# Infer operator computation cost#

This notebooks explores a way to predict the cost of operator Transpose based on some features.

```from jyquickhelper import add_notebook_menu
```
```%matplotlib inline
```
```%load_ext mlprodict
```

## ONNX graph and measures#

```import numpy
from skl2onnx.common.data_types import FloatTensorType
from skl2onnx.algebra.onnx_ops import OnnxTranspose

def create_onnx_graph(perm=(0, 1, 2, 3), target_opset=14):
tr = OnnxTranspose('X', perm=perm, output_names=['Y'], op_version=target_opset)
return tr.to_onnx({'X': FloatTensorType([None] * len(perm))})

onx = create_onnx_graph()

%onnxview onx
```
```from mlprodict.onnxrt import OnnxInference

onx = create_onnx_graph(perm=(1, 0, 3, 2))
oinf = OnnxInference(onx)
inputs = {'X': numpy.full((5, 6, 7, 8), 1, dtype=numpy.float32)}
res = oinf.run(inputs)['Y']
res.shape
```
```(6, 5, 8, 7)
```
```from onnxruntime import InferenceSession
sess = InferenceSession(onx.SerializeToString())
res = sess.run(None, inputs)[0]
res.shape
```
```(6, 5, 8, 7)
```
```from cpyquickhelper.numbers.speed_measure import measure_time

def measure_time_onnx(sess, X, number=50, repeat=30):
inputs = {'X': X}
return measure_time(lambda: sess.run(None, inputs), context=dict(sess=sess, inputs=inputs),
div_by_number=True, number=number, repeat=repeat)

X = numpy.random.random((3, 224, 224, 4)).astype(numpy.float32)
measure_time_onnx(sess, X)
```
```{'average': 0.0024677738666666646,
'deviation': 0.00022911153911864325,
'min_exec': 0.0022292380000000023,
'max_exec': 0.003265080000000005,
'repeat': 30,
'number': 50,
'context_size': 232}
```

