# 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: 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)