# Examples¶

Compute a 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

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)