# 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: 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)