## Simulation to build a database#

### Many dimensions, many permutations#

```from itertools import permutations
from tqdm import tqdm
from pandas import DataFrame

def process_shape(shape, rnd=False, number=50, repeat=30, bar=True):
X = numpy.random.random(shape).astype(numpy.float32)
obs = []
perms = list(permutations(list(range(len(X.shape)))))
baseline = None
itergen = perms if (rnd or not bar) else tqdm(perms)
for perm in itergen:
if baseline is not None and rnd:
if random.randint(0, 4) != 0:
continue
onx = create_onnx_graph(perm=perm)
sess = InferenceSession(onx.SerializeToString())
res = measure_time_onnx(sess, X, number=number, repeat=repeat)
res['perm'] = perm
res['shape'] = shape
if baseline is None:
baseline = res
res["ratio"] = res["average"] / baseline["average"]
res['dim'] = len(shape)
obs.append(res)
return DataFrame(obs).sort_values('average')

dfs = []
df = process_shape((12, 13, 15, 18))
dfs.append(df)
df
```
```100%|██████████| 24/24 [00:04<00:00,  5.73it/s]
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
3 0.000044 0.000006 0.000039 0.000057 30 50 232 (0, 2, 3, 1) (12, 13, 15, 18) 0.750316 4
1 0.000048 0.000003 0.000045 0.000058 30 50 232 (0, 1, 3, 2) (12, 13, 15, 18) 0.820821 4
18 0.000049 0.000003 0.000045 0.000062 30 50 232 (3, 0, 1, 2) (12, 13, 15, 18) 0.823070 4
9 0.000049 0.000001 0.000048 0.000053 30 50 232 (1, 2, 3, 0) (12, 13, 15, 18) 0.830604 4
12 0.000051 0.000004 0.000039 0.000062 30 50 232 (2, 0, 1, 3) (12, 13, 15, 18) 0.861994 4
4 0.000052 0.000005 0.000047 0.000073 30 50 232 (0, 3, 1, 2) (12, 13, 15, 18) 0.889753 4
8 0.000054 0.000006 0.000044 0.000067 30 50 232 (1, 2, 0, 3) (12, 13, 15, 18) 0.909477 4
2 0.000054 0.000007 0.000049 0.000081 30 50 232 (0, 2, 1, 3) (12, 13, 15, 18) 0.922354 4
14 0.000057 0.000006 0.000046 0.000064 30 50 232 (2, 1, 0, 3) (12, 13, 15, 18) 0.972198 4
0 0.000059 0.000019 0.000034 0.000093 30 50 232 (0, 1, 2, 3) (12, 13, 15, 18) 1.000000 4
6 0.000092 0.000019 0.000053 0.000139 30 50 232 (1, 0, 2, 3) (12, 13, 15, 18) 1.557903 4
11 0.000136 0.000020 0.000119 0.000186 30 50 232 (1, 3, 2, 0) (12, 13, 15, 18) 2.301556 4
13 0.000138 0.000023 0.000121 0.000181 30 50 232 (2, 0, 3, 1) (12, 13, 15, 18) 2.336826 4
10 0.000138 0.000018 0.000118 0.000176 30 50 232 (1, 3, 0, 2) (12, 13, 15, 18) 2.346118 4
16 0.000140 0.000015 0.000124 0.000193 30 50 232 (2, 3, 0, 1) (12, 13, 15, 18) 2.379168 4
15 0.000144 0.000019 0.000119 0.000196 30 50 232 (2, 1, 3, 0) (12, 13, 15, 18) 2.443392 4
17 0.000145 0.000022 0.000123 0.000199 30 50 232 (2, 3, 1, 0) (12, 13, 15, 18) 2.455098 4
23 0.000145 0.000017 0.000125 0.000196 30 50 232 (3, 2, 1, 0) (12, 13, 15, 18) 2.456431 4
20 0.000146 0.000015 0.000128 0.000184 30 50 232 (3, 1, 0, 2) (12, 13, 15, 18) 2.473250 4
22 0.000150 0.000017 0.000127 0.000170 30 50 232 (3, 2, 0, 1) (12, 13, 15, 18) 2.539817 4
19 0.000158 0.000021 0.000127 0.000192 30 50 232 (3, 0, 2, 1) (12, 13, 15, 18) 2.684876 4
21 0.000164 0.000045 0.000124 0.000231 30 50 232 (3, 1, 2, 0) (12, 13, 15, 18) 2.778193 4
7 0.000214 0.000060 0.000136 0.000295 30 50 232 (1, 0, 3, 2) (12, 13, 15, 18) 3.627240 4
5 0.000215 0.000071 0.000143 0.000340 30 50 232 (0, 3, 2, 1) (12, 13, 15, 18) 3.640132 4
```df = process_shape((43, 44, 45))
dfs.append(df)
df
```
```100%|██████████| 6/6 [00:01<00:00,  4.70it/s]
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
3 0.000073 0.000009 0.000062 0.000094 30 50 232 (1, 2, 0) (43, 44, 45) 0.985513 3
0 0.000074 0.000009 0.000065 0.000109 30 50 232 (0, 1, 2) (43, 44, 45) 1.000000 3
1 0.000077 0.000008 0.000069 0.000101 30 50 232 (0, 2, 1) (43, 44, 45) 1.032759 3
4 0.000097 0.000004 0.000083 0.000110 30 50 232 (2, 0, 1) (43, 44, 45) 1.300915 3
2 0.000113 0.000029 0.000061 0.000141 30 50 232 (1, 0, 2) (43, 44, 45) 1.515711 3
5 0.000375 0.000121 0.000292 0.000750 30 50 232 (2, 1, 0) (43, 44, 45) 5.054301 3
```df = process_shape((3, 244, 244))
dfs.append(df)
df
```
```100%|██████████| 6/6 [00:01<00:00,  3.05it/s]
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
2 0.000100 0.000009 0.000090 0.000125 30 50 232 (1, 0, 2) (3, 244, 244) 0.955203 3
0 0.000105 0.000016 0.000078 0.000138 30 50 232 (0, 1, 2) (3, 244, 244) 1.000000 3
1 0.000123 0.000013 0.000108 0.000161 30 50 232 (0, 2, 1) (3, 244, 244) 1.178827 3
4 0.000124 0.000017 0.000108 0.000171 30 50 232 (2, 0, 1) (3, 244, 244) 1.185666 3
3 0.000151 0.000016 0.000136 0.000197 30 50 232 (1, 2, 0) (3, 244, 244) 1.438446 3
5 0.000672 0.000083 0.000626 0.001030 30 50 232 (2, 1, 0) (3, 244, 244) 6.418195 3
```df = process_shape((3, 244, 244, 1))
dfs.append(df)
df
```
```100%|██████████| 24/24 [00:19<00:00,  1.26it/s]
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
4 0.000092 0.000008 0.000078 0.000107 30 50 232 (0, 3, 1, 2) (3, 244, 244, 1) 0.859903 4
0 0.000107 0.000018 0.000084 0.000157 30 50 232 (0, 1, 2, 3) (3, 244, 244, 1) 1.000000 4
6 0.000124 0.000068 0.000088 0.000323 30 50 232 (1, 0, 2, 3) (3, 244, 244, 1) 1.162456 4
12 0.000126 0.000017 0.000107 0.000185 30 50 232 (2, 0, 1, 3) (3, 244, 244, 1) 1.180996 4
3 0.000130 0.000009 0.000120 0.000163 30 50 232 (0, 2, 3, 1) (3, 244, 244, 1) 1.210077 4
18 0.000137 0.000047 0.000090 0.000250 30 50 232 (3, 0, 1, 2) (3, 244, 244, 1) 1.276642 4
1 0.000147 0.000017 0.000106 0.000175 30 50 232 (0, 1, 3, 2) (3, 244, 244, 1) 1.369978 4
8 0.000185 0.000017 0.000164 0.000246 30 50 232 (1, 2, 0, 3) (3, 244, 244, 1) 1.725391 4
9 0.000189 0.000044 0.000142 0.000265 30 50 232 (1, 2, 3, 0) (3, 244, 244, 1) 1.766905 4
2 0.000201 0.000054 0.000121 0.000289 30 50 232 (0, 2, 1, 3) (3, 244, 244, 1) 1.878802 4
7 0.000522 0.000061 0.000457 0.000733 30 50 232 (1, 0, 3, 2) (3, 244, 244, 1) 4.874009 4
10 0.000533 0.000157 0.000456 0.001128 30 50 232 (1, 3, 0, 2) (3, 244, 244, 1) 4.973916 4
13 0.000640 0.000189 0.000477 0.001289 30 50 232 (2, 0, 3, 1) (3, 244, 244, 1) 5.980796 4
16 0.000660 0.000106 0.000503 0.000860 30 50 232 (2, 3, 0, 1) (3, 244, 244, 1) 6.167703 4
5 0.000692 0.000136 0.000529 0.001021 30 50 232 (0, 3, 2, 1) (3, 244, 244, 1) 6.460759 4
19 0.000749 0.000206 0.000508 0.001324 30 50 232 (3, 0, 2, 1) (3, 244, 244, 1) 6.996362 4
14 0.000754 0.000105 0.000633 0.000994 30 50 232 (2, 1, 0, 3) (3, 244, 244, 1) 7.041007 4
11 0.000791 0.000264 0.000561 0.001386 30 50 232 (1, 3, 2, 0) (3, 244, 244, 1) 7.389431 4
15 0.000818 0.000278 0.000625 0.001522 30 50 232 (2, 1, 3, 0) (3, 244, 244, 1) 7.634646 4
17 0.000893 0.000212 0.000646 0.001477 30 50 232 (2, 3, 1, 0) (3, 244, 244, 1) 8.339926 4
21 0.000944 0.000293 0.000581 0.001626 30 50 232 (3, 1, 2, 0) (3, 244, 244, 1) 8.814785 4
20 0.000976 0.000347 0.000584 0.001742 30 50 232 (3, 1, 0, 2) (3, 244, 244, 1) 9.112243 4
22 0.001011 0.000337 0.000544 0.001810 30 50 232 (3, 2, 0, 1) (3, 244, 244, 1) 9.437403 4
23 0.001128 0.000322 0.000629 0.001737 30 50 232 (3, 2, 1, 0) (3, 244, 244, 1) 10.530182 4
```df = process_shape((1, 244, 244, 3))
dfs.append(df)
df
```
```100%|██████████| 24/24 [00:22<00:00,  1.07it/s]
