--- # required metadata title: "rx_logistic_regression: Logistic Regression" description: "Machine Learning Logistic Regression" keywords: "models, classification" author: WilliamDAssafMSFT ms.author: wiassaf manager: "cgronlun" ms.date: 07/15/2019 ms.topic: "reference" ms.prod: "sql" ms.technology: "machine-learning-services" ms.service: "" ms.assetid: "" # optional metadata ROBOTS: "" audience: "" ms.devlang: "Python" ms.reviewer: "" ms.suite: "" ms.tgt_pltfrm: "" ms.custom: "" monikerRange: ">=sql-server-2017||>=sql-server-linux-ver15" --- # *microsoftml.rx_logistic_regression*: Logistic Regression ## Usage ``` microsoftml.rx_logistic_regression(formula: str, data: [revoscalepy.datasource.RxDataSource.RxDataSource, pandas.core.frame.DataFrame], method: ['binary', 'multiClass'] = 'binary', l2_weight: float = 1, l1_weight: float = 1, opt_tol: float = 1e-07, memory_size: int = 20, init_wts_diameter: float = 0, max_iterations: int = 2147483647, show_training_stats: bool = False, sgd_init_tol: float = 0, train_threads: int = None, dense_optimizer: bool = False, normalize: ['No', 'Warn', 'Auto', 'Yes'] = 'Auto', ml_transforms: list = None, ml_transform_vars: list = None, row_selection: str = None, transforms: dict = None, transform_objects: dict = None, transform_function: str = None, transform_variables: list = None, transform_packages: list = None, transform_environment: dict = None, blocks_per_read: int = None, report_progress: int = None, verbose: int = 1, ensemble: microsoftml.modules.ensemble.EnsembleControl = None, compute_context: revoscalepy.computecontext.RxComputeContext.RxComputeContext = None) ``` ## Description Machine Learning Logistic Regression ## Details Logistic Regression is a classification method used to predict the value of a categorical dependent variable from its relationship to one or more independent variables assumed to have a logistic distribution. If the dependent variable has only two possible values (success/failure), then the logistic regression is binary. If the dependent variable has more than two possible values (blood type given diagnostic test results), then the logistic regression is multinomial. The optimization technique used for `rx_logistic_regression` is the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS). Both the L-BFGS and regular BFGS algorithms use quasi-Newtonian methods to estimate the computationally intensive Hessian matrix in the equation used by Newton’s method to calculate steps. But the L-BFGS approximation uses only a limited amount of memory to compute the next step direction, so that it is especially suited for problems with a large number of variables. The `memory_size` parameter specifies the number of past positions and gradients to store for use in the computation of the next step. This learner can use elastic net regularization: a linear combination of L1 (lasso) and L2 (ridge) regularizations. Regularization is a method that can render an ill-posed problem more tractable by imposing constraints that provide information to supplement the data and that prevents overfitting by penalizing models with extreme coefficient values. This can improve the generalization of the model learned by selecting the optimal complexity in the bias-variance tradeoff. Regularization works by adding the penalty that is associated with coefficient values to the error of the hypothesis. An accurate model with extreme coefficient values would be penalized more, but a less accurate model with more conservative values would be penalized less. L1 and L2 regularization have different effects and uses that are complementary in certain respects. * `l1_weight`: can be applied to sparse models, when working with high-dimensional data. It pulls small weights associated features that are relatively unimportant towards 0. * `l2_weight`: is preferable for data that is not sparse. It pulls large weights towards zero. Adding the ridge penalty to the regularization overcomes some of lasso’s limitations. It can improve its predictive accuracy, for example, when the number of predictors is greater than the sample size. If `x = l1_weight` and `y = l2_weight`, `ax + by = c` defines the linear span of the regularization terms. The default values of x and y are both `1`. An aggressive regularization can harm predictive capacity by excluding important variables out of the model. So choosing the optimal values for the regularization parameters is important for the performance of the logistic regression model. ## Arguments ### formula The formula as described