Examples

1. Compute a distance between two graphs.

2. Stochastic Gradient Descent applied to linear regression

Compute a distance between two graphs.

See Distance between two graphs.

<<<

import copy
from mlstatpy.graph import GraphDistance

# We define two graphs as list of edges.
graph1 = [("a", "b"), ("b", "c"), ("b", "X"), ("X", "c"),
          ("c", "d"), ("d", "e"), ("0", "b")]
graph2 = [("a", "b"), ("b", "c"), ("b", "X"), ("X", "c"),
          ("c", "t"), ("t", "d"), ("d", "e"), ("d", "g")]

# We convert them into objects GraphDistance.
graph1 = GraphDistance(graph1)
graph2 = GraphDistance(graph2)

distance, graph = graph1.distance_matching_graphs_paths(graph2, use_min=False)

print("distance", distance)
print("common paths:", graph)

>>>

    distance 0.3318250377073907
    common paths: 0
    X
    a
    b
    c
    d
    e
    00
    11
    g
    t
    a -> b []
    b -> c []
    b -> X []
    X -> c []
    c -> d []
    d -> e []
    0 -> b []
    00 -> a []
    00 -> 0 []
    e -> 11 []
    c -> 2a.t []
    2a.t -> d []
    d -> 2a.g []
    2a.g -> 11 []

(entrée originale : graph_distance.py:docstring of mlstatpy.graph.graph_distance.GraphDistance, line 3)

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: 88.79 lr=0.1 max(coef): 1.9 l1=0/2.9 l2=0/4.5
    1/15: loss: 47.22 lr=0.0302 max(coef): 1.7 l1=0.38/2.4 l2=0.084/3.2
    2/15: loss: 39.7 lr=0.0218 max(coef): 1.4 l1=1.8/3 l2=2.5/3.3
    3/15: loss: 22.29 lr=0.018 max(coef): 0.92 l1=0.0063/2.5 l2=2.3e-05/2.1
    4/15: loss: 10.18 lr=0.0156 max(coef): 0.85 l1=0.01/1.9 l2=3.5e-05/1.4
    5/15: loss: 4.194 lr=0.014 max(coef): 0.76 l1=0.00065/1.6 l2=2.4e-07/1.1
    6/15: loss: 1.646 lr=0.0128 max(coef): 0.71 l1=0.065/1.8 l2=0.0018/1.1
    7/15: loss: 0.7677 lr=0.0119 max(coef): 0.66 l1=0.13/1.8 l2=0.0076/1.1
    8/15: loss: 0.4433 lr=0.0111 max(coef): 0.63 l1=0.095/1.8 l2=0.0042/1.1
    9/15: loss: 0.272 lr=0.0105 max(coef): 0.6 l1=0.00051/1.8 l2=8.8e-08/1.1
    10/15: loss: 0.1774 lr=0.00995 max(coef): 0.6 l1=0.00076/1.8 l2=2e-07/1
    11/15: loss: 0.1309 lr=0.00949 max(coef): 0.61 l1=0.001/1.8 l2=3.4e-07/1
    12/15: loss: 0.1065 lr=0.00909 max(coef): 0.61 l1=0.071/1.7 l2=0.0042/1
    13/15: loss: 0.08566 lr=0.00874 max(coef): 0.62 l1=0.0081/1.7 l2=3.2e-05/1
    14/15: loss: 0.07239 lr=0.00842 max(coef): 0.62 l1=0.06/1.7 l2=0.003/1
    15/15: loss: 0.06085 lr=0.00814 max(coef): 0.63 l1=0.056/1.7 l2=0.0025/1
    optimized coefficients: [ 0.541  0.577 -0.629]

(entrée originale : sgd.py:docstring of mlstatpy.optim.sgd.SGDOptimizer, line 34)