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: 10.33 lr=0.1 max(coef): 1.5 l1=0/2.5 l2=0/2.7
    1/15: loss: 5.543 lr=0.0302 max(coef): 1.2 l1=0.046/2.1 l2=0.001/2
    2/15: loss: 2.077 lr=0.0218 max(coef): 0.98 l1=0.23/1.7 l2=0.028/1.4
    3/15: loss: 0.8827 lr=0.018 max(coef): 0.89 l1=0.016/1.8 l2=9.5e-05/1.3
    4/15: loss: 0.5161 lr=0.0156 max(coef): 0.86 l1=0.0022/1.8 l2=2.1e-06/1.2
    5/15: loss: 0.3542 lr=0.014 max(coef): 0.83 l1=0.03/1.8 l2=0.00057/1.2
    6/15: loss: 0.2752 lr=0.0128 max(coef): 0.82 l1=0.016/1.8 l2=0.00019/1.2
    7/15: loss: 0.2085 lr=0.0119 max(coef): 0.81 l1=0.021/1.8 l2=0.00017/1.2
    8/15: loss: 0.1621 lr=0.0111 max(coef): 0.8 l1=0.038/1.8 l2=0.00083/1.1
    9/15: loss: 0.1277 lr=0.0105 max(coef): 0.78 l1=0.0077/1.8 l2=2.8e-05/1.1
    10/15: loss: 0.1095 lr=0.00995 max(coef): 0.78 l1=0.018/1.8 l2=0.00012/1.1
    11/15: loss: 0.1003 lr=0.00949 max(coef): 0.77 l1=0.0046/1.8 l2=8.1e-06/1.1
    12/15: loss: 0.09159 lr=0.00909 max(coef): 0.77 l1=0.015/1.8 l2=0.00015/1.1
    13/15: loss: 0.08345 lr=0.00874 max(coef): 0.77 l1=0.036/1.8 l2=0.00055/1.1
    14/15: loss: 0.07681 lr=0.00842 max(coef): 0.76 l1=0.0039/1.8 l2=6e-06/1.1
    15/15: loss: 0.0663 lr=0.00814 max(coef): 0.76 l1=0.0037/1.8 l2=5.1e-06/1.1
    optimized coefficients: [ 0.425  0.603 -0.758]

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