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
8 0.000092 0.000014 0.000078 0.000132 30 50 232 (1, 2, 0, 3) (1, 244, 244, 3) 0.753009 4
6 0.000098 0.000013 0.000083 0.000142 30 50 232 (1, 0, 2, 3) (1, 244, 244, 3) 0.802808 4
9 0.000107 0.000018 0.000075 0.000137 30 50 232 (1, 2, 3, 0) (1, 244, 244, 3) 0.873932 4
3 0.000115 0.000015 0.000092 0.000147 30 50 232 (0, 2, 3, 1) (1, 244, 244, 3) 0.940606 4
0 0.000122 0.000028 0.000094 0.000201 30 50 232 (0, 1, 2, 3) (1, 244, 244, 3) 1.000000 4
1 0.000194 0.000036 0.000160 0.000311 30 50 232 (0, 1, 3, 2) (1, 244, 244, 3) 1.585479 4
4 0.000195 0.000019 0.000163 0.000258 30 50 232 (0, 3, 1, 2) (1, 244, 244, 3) 1.598770 4
18 0.000235 0.000058 0.000172 0.000345 30 50 232 (3, 0, 1, 2) (1, 244, 244, 3) 1.923654 4
2 0.000408 0.000156 0.000229 0.000718 30 50 232 (0, 2, 1, 3) (1, 244, 244, 3) 3.345406 4
12 0.000513 0.000215 0.000300 0.001430 30 50 232 (2, 0, 1, 3) (1, 244, 244, 3) 4.205477 4
10 0.000558 0.000131 0.000458 0.001023 30 50 232 (1, 3, 0, 2) (1, 244, 244, 3) 4.572658 4
7 0.000604 0.000188 0.000471 0.001065 30 50 232 (1, 0, 3, 2) (1, 244, 244, 3) 4.947937 4
14 0.000620 0.000142 0.000410 0.001121 30 50 232 (2, 1, 0, 3) (1, 244, 244, 3) 5.078387 4
23 0.000679 0.000097 0.000590 0.000928 30 50 232 (3, 2, 1, 0) (1, 244, 244, 3) 5.561888 4
22 0.000710 0.000161 0.000620 0.001390 30 50 232 (3, 2, 0, 1) (1, 244, 244, 3) 5.818089 4
17 0.000737 0.000240 0.000493 0.001174 30 50 232 (2, 3, 1, 0) (1, 244, 244, 3) 6.040189 4
11 0.000824 0.000288 0.000515 0.001879 30 50 232 (1, 3, 2, 0) (1, 244, 244, 3) 6.752663 4
21 0.000913 0.000216 0.000613 0.001410 30 50 232 (3, 1, 2, 0) (1, 244, 244, 3) 7.476378 4
20 0.000918 0.000328 0.000572 0.002079 30 50 232 (3, 1, 0, 2) (1, 244, 244, 3) 7.521481 4
16 0.001057 0.000609 0.000502 0.002702 30 50 232 (2, 3, 0, 1) (1, 244, 244, 3) 8.657076 4
5 0.001061 0.000612 0.000539 0.003790 30 50 232 (0, 3, 2, 1) (1, 244, 244, 3) 8.693870 4
19 0.001212 0.000417 0.000719 0.002561 30 50 232 (3, 0, 2, 1) (1, 244, 244, 3) 9.929308 4
15 0.001311 0.000505 0.000856 0.003377 30 50 232 (2, 1, 3, 0) (1, 244, 244, 3) 10.739398 4
13 0.001433 0.000505 0.000721 0.002335 30 50 232 (2, 0, 3, 1) (1, 244, 244, 3) 11.740772 4
```df = process_shape((3, 244, 244, 3), number=15, repeat=15)
dfs.append(df)
df
```
```100%|██████████| 24/24 [00:14<00:00,  1.62it/s]
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
0 0.001088 0.000085 0.000986 0.001291 15 15 232 (0, 1, 2, 3) (3, 244, 244, 3) 1.000000 4
4 0.001227 0.000088 0.001152 0.001474 15 15 232 (0, 3, 1, 2) (3, 244, 244, 3) 1.128126 4
18 0.001277 0.000118 0.001079 0.001490 15 15 232 (3, 0, 1, 2) (3, 244, 244, 3) 1.173721 4
6 0.001311 0.000320 0.001007 0.001925 15 15 232 (1, 0, 2, 3) (3, 244, 244, 3) 1.205182 4
1 0.001415 0.000307 0.001200 0.002498 15 15 232 (0, 1, 3, 2) (3, 244, 244, 3) 1.300901 4
3 0.001426 0.000221 0.001191 0.001863 15 15 232 (0, 2, 3, 1) (3, 244, 244, 3) 1.311361 4
9 0.001510 0.000432 0.001132 0.002417 15 15 232 (1, 2, 3, 0) (3, 244, 244, 3) 1.388068 4
8 0.001552 0.000030 0.001500 0.001602 15 15 232 (1, 2, 0, 3) (3, 244, 244, 3) 1.427105 4
12 0.001724 0.000193 0.001470 0.002142 15 15 232 (2, 0, 1, 3) (3, 244, 244, 3) 1.585155 4
2 0.001790 0.000191 0.001566 0.002238 15 15 232 (0, 2, 1, 3) (3, 244, 244, 3) 1.645717 4
7 0.002528 0.000154 0.002327 0.002983 15 15 232 (1, 0, 3, 2) (3, 244, 244, 3) 2.324384 4
19 0.002571 0.000186 0.002383 0.002922 15 15 232 (3, 0, 2, 1) (3, 244, 244, 3) 2.363443 4
21 0.002591 0.000253 0.002431 0.003403 15 15 232 (3, 1, 2, 0) (3, 244, 244, 3) 2.381860 4
22 0.002698 0.000412 0.002346 0.003689 15 15 232 (3, 2, 0, 1) (3, 244, 244, 3) 2.480308 4
20 0.002806 0.000783 0.002147 0.004296 15 15 232 (3, 1, 0, 2) (3, 244, 244, 3) 2.579517 4
16 0.003212 0.000304 0.002773 0.003851 15 15 232 (2, 3, 0, 1) (3, 244, 244, 3) 2.953032 4
14 0.003228 0.000796 0.002071 0.004791 15 15 232 (2, 1, 0, 3) (3, 244, 244, 3) 2.967523 4
11 0.003257 0.000287 0.002912 0.003739 15 15 232 (1, 3, 2, 0) (3, 244, 244, 3) 2.994043 4
17 0.003574 0.000479 0.003028 0.005042 15 15 232 (2, 3, 1, 0) (3, 244, 244, 3) 3.285842 4
10 0.003942 0.001860 0.002446 0.008241 15 15 232 (1, 3, 0, 2) (3, 244, 244, 3) 3.624145 4
15 0.004249 0.001217 0.003175 0.008041 15 15 232 (2, 1, 3, 0) (3, 244, 244, 3) 3.906361 4
5 0.004685 0.001343 0.002827 0.006868 15 15 232 (0, 3, 2, 1) (3, 244, 244, 3) 4.307072 4
13 0.005539 0.002180 0.002991 0.009602 15 15 232 (2, 0, 3, 1) (3, 244, 244, 3) 5.092422 4
23 0.005575 0.001930 0.002876 0.008157 15 15 232 (3, 2, 1, 0) (3, 244, 244, 3) 5.125597 4
```df = process_shape((3, 244, 244, 6), number=15, repeat=15)
dfs.append(df)
df
```
```100%|██████████| 24/24 [00:34<00:00,  1.43s/it]
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
1 0.002249 0.000144 0.002067 0.002627 15 15 232 (0, 1, 3, 2) (3, 244, 244, 6) 0.606961 4
3 0.002711 0.000171 0.002458 0.002995 15 15 232 (0, 2, 3, 1) (3, 244, 244, 6) 0.731795 4
12 0.002773 0.000683 0.002260 0.004103 15 15 232 (2, 0, 1, 3) (3, 244, 244, 6) 0.748578 4
4 0.002953 0.000677 0.002187 0.004132 15 15 232 (0, 3, 1, 2) (3, 244, 244, 6) 0.797062 4
2 0.003232 0.000963 0.002303 0.005088 15 15 232 (0, 2, 1, 3) (3, 244, 244, 6) 0.872427 4
6 0.003363 0.000372 0.002883 0.004025 15 15 232 (1, 0, 2, 3) (3, 244, 244, 6) 0.907834 4
8 0.003397 0.000237 0.002886 0.003846 15 15 232 (1, 2, 0, 3) (3, 244, 244, 6) 0.917011 4
9 0.003653 0.000874 0.002567 0.005244 15 15 232 (1, 2, 3, 0) (3, 244, 244, 6) 0.986071 4
14 0.003697 0.000186 0.003495 0.004150 15 15 232 (2, 1, 0, 3) (3, 244, 244, 6) 0.997901 4
0 0.003705 0.000797 0.002111 0.005164 15 15 232 (0, 1, 2, 3) (3, 244, 244, 6) 1.000000 4
18 0.003780 0.000882 0.002701 0.005402 15 15 232 (3, 0, 1, 2) (3, 244, 244, 6) 1.020432 4
10 0.004938 0.000367 0.004532 0.005844 15 15 232 (1, 3, 0, 2) (3, 244, 244, 6) 1.333061 4
7 0.005918 0.001085 0.004598 0.008312 15 15 232 (1, 0, 3, 2) (3, 244, 244, 6) 1.597357 4
13 0.006106 0.000556 0.005619 0.007305 15 15 232 (2, 0, 3, 1) (3, 244, 244, 6) 1.648325 4
11 0.006722 0.001807 0.005067 0.011245 15 15 232 (1, 3, 2, 0) (3, 244, 244, 6) 1.814552 4
20 0.007071 0.000982 0.005454 0.008559 15 15 232 (3, 1, 0, 2) (3, 244, 244, 6) 1.908667 4
21 0.007441 0.001732 0.006199 0.012169 15 15 232 (3, 1, 2, 0) (3, 244, 244, 6) 2.008635 4
15 0.007815 0.001757 0.005932 0.010779 15 15 232 (2, 1, 3, 0) (3, 244, 244, 6) 2.109489 4
16 0.008546 0.001384 0.005878 0.010614 15 15 232 (2, 3, 0, 1) (3, 244, 244, 6) 2.306951 4
5 0.010339 0.002789 0.005878 0.018301 15 15 232 (0, 3, 2, 1) (3, 244, 244, 6) 2.790823 4
17 0.010677 0.001457 0.008504 0.014070 15 15 232 (2, 3, 1, 0) (3, 244, 244, 6) 2.882191 4
23 0.012421 0.003052 0.007818 0.018106 15 15 232 (3, 2, 1, 0) (3, 244, 244, 6) 3.352770 4
22 0.013432 0.004496 0.006536 0.021250 15 15 232 (3, 2, 0, 1) (3, 244, 244, 6) 3.625680 4
19 0.014579 0.004026 0.007144 0.020739 15 15 232 (3, 0, 2, 1) (3, 244, 244, 6) 3.935483 4

### Random cases#