in revoscalepy.rx_formula Interaction terms and `F()` are not currently supported in [microsoftml](../../ref-py-microsoftml.md). ### data A data source object or a character string specifying a *.xdf* file or a data frame object. ### method A character string that specifies the type of Logistic Regression: `"binary"` for the default binary classification logistic regression or `"multiClass"` for multinomial logistic regression. ### l2_weight The L2 regularization weight. Its value must be greater than or equal to `0` and the default value is set to `1`. ### l1_weight The L1 regularization weight. Its value must be greater than or equal to `0` and the default value is set to `1`. ### opt_tol Threshold value for optimizer convergence. If the improvement between iterations is less than the threshold, the algorithm stops and returns the current model. Smaller values are slower, but more accurate. The default value is `1e-07`. ### memory_size Memory size for L-BFGS, specifying the number of past positions and gradients to store for the computation of the next step. This optimization parameter limits the amount of memory that is used to compute the magnitude and direction of the next step. When you specify less memory, training is faster but less accurate. Must be greater than or equal to `1` and the default value is `20`. ### max_iterations Sets the maximum number of iterations. After this number of steps, the algorithm stops even if it has not satisfied convergence criteria. ### show_training_stats Specify `True` to show the statistics of training data and the trained model; otherwise, `False`. The default value is `False`. For additional information about model statistics, see `summary.ml_model()`. ### sgd_init_tol Set to a number greater than 0 to use Stochastic Gradient Descent (SGD) to find the initial parameters. A non-zero value set specifies the tolerance SGD uses to determine convergence. The default value is `0` specifying that SGD is not used. ### init_wts_diameter Sets the initial weights diameter that specifies the range from which values are drawn for the initial weights. These weights are initialized randomly from within this range. For example, if the diameter is specified to be `d`, then the weights are uniformly distributed between `-d/2` and `d/2`. The default value is `0`, which specifies that all the weights are initialized to `0`. ### train_threads The number of threads to use in training the model. This should be set to the number of cores on the machine. Note that L-BFGS multi-threading attempts to load dataset into memory. In case of out-of-memory issues, set `train_threads` to `1` to turn off multi-threading. If *None* the number of threads to use is determined internally. The default value is *None*. ### dense_optimizer If `True`, forces densification of the internal optimization vectors. If `False`, enables the logistic regression optimizer use sparse or dense internal states as it finds appropriate. Setting `denseOptimizer` to `True` requires the internal optimizer to use a dense internal state, which may help alleviate load on the garbage collector for some varieties of larger problems. ### normalize Specifies the type of automatic normalization used: * `"Auto"`: if normalization is needed, it is performed automatically. This is the default choice. * `"No"`: no normalization is performed. * `"Yes"`: normalization is performed. * `"Warn"`: if normalization is needed, a warning message is displayed, but normalization is not performed. Normalization rescales disparate data ranges to a standard scale. Feature scaling insures the distances between data points are proportional and enables various optimization methods such as gradient descent to converge much faster. If normalization is performed, a `MaxMin` normalizer is used. It normalizes values in an interval [a, b] where `-1 <= a <= 0` and `0 <= b <= 1` and `b - a = 1`. This normalizer preserves sparsity by mapping zero to zero. ### ml_transforms Specifies a list of MicrosoftML transforms to be performed on the data before training or *None* if no transforms are to be performed. See [`featurize_text`](featurize-text.md), [`categorical`](categorical.md), and [`categorical_hash`](categorical-hash.md), for transformations that are supported. These transformations are performed after any specified Python transformations. The default value is *None*. ### ml_transform_vars Specifies a character vector of variable names to be used in `ml_transforms` or *None* if none are to be used. The default value is *None*. ### row_selection NOT SUPPORTED. Specifies the rows (observations) from the data set that are to be used by the model with the name of a logical variable from the data set (in quotes) or with a logical expression using variables in the data set. For example: * `row_selection = "old"` will only use observations in which the value of the variable `old` is `True`. * `row_selection = (age > 20) & (age < 65) & (log(income) > 10)` only uses observations in which the value of the `age` variable is between 20 and 65 and the value of the `log` of the `income` variable is greater than 10. The row selection is performed after processing any data transformations (see the arguments `transforms` or `transform_function`). As with all expressions, `row_selection` can be defined outside of the function call using the `expression` function. ### transforms NOT SUPPORTED. An expression of the form that represents the first round of variable transformations. As with all expressions, `transforms` (or `row_selection`) can be defined outside of the function call using the `expression` function. ### transform_objects NOT SUPPORTED. A named list that contains objects that can be referenced by `transforms`, `transform_function`, and `row_selection`. ### transform_function The variable transformation function. ### transform_variables A character vector of input data set variables needed for the transformation function. ### transform_packages NOT SUPPORTED. A character vector specifying additional Python packages (outside of those specified in `RxOptions.get_option("transform_packages")`) to be made available and preloaded for use in variable transformation functions. For example, those explicitly defined in [revoscalepy](/machine-learning-server/python-reference/revoscalepy/index) functions via their `transforms` and `transform_function` arguments or those defined implicitly via their `formula` or `row_selection` arguments. The `transform_packages` argument may also be *None*, indicating that no packages outside `RxOptions.get_option("transform_packages")` are preloaded. ### transform_environment NOT SUPPORTED. A user-defined environment to serve as a parent to all environments developed internally and used for variable data transformation. If `transform_environment = None`, a new “hash” environment with parent revoscalepy.baseenv is used instead. ### blocks_per_read Specifies the number of blocks to read for each chunk of data read from the data source. ### report_progress An integer value that specifies the level of reporting on the row processing progress: * `0`: no progress is reported. * `1`: the number of processed rows is printed and updated. * `2`: rows processed and timings are reported. * `3`: rows processed and all timings are reported. ### verbose An integer value that specifies the amount of output wanted. If `0`, no verbose output is printed during calculations. Integer values from `1` to `4` provide increasing amounts of information. ### compute_context Sets the context in which computations are executed, specified with a valid revoscalepy.RxComputeContext. Currently local and [revoscalepy.RxInSqlServer](/machine-learning-server/python-reference/revoscalepy/RxInSqlServer) compute contexts are supported. ### ensemble Control parameters for ensembling. ## Returns A [`LogisticRegression`](learners-object.md) object with the trained model. ## Note This algorithm will attempt to load the entire dataset into memory when `train_threads > 1` (multi-threading). ## See also [`rx_predict`](rx-predict.md) ## References [Wikipedia: L-BFGS](https://en.wikipedia.org/wiki/L-BFGS) [Wikipedia: Logistic regression](https://en.wikipedia.org/wiki/Logistic_regression) [Scalable Training of L1-Regularized Log-Linear Models](https://research.microsoft.com/apps/pubs/default.aspx?id=78900) [Test Run - L1 and L2 Regularization for Machine Learning](/archive/msdn-magazine/2015/february/test-run-l1-and-l2-regularization-for-machine-learning) ## Binary classification example ``` ''' Binary Classification. ''' import numpy import pandas from microsoftml import rx_logistic_regression, rx_predict from revoscalepy.etl.RxDataStep import rx_data_step from microsoftml.datasets.datasets import get_dataset infert = get_dataset("infert") import sklearn if sklearn.