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: 30.52 lr=0.1 max(coef): 1.2 l1=0/2 l2=0/2
    1/15: loss: 13.35 lr=0.0302 max(coef): 1.1 l1=0.021/1.9 l2=0.00021/1.7
    2/15: loss: 4.449 lr=0.0218 max(coef): 1.2 l1=0.0018/1.7 l2=1.8e-06/1.7
    3/15: loss: 2.828 lr=0.018 max(coef): 1.2 l1=0.16/2 l2=0.013/1.8
    4/15: loss: 2.103 lr=0.0156 max(coef): 1.1 l1=0.017/2.1 l2=0.00015/1.7
    5/15: loss: 1.62 lr=0.014 max(coef): 1 l1=0.11/2 l2=0.0068/1.6
    6/15: loss: 1.278 lr=0.0128 max(coef): 0.98 l1=0.055/2 l2=0.0015/1.5
    7/15: loss: 1.045 lr=0.0119 max(coef): 0.94 l1=0.071/2 l2=0.0023/1.4
    8/15: loss: 0.9118 lr=0.0111 max(coef): 0.92 l1=0.024/1.9 l2=0.00021/1.4
    9/15: loss: 0.8102 lr=0.0105 max(coef): 0.9 l1=0.061/1.9 l2=0.0017/1.3
    10/15: loss: 0.7054 lr=0.00995 max(coef): 0.87 l1=0.042/1.9 l2=0.00089/1.3
    11/15: loss: 0.621 lr=0.00949 max(coef): 0.85 l1=0.068/1.9 l2=0.0026/1.3
    12/15: loss: 0.5378 lr=0.00909 max(coef): 0.83 l1=0.032/1.9 l2=0.00051/1.3
    13/15: loss: 0.4942 lr=0.00874 max(coef): 0.82 l1=0.042/1.9 l2=0.00085/1.2
    14/15: loss: 0.4532 lr=0.00842 max(coef): 0.81 l1=0.074/1.9 l2=0.0029/1.2
    15/15: loss: 0.4202 lr=0.00814 max(coef): 0.8 l1=0.0091/1.9 l2=4.6e-05/1.2
    optimized coefficients: [ 0.587  0.798 -0.491]

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