```import random

if False:  # comment out for more training data
for i in tqdm(range(0, 30)):
dim = random.randint(3, 5)
total = 1e8
while total > 1e6 or total < 0:
if dim == 3:
shape = [random.randint(3, 64), random.randint(3, 224), random.randint(3, 64)]
elif dim == 4:
shape = (
[random.randint(3, 8)] +
[random.randint(16, 224) for d in range(2)] +
[random.randint(16, 64)])
elif dim == 5:
shape = (
[random.randint(3, 8)] +
[random.randint(16, 32) for d in range(3)] +
[random.randint(16, 64)])
else:
raise NotImplementedError()
ashape = numpy.array(shape, dtype=numpy.float64)
total = numpy.prod(ashape)

if total > 1000000:
number, repeat = 2, 2
elif total > 800000:
number, repeat = 3, 3
elif total > 500000:
number, repeat = 5, 5
elif total > 200000:
number, repeat = 7, 7
else:
number, repeat = 10, 10

df = process_shape(tuple(shape), number=number, repeat=repeat, bar=False)
dfs.append(df)

for i in range(len(shape)):
shape2 = shape.copy()
shape2[i] = 1
df = process_shape(tuple(shape), number=number, repeat=repeat, bar=False)
dfs.append(df)

len(dfs)
```
```7
```
```import pandas

data = pandas.concat(dfs, axis=0).reset_index(drop=True)
data.tail()
```
average deviation min_exec max_exec repeat number context_size perm shape ratio dim
127 0.010339 0.002789 0.005878 0.018301 15 15 232 (0, 3, 2, 1) (3, 244, 244, 6) 2.790823 4
128 0.010677 0.001457 0.008504 0.014070 15 15 232 (2, 3, 1, 0) (3, 244, 244, 6) 2.882191 4
129 0.012421 0.003052 0.007818 0.018106 15 15 232 (3, 2, 1, 0) (3, 244, 244, 6) 3.352770 4
130 0.013432 0.004496 0.006536 0.021250 15 15 232 (3, 2, 0, 1) (3, 244, 244, 6) 3.625680 4
131 0.014579 0.004026 0.007144 0.020739 15 15 232 (3, 0, 2, 1) (3, 244, 244, 6) 3.935483 4
```data.shape
```
```(132, 11)
```
```data[['dim', 'shape', 'ratio']].groupby(['dim', 'shape']).agg({'ratio': [min, max, numpy.mean, numpy.median]})
```
ratio
min max mean median
dim shape
3 (3, 244, 244) 0.955203 6.418195 2.029389 1.182247
(43, 44, 45) 0.985513 5.054301 1.814867 1.166837
4 (1, 244, 244, 3) 0.753009 11.740772 5.023301 5.013162
(3, 244, 244, 1) 0.859903 10.530182 4.882680 5.477356
(3, 244, 244, 3) 1.000000 5.125597 2.481287 2.372651
(3, 244, 244, 6) 0.606961 3.935483 1.704169 1.465209
(12, 13, 15, 18) 0.750316 3.640132 1.866691 2.319191

## features#

### Computing the features#

```def _edit_distance(mot1, mot2):
dist = {(-1, -1): 0}
pred = {(-1, -1): None}
if len(mot1) == 0:
for j, d in enumerate(mot2):
dist[-1, j] = dist[-1, j - 1] + 1
pred[-1, j] = (-1, j - 1)
dist[j, -1] = dist[j - 1, -1] + 1
pred[j, -1] = (j - 1, -1)
for i, c in enumerate(mot1):
dist[i, -1] = dist[i - 1, -1] + 1
pred[i, -1] = (i - 1, -1)
dist[-1, i] = dist[-1, i - 1] + 1
pred[-1, i] = (-1, i - 1)
for j, d in enumerate(mot2):
opt = []
if (i - 1, j) in dist:
x = dist[i - 1, j] + 1
opt.append((x, (i - 1, j)))
if (i, j - 1) in dist:
x = dist[i, j - 1] + 1
opt.append((x, (i, j - 1)))
if (i - 1, j - 1) in dist:
x = dist[i - 1, j - 1] + (1 if c != d else 0)
opt.append((x, (i - 1, j - 1)))
mi = min(opt)
dist[i, j] = mi[0]
pred[i, j] = mi[1]

return dist[len(mot1) - 1, len(mot2) - 1]

_edit_distance("abdc", "cbda")
```
```2
```
```_edit_distance((0, 1, 2, 3), (0, 2, 1, 3))
```
```2
```
```from math import log

def _is_rotation(perm):
t = tuple(perm)
c = list(range(len(perm)))
for i in range(len(c)):
for k in range(len(c)):
c[k] = (k + i) % len(c)
if t == tuple(c):
return True
return False

def _relu(x, origin=0):
return origin if x < origin else x

def compute_features(shape, perm):
total = numpy.prod(numpy.array(shape, dtype=numpy.int64))

begin = 1
dbegin = 0
for i, p in enumerate(perm):
if p != i:
break
dbegin += 1
begin *= shape[i]

end = 1
dend = 0
for i in range(len(perm)-1, -1, -1):
if perm[i] != i:
break
dend += 1
end *= shape[i]

dis_cont = 0
for i in range(1, len(shape)):
if perm[i] != perm[i-1] + 1:
dis_cont += 1

middle = max(1, int(total / (end * begin)))
feat = dict(size=total, begin=begin, end=end, middle=middle,
dim=len(shape), discont=dis_cont)

for c in [16, 32]:
feat["end%d" % c] = _relu(end, c)

keys = list(feat)
for k in keys:
if k in {'dim', 'cpu', 'size'}:
continue
feat['r%s' % k] = float(feat[k] / total)

for c in [2, 4, 8, 16, 32, 64]:
feat["iend%d" % c] = float(end >= c)
feat["ibegin%d" % c] = float(begin >= c)

# feat['CST'] = 1
feat['CST_'] = -1
feat['dbegin'] = - dbegin
feat['dend'] = - dend

keys = list(feat)
for k in keys:
if k.startswith('end') or k.startswith('begin'):
feat[k] = - feat[k]
elif k.startswith('rend') or k.startswith('rbegin'):
feat[k] = - feat[k]
elif k.startswith('iend') or k.startswith('ibegin'):
feat[k] = - feat[k]
elif k == "rdiscont":
feat[k] = - feat[k]

idp = list(range(len(perm)))
feat["rot"] = -1 if _is_rotation(perm) else 0
feat["rev"] = 1 if perm == tuple(idp[::-1]) else 0
feat["edit"] = _edit_distance(idp, perm)
feat["redit"] = feat["edit"] / len(idp)
return feat

