccbf62b2d5494388d">00447</a> col_ind DOUBLE PRECISION[], |
| <a name="l00448"></a>00448 col_dep BOOLEAN |
| <a name="l00449"></a>00449 ) RETURNS INTEGER AS $$ |
| <a name="l00450"></a>00450 PythonFunction(validation, cross_validation, <a class="code" href="cross__validation_8sql__in.html#a2d1571ffa794176a5dfed9d35e70fed7" title="Metric function for logistic regression.">logregr_accuracy</a>) |
| <a name="l00451"></a>00451 $$ LANGUAGE plpythonu; |
| <a name="l00452"></a>00452 <span class="comment"></span> |
| <a name="l00453"></a>00453 <span class="comment">/**</span> |
| <a name="l00454"></a>00454 <span class="comment"> * @brief Metric function for logistic regression</span> |
| <a name="l00455"></a>00455 <span class="comment"> *</span> |
| <a name="l00456"></a>00456 <span class="comment"> * It computes the percentage of correct predictions.</span> |
| <a name="l00457"></a>00457 <span class="comment"> * The result is stored in the table of tbl_accuracy</span> |
| <a name="l00458"></a>00458 <span class="comment"> */</span> |
| <a name="l00459"></a>00459 CREATE OR REPLACE FUNCTION MADLIB_SCHEMA.cv_logregr_accuracy( |
| <a name="l00460"></a>00460 tbl_predict VARCHAR, |
| <a name="l00461"></a>00461 tbl_source VARCHAR, |
| <a name="l00462"></a>00462 col_id VARCHAR, |
| <a name="l00463"></a>00463 col_dep_var VARCHAR, |
| <a name="l00464"></a>00464 tbl_accuracy VARCHAR |
| <a name="l00465"></a>00465 ) RETURNS VOID AS $$ |
| <a name="l00466"></a>00466 PythonFunction(validation, cross_validation, <a class="code" href="cross__validation_8sql__in.html#ac1b5c57473ff672af45191c8d53f46ed" title="Metric function for logistic regression.">cv_logregr_accuracy</a>) |
| <a name="l00467"></a><a class="code" href="cross__validation_8sql__in.html#a2d1571ffa794176a5dfed9d35e70fed7">00467</a> $$ LANGUAGE plpythonu; |
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