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: 27.38 lr=0.1 max(coef): 2 l1=0/3 l2=0/4.9
    1/15: loss: 19.71 lr=0.0302 max(coef): 1.9 l1=1.3/2.9 l2=0.66/4.3
    2/15: loss: 6.997 lr=0.0218 max(coef): 1.5 l1=0.37/2.7 l2=0.054/3
    3/15: loss: 2.568 lr=0.018 max(coef): 1.1 l1=0.85/2.2 l2=0.27/2
    4/15: loss: 1.97 lr=0.0156 max(coef): 0.88 l1=0.15/1.6 l2=0.0083/1.2
    5/15: loss: 2.375 lr=0.014 max(coef): 0.79 l1=0.024/1.5 l2=0.00026/0.97
    6/15: loss: 2.163 lr=0.0128 max(coef): 0.77 l1=0.03/1.5 l2=0.00042/0.93
    7/15: loss: 1.489 lr=0.0119 max(coef): 0.8 l1=0.13/1.5 l2=0.0061/0.99
    8/15: loss: 0.9851 lr=0.0111 max(coef): 0.83 l1=0.016/1.6 l2=0.00011/1.1
    9/15: loss: 0.7076 lr=0.0105 max(coef): 0.85 l1=0.069/1.7 l2=0.0017/1.1
    10/15: loss: 0.5459 lr=0.00995 max(coef): 0.86 l1=0.012/1.7 l2=6.8e-05/1.2
    11/15: loss: 0.4578 lr=0.00949 max(coef): 0.87 l1=0.0064/1.8 l2=1.6e-05/1.2
    12/15: loss: 0.4037 lr=0.00909 max(coef): 0.88 l1=0.026/1.8 l2=0.00025/1.2
    13/15: loss: 0.3503 lr=0.00874 max(coef): 0.88 l1=0.016/1.8 l2=9.7e-05/1.2
    14/15: loss: 0.3079 lr=0.00842 max(coef): 0.88 l1=0.062/1.8 l2=0.0018/1.2
    15/15: loss: 0.268 lr=0.00814 max(coef): 0.88 l1=0.16/1.8 l2=0.01/1.2
    optimized coefficients: [ 0.538  0.398 -0.88 ]

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