compute_features((3, 5, 7), (0, 1, 2))
```
```{'size': 105,
'begin': -105,
'end': -105,
'middle': 1,
'dim': 3,
'discont': 0,
'end16': -105,
'end32': -105,
'rbegin': -1.0,
'rend': -1.0,
'rmiddle': 0.009523809523809525,
'rdiscont': -0.0,
'rend16': -1.0,
'rend32': -1.0,
'iend2': -1.0,
'ibegin2': -1.0,
'iend4': -1.0,
'ibegin4': -1.0,
'iend8': -1.0,
'ibegin8': -1.0,
'iend16': -1.0,
'ibegin16': -1.0,
'iend32': -1.0,
'ibegin32': -1.0,
'iend64': -1.0,
'ibegin64': -1.0,
'CST_': -1,
'dbegin': -3,
'dend': -3,
'rot': -1,
'rev': 0,
'edit': 0,
'redit': 0.0}
```
```compute_features((3, 5, 7), (2, 1, 0))
```
```{'size': 105,
'begin': -1,
'end': -1,
'middle': 105,
'dim': 3,
'discont': 2,
'end16': -16,
'end32': -32,
'rbegin': -0.009523809523809525,
'rend': -0.009523809523809525,
'rmiddle': 1.0,
'rdiscont': -0.01904761904761905,
'rend16': -0.1523809523809524,
'rend32': -0.3047619047619048,
'iend2': -0.0,
'ibegin2': -0.0,
'iend4': -0.0,
'ibegin4': -0.0,
'iend8': -0.0,
'ibegin8': -0.0,
'iend16': -0.0,
'ibegin16': -0.0,
'iend32': -0.0,
'ibegin32': -0.0,
'iend64': -0.0,
'ibegin64': -0.0,
'CST_': -1,
'dbegin': 0,
'dend': 0,
'rot': 0,
'rev': 1,
'edit': 2,
'redit': 0.6666666666666666}
```
```compute_features((3, 5, 7), (1, 2, 0))
```
```{'size': 105,
'begin': -1,
'end': -1,
'middle': 105,
'dim': 3,
'discont': 1,
'end16': -16,
'end32': -32,
'rbegin': -0.009523809523809525,
'rend': -0.009523809523809525,
'rmiddle': 1.0,
'rdiscont': -0.009523809523809525,
'rend16': -0.1523809523809524,
'rend32': -0.3047619047619048,
'iend2': -0.0,
'ibegin2': -0.0,
'iend4': -0.0,
'ibegin4': -0.0,
'iend8': -0.0,
'ibegin8': -0.0,
'iend16': -0.0,
'ibegin16': -0.0,
'iend32': -0.0,
'ibegin32': -0.0,
'iend64': -0.0,
'ibegin64': -0.0,
'CST_': -1,
'dbegin': 0,
'dend': 0,
'rot': -1,
'rev': 0,
'edit': 2,
'redit': 0.6666666666666666}
```

### Computing the features for all simulations#

```def compute_features_dataframe(df):

def merge(row):
feat = compute_features(row['shape'], row['perm'])
feat['yt'] = row['average']
feat['yr'] = row['ratio']
return feat

rows = []
for i in tqdm(range(df.shape[0])):
rows.append(dict(shape=df.loc[i, "shape"], perm=df.loc[i, "perm"],
average=df.loc[i, "average"], ratio=df.loc[i, "ratio"]))
obs = []
for row in tqdm(rows):
obs.append(merge(row))
return DataFrame(obs)

fdata = compute_features_dataframe(data)
col_sort = list(sorted(fdata.columns))
fdata = fdata[col_sort]
fdata.tail()
```
```100%|██████████| 132/132 [00:00<00:00, 9459.22it/s]
100%|██████████| 132/132 [00:00<00:00, 3601.95it/s]
```
CST_ begin dbegin dend dim discont edit end end16 end32 ... redit rend rend16 rend32 rev rmiddle rot size yr yt
127 -1 -3 -1 0 4 3 2 -1 -16 -32 ... 0.50 -9.331422e-07 -0.000015 -0.00003 0 0.333333 0 1071648 2.790823 0.010339
128 -1 -1 0 0 4 2 4 -1 -16 -32 ... 1.00 -9.331422e-07 -0.000015 -0.00003 0 1.000000 0 1071648 2.882191 0.010677
129 -1 -1 0 0 4 3 4 -1 -16 -32 ... 1.00 -9.331422e-07 -0.000015 -0.00003 1 1.000000 0 1071648 3.352770 0.012421
130 -1 -1 0 0 4 2 4 -1 -16 -32 ... 1.00 -9.331422e-07 -0.000015 -0.00003 0 1.000000 0 1071648 3.625680 0.013432
131 -1 -1 0 0 4 3 3 -1 -16 -32 ... 0.75 -9.331422e-07 -0.000015 -0.00003 0 1.000000 0 1071648 3.935483 0.014579

5 rows × 35 columns

### correlations#

