diff options
Diffstat (limited to 'python')
-rw-r--r-- | python/pyspark/mllib/regression.py | 34 |
1 files changed, 21 insertions, 13 deletions
diff --git a/python/pyspark/mllib/regression.py b/python/pyspark/mllib/regression.py index 13b3397501..4dd7083d79 100644 --- a/python/pyspark/mllib/regression.py +++ b/python/pyspark/mllib/regression.py @@ -219,8 +219,10 @@ class LinearRegressionWithSGD(object): """ Train a linear regression model with no regularization using Stochastic Gradient Descent. This solves the least squares regression formulation - f(weights) = 1/n ||A weights-y||^2^ - (which is the mean squared error). + + f(weights) = 1/n ||A weights-y||^2 + + which is the mean squared error. Here the data matrix has n rows, and the input RDD holds the set of rows of A, each with its corresponding right hand side label y. See also the documentation for the precise formulation. @@ -367,8 +369,10 @@ class LassoModel(LinearRegressionModelBase): class LassoWithSGD(object): """ Train a regression model with L1-regularization using Stochastic Gradient Descent. - This solves the l1-regularized least squares regression formulation - f(weights) = 1/2n ||A weights-y||^2^ + regParam ||weights||_1 + This solves the L1-regularized least squares regression formulation + + f(weights) = 1/2n ||A weights-y||^2 + regParam ||weights||_1 + Here the data matrix has n rows, and the input RDD holds the set of rows of A, each with its corresponding right hand side label y. See also the documentation for the precise formulation. @@ -505,8 +509,10 @@ class RidgeRegressionModel(LinearRegressionModelBase): class RidgeRegressionWithSGD(object): """ Train a regression model with L2-regularization using Stochastic Gradient Descent. - This solves the l2-regularized least squares regression formulation - f(weights) = 1/2n ||A weights-y||^2^ + regParam/2 ||weights||^2^ + This solves the L2-regularized least squares regression formulation + + f(weights) = 1/2n ||A weights-y||^2 + regParam/2 ||weights||^2 + Here the data matrix has n rows, and the input RDD holds the set of rows of A, each with its corresponding right hand side label y. See also the documentation for the precise formulation. @@ -655,17 +661,19 @@ class IsotonicRegression(object): Only univariate (single feature) algorithm supported. Sequential PAV implementation based on: - Tibshirani, Ryan J., Holger Hoefling, and Robert Tibshirani. + + Tibshirani, Ryan J., Holger Hoefling, and Robert Tibshirani. "Nearly-isotonic regression." Technometrics 53.1 (2011): 54-61. - Available from [[http://www.stat.cmu.edu/~ryantibs/papers/neariso.pdf]] + Available from http://www.stat.cmu.edu/~ryantibs/papers/neariso.pdf Sequential PAV parallelization based on: - Kearsley, Anthony J., Richard A. Tapia, and Michael W. Trosset. - "An approach to parallelizing isotonic regression." - Applied Mathematics and Parallel Computing. Physica-Verlag HD, 1996. 141-147. - Available from [[http://softlib.rice.edu/pub/CRPC-TRs/reports/CRPC-TR96640.pdf]] - @see [[http://en.wikipedia.org/wiki/Isotonic_regression Isotonic regression (Wikipedia)]] + Kearsley, Anthony J., Richard A. Tapia, and Michael W. Trosset. + "An approach to parallelizing isotonic regression." + Applied Mathematics and Parallel Computing. Physica-Verlag HD, 1996. 141-147. + Available from http://softlib.rice.edu/pub/CRPC-TRs/reports/CRPC-TR96640.pdf + + See `Isotonic regression (Wikipedia) <http://en.wikipedia.org/wiki/Isotonic_regression>`_. .. versionadded:: 1.4.0 """ |