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- The sample data set and an introduction to logistic regression are described here.
The MADlib function used in this example is described in the MADlib logistic regression documentation.
Suppose that we are working with doctors on a project related to heart failure. The dependent variable in the data set is whether the patient has had a second heart attack within 1 year (yes=1). We have two independent variables: one is whether the patient completed a treatment on anger control (yes=1), and the other is a score on a trait anxiety scale (higher score means more anxious).
The idea is to train a model using labeled data, then use this model to predict second heart attack occurrence for other patients.
To interact with the data using MADlib, use the standard
psql
terminal provided by the database. You could also use a tool likepgAdmin.
In this example, we launch
psql
and create the following training data table:Code Block language sql DROP TABLE IF EXISTS patients, patients_logregr, patients_logregr_summary; CREATE TABLE patients( id INTEGER NOT NULL, second_attack INTEGER, treatment INTEGER, trait_anxiety INTEGER); INSERT INTO patients VALUES (1, 1, 1, 70), (3, 1, 1, 50), (5, 1, 0, 40), (7, 1, 0, 75), (9, 1, 0, 70), (11, 0, 1, 65), (13, 0, 1, 45), (15, 0, 1, 40), (17, 0, 0, 55), (19, 0, 0, 50), (2, 1, 1, 80), (4, 1, 0, 60), (6, 1, 0, 65), (8, 1, 0, 80), (10, 1, 0, 60), (12, 0, 1, 50), (14, 0, 1, 35), (16, 0, 1, 50), (18, 0, 0, 45), (20, 0, 0, 60);
Call MADlib built-in function to train a classification model using the training data table as input:
Code Block language sql SELECT madlib.logregr_train( 'patients', -- source table 'patients_logregr', -- output table 'second_attack', -- labels 'ARRAY[1, treatment, trait_anxiety]', -- features NULL, -- grouping columns 20, -- max number of iteration 'irls' -- optimizer );
View the model that has just been trained:
Code Block language sql -- Set extended display on for easier reading of output (\x is for psql only) \x on SELECT * from patients_logregr; -- ************ -- -- Result -- -- ************ -- coef | [-6.36346994178187, -1.02410605239327, 0.119044916668606] log_likelihood | -9.41018298389 std_err | [3.21389766375094, 1.17107844860319, 0.0549790458269309] z_stats | [-1.97998524145759, -0.874498248699549, 2.16527796868918] p_values | [0.0477051870698128, 0.38184697353045, 0.0303664045046168] odds_ratios | [0.0017233763092323, 0.359117354054954, 1.12642051220895] condition_no | 326.081922792 num_rows_processed | 20 num_missing_rows_skipped | 0 num_iterations | 5 variance_covariance | [[10.3291381930637, -0.47430466519573, -0.171995901260052], [-0.47430466519573, 1.37142473278285, -0.00119520703381598], [-0.171995901260052, -0.00119520703381598, 0.00302269548003977]] -- Alternatively, unnest the arrays in the results for easier reading of output (\x is for psql only) \x off SELECT unnest(array['intercept', 'treatment', 'trait_anxiety']) as attribute, unnest(coef) as coefficient, unnest(std_err) as standard_error, unnest(z_stats) as z_stat, unnest(p_values) as pvalue, unnest(odds_ratios) as odds_ratio FROM patients_logregr; -- ************ -- -- Result -- -- ************ -- +---------------+---------------+------------------+-----------+-----------+--------------+ | attribute | coefficient | standard_error | z_stat | pvalue | odds_ratio | |---------------+---------------+------------------+-----------+-----------+--------------| | intercept | -6.36347 | 3.2139 | -1.97999 | 0.0477052 | 0.00172338 | | treatment | -1.02411 | 1.17108 | -0.874498 | 0.381847 | 0.359117 | | trait_anxiety | 0.119045 | 0.054979 | 2.16528 | 0.0303664 | 1.12642 | +---------------+---------------+------------------+-----------+-----------+--------------+
Now use the model to predict the dependent variable (second heart attack within 1 year) using the logistic regression model. For the purpose of demonstration, we will use 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.
Code Block language sql -- Display prediction value along with the original value SELECT p.id, madlib.logregr_predict(coef, ARRAY[1, treatment, trait_anxiety]), p.second_attack FROM patients p, patients_logregr m ORDER BY p.id; -- ************ -- -- Result -- -- ************ -- +------+-------------------+-----------------+ | id | logregr_predict | second_attack | |------+-------------------+-----------------| | 1 | True | 1 | | 2 | True | 1 | | 3 | False | 1 | | 4 | True | 1 | | 5 | False | 1 | | 6 | True | 1 | | 7 | True | 1 | | 8 | True | 1 | | 9 | True | 1 | | 10 | True | 1 | | 11 | True | 0 | | 12 | False | 0 | | 13 | False | 0 | | 14 | False | 0 | | 15 | False | 0 | | 16 | False | 0 | | 17 | True | 0 | | 18 | False | 0 | | 19 | False | 0 | | 20 | True | 0 | +------+-------------------+-----------------+ -- Predicting the probability of the dependent variable being TRUE. -- Display prediction value along with the original value SELECT p.id, madlib.logregr_predict_prob(coef, ARRAY[1, treatment, trait_anxiety]) FROM patients p, patients_logregr m ORDER BY p.id; -- ************ -- -- Result -- -- ************ -- +------+------------------------+ | id | logregr_predict_prob | |------+------------------------| | 1 | 0.720223 | | 2 | 0.894355 | | 3 | 0.19227 | | 4 | 0.685513 | | 5 | 0.167748 | | 6 | 0.798098 | | 7 | 0.928568 | | 8 | 0.959306 | | 9 | 0.877576 | | 10 | 0.685513 | | 11 | 0.586701 | | 12 | 0.19227 | | 13 | 0.116032 | | 14 | 0.0383829 | | 15 | 0.0674976 | | 16 | 0.19227 | | 17 | 0.545871 | | 18 | 0.267675 | | 19 | 0.398619 | | 20 | 0.685513 | +------+------------------------+
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