```fdata.corr()
```
CST_ begin dbegin dend dim discont edit end end16 end32 ... redit rend rend16 rend32 rev rmiddle rot size yr yt
CST_ NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
begin NaN 1.000000 0.596816 0.596414 0.014118 0.404952 0.405175 0.999998 0.999998 0.999998 ... 0.418022 0.681573 0.681573 0.681573 0.038216 0.256349 0.325594 -0.133581 0.127658 -0.008816
dbegin NaN 0.596816 1.000000 0.676899 0.077162 0.486887 0.669598 0.596384 0.596374 0.596363 ... 0.690333 0.831887 0.831895 0.831903 0.111636 0.605990 0.298090 0.016411 0.291318 0.139951
dend NaN 0.596414 0.676899 1.000000 0.077162 0.486887 0.669598 0.596936 0.596907 0.596881 ... 0.690333 0.833059 0.832975 0.832924 0.111636 0.623582 0.298090 0.016411 0.305489 0.155098
dim NaN 0.014118 0.077162 0.077162 1.000000 0.305320 0.272614 0.014153 0.014145 0.014135 ... 0.115902 0.160407 0.160417 0.160414 -0.160357 0.106693 0.240946 0.212685 0.138961 0.192305
discont NaN 0.404952 0.486887 0.486887 0.305320 1.000000 0.531254 0.404971 0.404961 0.404948 ... 0.504206 0.594219 0.594226 0.594223 0.150144 0.225854 0.823937 0.064937 0.388140 0.203342
edit NaN 0.405175 0.669598 0.669598 0.272614 0.531254 1.000000 0.405223 0.405204 0.405189 ... 0.984655 0.594688 0.594639 0.594619 0.208568 0.652532 0.338994 0.057981 0.464225 0.283262
end NaN 0.999998 0.596384 0.596936 0.014153 0.404971 0.405223 1.000000 1.000000 1.000000 ... 0.418062 0.681565 0.681565 0.681565 0.038236 0.256479 0.325559 -0.133665 0.127730 -0.008844
end16 NaN 0.999998 0.596374 0.596907 0.014145 0.404961 0.405204 1.000000 1.000000 1.000000 ... 0.418044 0.681550 0.681550 0.681550 0.038231 0.256451 0.325557 -0.133671 0.127716 -0.008852
end32 NaN 0.999998 0.596363 0.596881 0.014135 0.404948 0.405189 1.000000 1.000000 1.000000 ... 0.418029 0.681533 0.681533 0.681533 0.038228 0.256430 0.325552 -0.133677 0.127707 -0.008859
ibegin16 NaN 0.488586 0.854056 0.553792 0.160800 0.476225 0.528132 0.487938 0.487930 0.487919 ... 0.533981 0.715870 0.715889 0.715901 0.078215 0.522399 0.283800 0.037462 0.254352 0.136416
ibegin2 NaN 0.297779 0.792225 0.326418 0.080033 0.230393 0.539082 0.297285 0.297281 0.297277 ... 0.548605 0.436111 0.436126 0.436148 0.128338 0.685605 0.049586 -0.027198 0.324851 0.109929
ibegin32 NaN 0.488586 0.854056 0.553792 0.160800 0.476225 0.528132 0.487938 0.487930 0.487919 ... 0.533981 0.715870 0.715889 0.715901 0.078215 0.522399 0.283800 0.037462 0.254352 0.136416
ibegin4 NaN 0.420023 0.814178 0.474232 0.114432 0.388689 0.517951 0.419433 0.419424 0.419415 ... 0.528284 0.615385 0.615471 0.615584 0.090985 0.594774 0.207651 0.116460 0.278810 0.179014
ibegin64 NaN 0.510659 0.869357 0.586430 0.083333 0.488512 0.533376 0.509999 0.509990 0.509979 ... 0.555529 0.748243 0.748253 0.748257 0.074833 0.501069 0.307207 0.017724 0.243128 0.124459
ibegin8 NaN 0.420023 0.814178 0.474232 0.114432 0.388689 0.517951 0.419433 0.419424 0.419415 ... 0.528284 0.615385 0.615471 0.615584 0.090985 0.594774 0.207651 0.116460 0.278810 0.179014
iend16 NaN 0.405858 0.452474 0.807989 0.181503 0.383654 0.517311 0.406614 0.406575 0.406542 ... 0.513917 0.597165 0.597061 0.597069 0.094032 0.619928 0.191751 0.125689 0.307633 0.182267
iend2 NaN 0.297323 0.326418 0.792225 0.080033 0.230393 0.539082 0.297930 0.297895 0.297872 ... 0.548605 0.437541 0.437398 0.437338 0.128338 0.724562 0.049586 -0.027198 0.337071 0.146321
iend32 NaN 0.468224 0.524298 0.841277 0.233408 0.465593 0.524167 0.469061 0.469029 0.468993 ... 0.514805 0.688714 0.688640 0.688553 0.081511 0.544599 0.262448 0.049643 0.261930 0.139099
iend4 NaN 0.360597 0.400119 0.792963 0.141421 0.321878 0.519634 0.361290 0.361251 0.361222 ... 0.521120 0.530594 0.530467 0.530439 0.105830 0.673384 0.136300 -0.039355 0.351151 0.127468
iend64 NaN 0.487959 0.553792 0.854056 0.160800 0.476225 0.528132 0.488816 0.488786 0.488752 ... 0.533981 0.717677 0.717612 0.717534 0.078215 0.523746 0.283800 0.030938 0.255567 0.127728
iend8 NaN 0.405858 0.452474 0.807989 0.181503 0.383654 0.517311 0.406614 0.406575 0.406542 ... 0.513917 0.597165 0.597061 0.597069 0.094032 0.619928 0.191751 0.125689 0.307633 0.182267
middle NaN 0.126896 0.303868 0.319057 0.178317 0.152095 0.377874 0.126960 0.126947 0.126937 ... 0.355980 0.186472 0.186669 0.186918 0.052991 0.467981 0.000903 0.728990 -0.008120 0.821357
rbegin NaN 0.681576 0.832794 0.831933 0.160296 0.594171 0.594568 0.681564 0.681549 0.681532 ... 0.613417 0.999992 0.999993 0.999993 0.056108 0.376357 0.477649 0.034328 0.187411 0.095471
rdiscont NaN -0.132163 -0.158903 -0.158903 -0.077379 -0.320270 -0.168278 -0.132191 -0.132195 -0.132192 ... -0.163660 -0.193464 -0.193106 -0.192632 -0.054527 -0.001602 -0.265672 0.551880 0.004517 0.386893
redit NaN 0.418022 0.690333 0.690333 0.115902 0.504206 0.984655 0.418062 0.418044 0.418029 ... 1.000000 0.613517 0.613466 0.613446 0.244134 0.655658 0.317106 0.024651 0.450928 0.256097
rend NaN 0.681573 0.831887 0.833059 0.160407 0.594219 0.594688 0.681565 0.681550 0.681533 ... 0.613517 1.000000 1.000000 0.999999 0.056153 0.376658 0.477579 0.034412 0.187551 0.095557
rend16 NaN 0.681573 0.831895 0.832975 0.160417 0.594226 0.594639 0.681565 0.681550 0.681533 ... 0.613466 1.000000 1.000000 1.000000 0.056129 0.376574 0.477613 0.034679 0.187559 0.095755
rend32 NaN 0.681573 0.831903 0.832924 0.160414 0.594223 0.594619 0.681565 0.681550 0.681533 ... 0.613446 0.999999 1.000000 1.000000 0.056116 0.376557 0.477630 0.035005 0.187607 0.095996
rev NaN 0.038216 0.111636 0.111636 -0.160357 0.150144 0.208568 0.038236 0.038231 0.038228 ... 0.244134 0.056153 0.056129 0.056116 1.000000 0.180470 0.117200 -0.034106 0.218387 0.094260
rmiddle NaN 0.256349 0.605990 0.623582 0.106693 0.225854 0.652532 0.256479 0.256451 0.256430 ... 0.655658 0.376658 0.376574 0.376557 0.180470 1.000000 -0.064351 -0.013771 0.468925 0.195497
rot NaN 0.325594 0.298090 0.298090 0.240946 0.823937 0.338994 0.325559 0.325557 0.325552 ... 0.317106 0.477579 0.477613 0.477630 0.117200 -0.064351 1.000000 0.051246 0.243294 0.126195
size NaN -0.133581 0.016411 0.016411 0.212685 0.064937 0.057981 -0.133665 -0.133671 -0.133677 ... 0.024651 0.034412 0.034679 0.035005 -0.034106 -0.013771 0.051246 1.000000 -0.236289 0.805926
yr NaN 0.127658 0.291318 0.305489 0.138961 0.388140 0.464225 0.127730 0.127716 0.127707 ... 0.450928 0.187551 0.187559 0.187607 0.218387 0.468925 0.243294 -0.236289 1.000000 -0.013907
yt NaN -0.008816 0.139951 0.155098 0.192305 0.203342 0.283262 -0.008844 -0.008852 -0.008859 ... 0.256097 0.095557 0.095755 0.095996 0.094260 0.195497 0.126195 0.805926 -0.013907 1.000000

35 rows × 35 columns

```fdata.corr()['yt']
```
```CST_             NaN
begin      -0.008816
dbegin      0.139951
dend        0.155098
dim         0.192305
discont     0.203342
edit        0.283262
end        -0.008844
end16      -0.008852
end32      -0.008859
ibegin16    0.136416
ibegin2     0.109929
ibegin32    0.136416
ibegin4     0.179014
ibegin64    0.124459
ibegin8     0.179014
iend16      0.182267
iend2       0.146321
iend32      0.139099
iend4       0.127468
iend64      0.127728
iend8       0.182267
middle      0.821357
rbegin      0.095471
rdiscont    0.386893
redit       0.256097
rend        0.095557
rend16      0.095755
rend32      0.095996
rev         0.094260
rmiddle     0.195497
rot         0.126195
size        0.805926
yr         -0.013907
yt          1.000000
Name: yt, dtype: float64
```

We check the sign of the correlations of all features with yt. If it is positive, increasing the feature increases the processing time. We try to get only positive correlations. end is the flattened last dimensions left unchanged by the permutation. The bigger it is, the faster the transposition is. That’s why the function computing all features multiplies this number by `-1` to get a feature positively correlated to the processing time. end16 is equal to end when `end<-16` and `-16` when `end>=-16`. This is a simplification of the cost of moving data from memory to cache L1. This cost is linear when the data to move is big enough, but almost constant for small chunks.

## Linear regression#

We choose a linear regression because the prediction are not limited. The training set does not include all configuration and surely does not include all possible high value the model may have to predict.

The goal is not necessarily to predict the fastest permutation but to predict the processing time as the goal is to find the best combination of transpositions in a ONNX graph (einsum). The final goal is to predict which graphs optimizes a series of transpositions.

The target could be the processing time or the logarithm of this time. However, making mistakes on small times is not an issue but errors on high processing time is not a good thing.

We could also try to predict a ratio transposition time /copy time but it still gives more important to small matrix size.

Many variables are correlated. Variables should be selected.

### Dataset#

