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: 44.52 lr=0.1 max(coef): 3.3 l1=0/5.7 l2=0/14
    1/15: loss: 32.4 lr=0.0302 max(coef): 3 l1=0.084/5.1 l2=0.0036/12
    2/15: loss: 21.37 lr=0.0218 max(coef): 2.8 l1=0.14/4.4 l2=0.0093/10
    3/15: loss: 16.87 lr=0.018 max(coef): 2.6 l1=0.17/4.4 l2=0.012/8.8
    4/15: loss: 14.68 lr=0.0156 max(coef): 2.5 l1=0.44/4.3 l2=0.085/8.3
    5/15: loss: 12.61 lr=0.014 max(coef): 2.4 l1=0.22/4.3 l2=0.04/7.8
    6/15: loss: 11.29 lr=0.0128 max(coef): 2.3 l1=0.12/4.3 l2=0.0062/7.4
    7/15: loss: 10.44 lr=0.0119 max(coef): 2.2 l1=0.041/4.2 l2=0.00065/7.1
    8/15: loss: 9.817 lr=0.0111 max(coef): 2.2 l1=0.11/4.2 l2=0.0088/6.9
    9/15: loss: 9.236 lr=0.0105 max(coef): 2.2 l1=0.21/4.2 l2=0.022/6.7
    10/15: loss: 8.8 lr=0.00995 max(coef): 2.1 l1=0.2/4.1 l2=0.021/6.6
    11/15: loss: 8.464 lr=0.00949 max(coef): 2.1 l1=0.24/4.1 l2=0.026/6.5
    12/15: loss: 8.203 lr=0.00909 max(coef): 2.1 l1=0.1/4.1 l2=0.0044/6.4
    13/15: loss: 7.948 lr=0.00874 max(coef): 2 l1=0.22/4.1 l2=0.022/6.3
    14/15: loss: 7.672 lr=0.00842 max(coef): 2 l1=0.045/4.1 l2=0.00078/6.2
    15/15: loss: 7.381 lr=0.00814 max(coef): 2 l1=0.19/4.1 l2=0.017/6.1
    optimized coefficients: [ 0.985 -1.951 -1.147]

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