mlstatpy.optim.sgd#
- class mlstatpy.optim.sgd.BaseOptimizer(coef, learning_rate_init=0.1, min_threshold=None, max_threshold=None, l1=0.0, l2=0.0)[source][source]#
Base stochastic gradient descent optimizer.
- Paramètres:
coef – array, initial coefficient
learning_rate_init – float The initial learning rate used. It controls the step-size in updating the weights.
min_threshold – coefficients must be higher than min_thresold
max_threshold – coefficients must be below than max_thresold
The class holds the following attributes:
learning_rate: float, the current learning rate
coef: optimized coefficients
min_threshold, max_threshold: coefficients thresholds
l2: L2 regularization
l1: L1 regularization
- iteration_ends(time_step)[source][source]#
Performs update to learning rate and potentially other states at the end of an iteration.
- train(X, y, fct_loss, fct_grad, max_iter=100, early_th=None, verbose=False)[source][source]#
Optimizes the coefficients.
- Paramètres:
X – datasets (array)
y – expected target
fct_loss – loss function, signature: f(coef, X, y) -> float
fct_grad – gradient function, signature: g(coef, x, y, i) -> array
max_iter – number maximum of iteration
early_th – stops the training if the error goes below this threshold
verbose – display information
- Renvoie:
loss
The method keeps the best coefficients for the minimal loss.
- class mlstatpy.optim.sgd.SGDOptimizer(coef, learning_rate_init=0.1, lr_schedule='invscaling', momentum=0.9, power_t=0.5, early_th=None, min_threshold=None, max_threshold=None, l1=0.0, l2=0.0)[source][source]#
Stochastic gradient descent optimizer with momentum.
- Paramètres:
coef – array, initial coefficient
learning_rate_init – float The initial learning rate used. It controls the step-size in updating the weights,
lr_schedule – {“constant”, “adaptive”, “invscaling”}, learning rate schedule for weight updates, “constant” for a constant learning rate given by learning_rate_init. “invscaling” gradually decreases the learning rate learning_rate_ at each time step t using an inverse scaling exponent of power_t. learning_rate_ = learning_rate_init / pow(t, power_t), “adaptive”, keeps the learning rate constant to learning_rate_init as long as the training keeps decreasing. Each time 2 consecutive epochs fail to decrease the training loss by tol, or fail to increase validation score by tol if “early_stopping” is on, the current learning rate is divided by 5.
momentum – float Value of momentum used, must be larger than or equal to 0
power_t – double The exponent for inverse scaling learning rate.
early_th – stops if the error goes below that threshold
min_threshold – lower bound for parameters (can be None)
max_threshold – upper bound for parameters (can be None)
l1 – L1 regularization
l2 – L2 regularization
The class holds the following attributes:
learning_rate: float, the current learning rate
velocity*: array, velocity that are used to update params
Stochastic Gradient Descent applied to linear regression
The following example how to optimize a simple linear regression.
<<<
import numpy from mlstatpy.optim import SGDOptimizer def fct_loss(c, X, y): return numpy.linalg.norm(X @ c - y) ** 2 def fct_grad(c, x, y, i=0): return x * (x @ c - y) * 0.1 coef = numpy.array([0.5, 0.6, -0.7]) X = numpy.random.randn(10, 3) y = X @ coef sgd = SGDOptimizer(numpy.random.randn(3)) sgd.train(X, y, fct_loss, fct_grad, max_iter=15, verbose=True) print("optimized coefficients:", sgd.coef)
>>>
0/15: loss: 24.38 lr=0.1 max(coef): 1.6 l1=0/2.4 l2=0/3 1/15: loss: 4.771 lr=0.0302 max(coef): 0.93 l1=0.00049/1.9 l2=1.7e-07/1.5 2/15: loss: 22.24 lr=0.0218 max(coef): 1.4 l1=0.092/1.8 l2=0.0063/2.2 3/15: loss: 25.76 lr=0.018 max(coef): 1.4 l1=1.2/1.9 l2=0.48/2.3 4/15: loss: 18.03 lr=0.0156 max(coef): 1.3 l1=0.025/1.9 l2=0.00021/2 5/15: loss: 13.3 lr=0.014 max(coef): 1.2 l1=0.0037/1.9 l2=4.7e-06/1.8 6/15: loss: 9.176 lr=0.0128 max(coef): 1.1 l1=0.6/1.9 l2=0.15/1.6 7/15: loss: 4.523 lr=0.0119 max(coef): 0.94 l1=0.15/1.9 l2=0.01/1.4 8/15: loss: 2.377 lr=0.0111 max(coef): 0.84 l1=0.036/1.9 l2=0.00099/1.3 9/15: loss: 1.259 lr=0.0105 max(coef): 0.77 l1=0.035/1.9 l2=0.00042/1.3 10/15: loss: 0.6979 lr=0.00995 max(coef): 0.72 l1=0.16/1.9 l2=0.012/1.3 11/15: loss: 0.3994 lr=0.00949 max(coef): 0.68 l1=0.12/1.9 l2=0.0048/1.3 12/15: loss: 0.2629 lr=0.00909 max(coef): 0.66 l1=0.017/1.9 l2=0.00015/1.2 13/15: loss: 0.1999 lr=0.00874 max(coef): 0.66 l1=0.015/1.9 l2=0.00017/1.2 14/15: loss: 0.1541 lr=0.00842 max(coef): 0.66 l1=0.042/1.9 l2=0.00062/1.2 15/15: loss: 0.1175 lr=0.00814 max(coef): 0.66 l1=0.022/1.9 l2=0.00021/1.2 optimized coefficients: [ 0.617 0.631 -0.662]