```X = fdata.drop(["yt", "yr"], axis=1)
x_names = list(X.columns)
yt = fdata['yt'] * 1000
```
```numpy.mean(yt)
```
```1.8809171132996723
```

### Simple model#

```from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import make_pipeline
from sklearn.metrics import r2_score, mean_absolute_error

pipe = make_pipeline(StandardScaler(with_mean=False), LinearRegression(fit_intercept=False))
pipe.fit(X, yt)
model = pipe.steps[1][1]
coef = {k: v for k, v in zip(X.columns, model.coef_)}
coef['name'] = 'reg'
coef['intercept_'] = model.intercept_
pred = numpy.maximum(pipe.predict(X), 0)
coef['r2'] = r2_score(yt, pred)
coef['mae'] = mean_absolute_error(yt, pred)
coef['model'] = pipe
coefs = [coef]
coef["r2"], coef['mae']
```
```(0.8157414076410756, 0.6368865305095469)
```
```df = DataFrame([(k, v) for k, v in coef.items() if k not in {'name', 'model'}],
columns=["feature", "value"]).set_index("feature")
df.plot(kind="bar", figsize=(14, 2));
```
```df
```
value
feature
CST_ -3.076618e+08
begin -2.941725e+01
dbegin -1.854147e-01
dend -9.638954e-02
dim -1.037599e-01
discont 5.204404e-01
edit 3.582481e-01
end -1.046584e+12
end16 -2.278042e+10
end32 1.069321e+12
ibegin16 -3.713466e+00
ibegin2 1.439716e-02
ibegin32 3.784367e+00
ibegin4 -6.813416e+00
ibegin64 -7.576102e-02
ibegin8 6.927856e+00
iend16 2.028144e+07
iend2 8.225773e+06
iend32 4.322857e+07
iend4 1.097274e+07
iend64 1.996315e-01
iend8 2.028143e+07
middle 1.541218e+00
rbegin 4.940619e+01
rdiscont 7.614642e-01
redit 8.622710e-02
rend 6.615750e+02
rend16 3.459172e+02
rend32 -1.057057e+03
rev 1.537206e-01
rmiddle -4.563712e-01
rot 7.771901e-02
size 1.295707e+00
intercept_ 0.000000e+00
r2 8.157414e-01
mae 6.368865e-01

Coefficients associated to features end, end16 are almost opposed and it would better to get a model which keeps only one.

### Quantile Regression#

```from mlinsights.mlmodel import QuantileLinearRegression
pipe = make_pipeline(StandardScaler(with_mean=False), QuantileLinearRegression(fit_intercept=False))
pipe.fit(X, yt)
model = pipe.steps[1][1]
coef = {k: v for k, v in zip(X.columns, model.coef_)}
coef['name'] = 'med'
coef['intercept_'] = model.intercept_
pred = numpy.maximum(pipe.predict(X), 0)
coef['r2'] = r2_score(yt, pred)
coef['mae'] = mean_absolute_error(yt, pred)
coef['model'] = pipe
coefs.append(coef)
coef["r2"], coef['mae']
```
```(0.7924498414927943, 0.5679387557069854)
```
```DataFrame(coef.items(), columns=["feature", "value"]).set_index("feature")
```
value
feature
CST_ 1433409.249051
begin 27.13405
dbegin 0.07931
dend 0.087576
dim 0.006919
discont 0.413378
edit 0.186032
end 4876069525.422424
end16 106134745.367844
end32 -4982003112.711292
ibegin16 0.129918
ibegin2 -0.069604
ibegin32 -0.221099
ibegin4 -0.045585
ibegin64 -0.1085
ibegin8 0.073031
iend16 -94492.918693
iend2 -38324.37475
iend32 -201401.795017
iend4 -51122.392443
iend64 0.15928
iend8 -94492.881923
middle 1.588707
rbegin 36.958438
rdiscont 0.375421
redit 0.071189
rend 4424.263222
rend16 -7664.018684
rend32 3202.681647
rev 0.08288
rmiddle -0.207068
rot -0.095643
size 0.938597
name med
intercept_ 0
r2 0.79245
mae 0.567939
model (StandardScaler(with_mean=False), QuantileLine...

### Lasso#

To select features.

```from sklearn.linear_model import Lasso

scores = []
models = []
for a in tqdm([0.001, 0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1., 2.]):
alpha = a * 1.
pipe = make_pipeline(
StandardScaler(with_mean=False),
Lasso(alpha=alpha, fit_intercept=False, max_iter=5000))
pipe.fit(X, yt)
pred = numpy.maximum(pipe.predict(X), 0)
model = pipe.steps[1][1]
scores.append(dict(r2=r2_score(yt, pred), mae=mean_absolute_error(yt, pred),
alpha=alpha, null=(numpy.abs(model.coef_) < 1e-6).sum(),
n=len(model.coef_)))
models.append(pipe)
if alpha >= 0.01 and alpha <= 0.2:
coef = {k: v for k, v in zip(X.columns, pipe.steps[1][1].coef_)}
coef['name'] = "Lasso-%f" % alpha
coef['model'] = pipe
coef['r2'] = r2_score(yt, pred)
coef['mae'] = mean_absolute_error(yt, pred)
coefs.append(coef)

DataFrame(scores)
```
```100%|██████████| 13/13 [00:00<00:00, 69.97it/s]
```
r2 mae alpha null n
0 0.809704 0.629480 0.001 4 33
1 0.807546 0.629886 0.010 10 33
2 0.782541 0.676499 0.100 23 33
3 0.766911 0.680344 0.200 28 33
4 0.751546 0.703684 0.300 29 33
5 0.738223 0.742962 0.400 30 33
6 0.730937 0.735958 0.500 31 33
7 0.718437 0.758143 0.600 30 33
8 0.701329 0.800503 0.700 30 33
9 0.681590 0.848549 0.800 30 33
10 0.659218 0.898770 0.900 30 33
11 0.634218 0.949493 1.000 30 33
12 0.239413 1.600542 2.000 30 33
```coef = {k: v for k, v in zip(X.columns, models[1].steps[1][1].coef_)}
df = DataFrame(coef.items(), columns=["feature", "value"]).set_index("feature")
df.plot(kind="bar", figsize=(14, 2), title="alpha=%f" % scores[1]["alpha"]);
```
```coef = {k: v for k, v in zip(X.columns, models[2].steps[1][1].coef_)}
df = DataFrame(coef.items(), columns=["feature", "value"]).set_index("feature")
df.plot(kind="bar", figsize=(14, 2), title="alpha=%f" % scores[2]["alpha"]);
```

### Linear regression with positive weights#

```pipe = make_pipeline(StandardScaler(with_mean=False), LinearRegression(positive=True, fit_intercept=False))
pipe.fit(X, yt)
model = pipe.steps[1][1]
coef = {k: v for k, v in zip(X.columns, model.coef_)}
coef['name'] = 'pos'
coef['intercept_'] = model.intercept_
pred = numpy.maximum(pipe.predict(X), 0)
coef['r2'] = r2_score(yt, pred)
coef['mae'] = mean_absolute_error(yt, pred)
coef['model'] = pipe
coefs.append(coef)
coef["r2"], coef['mae']
```
```(0.7905447080626958, 0.6768663007518693)
```
```coef = {k: v for k, v in zip(X.columns, pipe.steps[1][1].coef_)}
df = DataFrame(coef.items(), columns=["feature", "value"]).set_index("feature")
df.plot(kind="bar", figsize=(14, 2), title="positive");
```

### Quantile regression with positive weights#