__version__ < "0.18": from sklearn.cross_validation import train_test_split else: from sklearn.model_selection import train_test_split infertdf = infert.as_df() infertdf["isCase"] = infertdf.case == 1 data_train, data_test, y_train, y_test = train_test_split(infertdf, infertdf.isCase) model = rx_logistic_regression( formula=" isCase ~ age + parity + education + spontaneous + induced ", data=data_train) print(model.coef_) # RuntimeError: The type (RxTextData) for file is not supported. score_ds = rx_predict(model, data=data_test, extra_vars_to_write=["isCase", "Score"]) # Print the first five rows print(rx_data_step(score_ds, number_rows_read=5)) ``` Output: ``` Automatically adding a MinMax normalization transform, use 'norm=Warn' or 'norm=No' to turn this behavior off. Beginning processing data. Rows Read: 186, Read Time: 0, Transform Time: 0 Beginning processing data. Beginning processing data. Rows Read: 186, Read Time: 0.001, Transform Time: 0 Beginning processing data. Beginning processing data. Rows Read: 186, Read Time: 0, Transform Time: 0 Beginning processing data. LBFGS multi-threading will attempt to load dataset into memory. In case of out-of-memory issues, turn off multi-threading by setting trainThreads to 1. Beginning optimization num vars: 6 improvement criterion: Mean Improvement L1 regularization selected 5 of 6 weights. Not training a calibrator because it is not needed. Elapsed time: 00:00:00.0646405 Elapsed time: 00:00:00.0083991 OrderedDict([('(Bias)', -1.2366217374801636), ('spontaneous', 1.9391206502914429), ('induced', 0.7497404217720032), ('parity', -0.31517016887664795), ('age', -3.162723260174971e-06)]) Beginning processing data. Rows Read: 62, Read Time: 0, Transform Time: 0 Beginning processing data. Elapsed time: 00:00:00.0287290 Finished writing 62 rows. Writing completed. Rows Read: 5, Total Rows Processed: 5, Total Chunk Time: 0.001 seconds isCase PredictedLabel Score Probability 0 False False -1.341681 0.207234 1 True True 0.597440 0.645070 2 False True 0.544912 0.632954 3 False False -1.289152 0.215996 4 False False -1.019339 0.265156 ``` ## MultiClass classification example ``` ''' MultiClass Classification ''' import numpy import pandas from microsoftml import rx_logistic_regression, rx_predict from revoscalepy.etl.RxDataStep import rx_data_step from microsoftml.datasets.datasets import get_dataset iris = get_dataset("iris") import sklearn if sklearn.__version__ < "0.18": from sklearn.cross_validation import train_test_split else: from sklearn.model_selection import train_test_split irisdf = iris.as_df() irisdf["Species"] = irisdf["Species"].astype("category") data_train, data_test, y_train, y_test = train_test_split(irisdf, irisdf.Species) model = rx_logistic_regression( formula=" Species ~ Sepal_Length + Sepal_Width + Petal_Length + Petal_Width ", method="multiClass", data=data_train) print(model.coef_) # RuntimeError: The type (RxTextData) for file is not supported. score_ds = rx_predict(model, data=data_test, extra_vars_to_write=["Species", "Score"]) # Print the first five rows print(rx_data_step(score_ds, number_rows_read=5)) ``` Output: ``` Automatically adding a MinMax normalization transform, use 'norm=Warn' or 'norm=No' to turn this behavior off. Beginning processing data. Rows Read: 112, Read Time: 0, Transform Time: 0 Beginning processing data. Beginning processing data. Rows Read: 112, Read Time: 0, Transform Time: 0 Beginning processing data. Beginning processing data. Rows Read: 112, Read Time: 0, Transform Time: 0 Beginning processing data. LBFGS multi-threading will attempt to load dataset into memory. In case of out-of-memory issues, turn off multi-threading by setting trainThreads to 1. Beginning optimization num vars: 15 improvement criterion: Mean Improvement L1 regularization selected 9 of 15 weights. Not training a calibrator because it is not needed. Elapsed time: 00:00:00.0493224 Elapsed time: 00:00:00.0080558 OrderedDict([('setosa+(Bias)', 2.074636697769165), ('versicolor+(Bias)', 0.4899507164955139), ('virginica+(Bias)', -2.564580202102661), ('setosa+Petal_Width', -2.8389241695404053), ('setosa+Petal_Length', -2.4824044704437256), ('setosa+Sepal_Width', 0.274869441986084), ('versicolor+Sepal_Width', -0.2645561397075653), ('virginica+Petal_Width', 2.6924400329589844), ('virginica+Petal_Length', 1.5976412296295166)]) Beginning processing data. Rows Read: 38, Read Time: 0, Transform Time: 0 Beginning processing data. Elapsed time: 00:00:00.0331861 Finished writing 38 rows. Writing completed. Rows Read: 5, Total Rows Processed: 5, Total Chunk Time: 0.001 seconds Species Score.0 Score.1 Score.2 0 virginica 0.044230 0.364927 0.590843 1 setosa 0.767412 0.210586 0.022002 2 setosa 0.756523 0.221933 0.021543 3 setosa 0.767652 0.211191 0.021157 4 versicolor 0.116369 0.498615 0.385016 ```