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: 49.82 lr=0.1 max(coef): 1.3 l1=0/3 l2=0/3.1 1/15: loss: 13.98 lr=0.0302 max(coef): 0.8 l1=0.088/1.5 l2=0.0054/1.1 2/15: loss: 3.738 lr=0.0218 max(coef): 0.63 l1=0.022/1.3 l2=0.00018/0.67 3/15: loss: 1.999 lr=0.018 max(coef): 0.72 l1=0.24/1.4 l2=0.02/0.83 4/15: loss: 1.567 lr=0.0156 max(coef): 0.8 l1=0.06/1.5 l2=0.0026/0.93 5/15: loss: 1.402 lr=0.014 max(coef): 0.82 l1=0.0064/1.6 l2=1.8e-05/0.99 6/15: loss: 1.126 lr=0.0128 max(coef): 0.81 l1=0.036/1.6 l2=0.00045/0.97 7/15: loss: 0.925 lr=0.0119 max(coef): 0.79 l1=0.00078/1.6 l2=2.2e-07/0.95 8/15: loss: 0.7864 lr=0.0111 max(coef): 0.77 l1=0.0012/1.6 l2=5.3e-07/0.93 9/15: loss: 0.6454 lr=0.0105 max(coef): 0.76 l1=0.0088/1.6 l2=3.3e-05/0.91 10/15: loss: 0.5454 lr=0.00995 max(coef): 0.74 l1=0.042/1.6 l2=0.0012/0.89 11/15: loss: 0.4745 lr=0.00949 max(coef): 0.73 l1=0.039/1.6 l2=0.001/0.88 12/15: loss: 0.4059 lr=0.00909 max(coef): 0.71 l1=0.11/1.6 l2=0.0041/0.86 13/15: loss: 0.363 lr=0.00874 max(coef): 0.71 l1=0.047/1.6 l2=0.00086/0.86 14/15: loss: 0.3138 lr=0.00842 max(coef): 0.7 l1=0.0037/1.6 l2=5.1e-06/0.85 15/15: loss: 0.2867 lr=0.00814 max(coef): 0.69 l1=0.083/1.6 l2=0.0028/0.85 optimized coefficients: [ 0.415 0.691 -0.45 ]