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: 27.2 lr=0.1 max(coef): 1.7 l1=0/3.3 l2=0/4.3
    1/15: loss: 24 lr=0.0302 max(coef): 1.6 l1=1/3.1 l2=0.49/3.6
    2/15: loss: 15.14 lr=0.0218 max(coef): 1.2 l1=0.049/2.3 l2=0.001/2
    3/15: loss: 11.05 lr=0.018 max(coef): 0.9 l1=0.0009/1.9 l2=2.9e-07/1.3
    4/15: loss: 8.14 lr=0.0156 max(coef): 0.69 l1=0.074/1.6 l2=0.0037/0.92
    5/15: loss: 6.211 lr=0.014 max(coef): 0.59 l1=0.42/1.4 l2=0.084/0.7
    6/15: loss: 5.078 lr=0.0128 max(coef): 0.56 l1=0.065/1.2 l2=0.0017/0.54
    7/15: loss: 4.407 lr=0.0119 max(coef): 0.55 l1=0.024/1.1 l2=0.00025/0.46
    8/15: loss: 3.99 lr=0.0111 max(coef): 0.54 l1=0.11/1 l2=0.0059/0.41
    9/15: loss: 3.653 lr=0.0105 max(coef): 0.53 l1=0.28/0.95 l2=0.036/0.37
    10/15: loss: 3.296 lr=0.00995 max(coef): 0.52 l1=0.041/0.87 l2=0.00057/0.33
    11/15: loss: 3.029 lr=0.00949 max(coef): 0.52 l1=0.019/0.83 l2=0.00018/0.31
    12/15: loss: 2.849 lr=0.00909 max(coef): 0.52 l1=0.16/0.8 l2=0.012/0.31
    13/15: loss: 2.716 lr=0.00874 max(coef): 0.53 l1=0.06/0.79 l2=0.0024/0.31
    14/15: loss: 2.536 lr=0.00842 max(coef): 0.55 l1=0.14/0.77 l2=0.0092/0.33
    15/15: loss: 2.368 lr=0.00814 max(coef): 0.57 l1=0.021/0.77 l2=0.00015/0.35
    optimized coefficients: [-0.071 -0.127 -0.571]

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