```pipe = make_pipeline(StandardScaler(with_mean=False), QuantileLinearRegression(positive=True, fit_intercept=False))
pipe.fit(X, yt)
model = pipe.steps[1][1]
coef = {k: v for k, v in zip(X.columns, model.coef_)}
coef['name'] = 'medpos'
coef['intercept_'] = model.intercept_
pred = numpy.maximum(pipe.predict(X), 0)
coef['r2'] = r2_score(yt, pred)
coef['mae'] = mean_absolute_error(yt, pred)
coef['model'] = pipe
coefs.append(coef)
coef["r2"], coef['mae']
```
```(0.752689515971656, 0.6468340444504788)
```
```coef = {k: v for k, v in zip(X.columns, pipe.steps[1][1].coef_)}
df = DataFrame(coef.items(), columns=["feature", "value"]).set_index("feature")
df.plot(kind="bar", figsize=(14, 2), title="positive");
```

### Summary#

```dfcoef = DataFrame(coefs)
dfcoef[::-1].T
```
6 5 4 3 2 1 0
CST_ 0.829482 0.821048 0.0 0.0 0.0 1433409.249051 -307661768.128088
begin 0.0 0.0 -0.0 -0.0 -0.03443 27.13405 -29.417247
dbegin 0.0 0.0 -0.0 -0.0 -0.044705 0.07931 -0.185415
dend 0.0 0.0 -0.0 -0.0 -0.0 0.087576 -0.09639
dim 0.023846 0.0 -0.014763 -0.030446 -0.120949 0.006919 -0.10376
discont 0.060636 0.056297 0.0 0.0 0.210421 0.413378 0.52044
edit 0.03823 0.094856 0.0 0.0418 0.396052 0.186032 0.358248
end 0.0 0.0 -0.0 -0.0 -0.007053 4876069525.422424 -1046583604803.358887
end16 0.0 0.0 -0.0 -0.0 -0.000036 106134745.367844 -22780416305.902706
end32 0.0 0.0 -0.0 -0.0 -0.00004 -4982003112.711292 1069320839370.567505
ibegin16 0.0 0.0 -0.0 -0.0 0.066669 0.129918 -3.713466
ibegin2 0.0 0.0 -0.0 -0.0 -0.02181 -0.069604 0.014397
ibegin32 0.0 0.0 -0.0 -0.0 0.0 -0.221099 3.784367
ibegin4 0.0 0.0 -0.0 -0.0 0.0 -0.045585 -6.813416
ibegin64 0.0 0.0 -0.0 -0.0 0.0 -0.1085 -0.075761
ibegin8 0.0 0.0 -0.0 -0.0 0.0 0.073031 6.927856
iend16 0.0 0.0 -0.0 -0.0 -0.022416 -94492.918693 20281439.108194
iend2 0.0 0.0 0.0 -0.0 0.0 -38324.37475 8225773.255917
iend32 0.0 0.0 -0.0 -0.0 -0.0 -201401.795017 43228573.054944
iend4 0.0 0.0 -0.0 -0.0 0.151081 -51122.392443 10972737.091606
iend64 0.0 0.0 -0.0 -0.0 -0.0 0.15928 0.199631
iend8 0.0 0.0 -0.0 -0.0 -0.08907 -94492.881923 20281426.580972
middle 1.101543 1.30347 1.290699 1.325916 1.466733 1.588707 1.541218
rbegin 0.0 0.0 -0.0 -0.020369 -0.28295 36.958438 49.406192
rdiscont 0.0 0.0 0.0 -0.0 -0.066385 0.375421 0.761464
redit 0.0 0.0 0.0 0.0 0.0 0.071189 0.086227
rend 0.0 0.0 -0.0 -0.007655 -0.007593 4424.263222 661.575013
rend16 0.0 0.0 -0.0 -0.003393 -0.010514 -7664.018684 345.917179
rend32 0.0 0.0 -0.0 -0.005349 -0.013172 3202.681647 -1057.05651
rev 0.026757 0.189909 0.013992 0.097585 0.142791 0.08288 0.153721
rmiddle 0.0 0.0 -0.0 -0.0 -0.324716 -0.207068 -0.456371
rot 0.009222 0.185687 0.108468 0.197021 0.108146 -0.095643 0.077719
size 1.100532 1.300222 1.099463 1.183553 1.22329 0.938597 1.295707
name medpos pos Lasso-0.200000 Lasso-0.100000 Lasso-0.010000 med reg
intercept_ 0.0 0.0 NaN NaN NaN 0.0 0.0
r2 0.75269 0.790545 0.766911 0.782541 0.807546 0.79245 0.815741
mae 0.646834 0.676866 0.680344 0.676499 0.629886 0.567939 0.636887
model (StandardScaler(with_mean=False), QuantileLine... (StandardScaler(with_mean=False), LinearRegres... (StandardScaler(with_mean=False), Lasso(alpha=... (StandardScaler(with_mean=False), Lasso(alpha=... (StandardScaler(with_mean=False), Lasso(alpha=... (StandardScaler(with_mean=False), QuantileLine... (StandardScaler(with_mean=False), LinearRegres...
```dfcoef[["name", "r2", "mae"]].set_index('name').plot(kind="bar", title="performance accross models");
```
```import matplotlib.pyplot as plt

dfp = dfcoef.drop(['name', 'model'], axis=1).T.drop([0, 1], axis=1).copy()
dfp.columns = dfcoef['name'][2:]
ax = dfp.plot(figsize=(14, 4), kind="line")
ax.set_xticks(numpy.arange(0, dfp.shape[0]))
ax.set_xticklabels(dfp.index)
plt.setp(ax.get_xticklabels(), rotation=45, horizontalalignment='right');
```

## Investigation#

```data_err = data.drop(["context_size", "repeat"], axis=1).copy()
data_err['predict'] = numpy.maximum(coefs[0]['model'].predict(X), 0) / 1000
data_err['err'] = (data_err['predict'] - data_err['average'])
data_err['abserr'] = numpy.abs(data_err['predict'] - data_err['average'])
data_err['rel'] = (data_err['predict'] - data_err['average']) / data_err['average']
s = data_err.sort_values('abserr')
```
average deviation min_exec max_exec number perm shape ratio dim predict err abserr rel
28 0.000113 0.000029 0.000061 0.000141 50 (1, 0, 2) (43, 44, 45) 1.515711 3 0.000113 1.251063e-07 1.251063e-07 0.001111
55 0.000893 0.000212 0.000646 0.001477 50 (2, 3, 1, 0) (3, 244, 244, 1) 8.339926 4 0.000893 -2.410649e-07 2.410649e-07 -0.000270
26 0.000077 0.000008 0.000069 0.000101 50 (0, 2, 1) (43, 44, 45) 1.032759 3 0.000077 4.172780e-07 4.172780e-07 0.005440
39 0.000126 0.000017 0.000107 0.000185 50 (2, 0, 1, 3) (3, 244, 244, 1) 1.180996 4 0.000115 -1.179187e-05 1.179187e-05 -0.093246
66 0.000195 0.000019 0.000163 0.000258 50 (0, 3, 1, 2) (1, 244, 244, 3) 1.598770 4 0.000210 1.510728e-05 1.510728e-05 0.077417
50 0.000692 0.000136 0.000529 0.001021 50 (0, 3, 2, 1) (3, 244, 244, 1) 6.460759 4 0.000709 1.714180e-05 1.714180e-05 0.024778
76 0.000824 0.000288 0.000515 0.001879 50 (1, 3, 2, 0) (1, 244, 244, 3) 6.752663 4 0.000843 1.902846e-05 1.902846e-05 0.023087
54 0.000818 0.000278 0.000625 0.001522 50 (2, 1, 3, 0) (3, 244, 244, 1) 7.634646 4 0.000843 2.572773e-05 2.572773e-05 0.031471
1 0.000048 0.000003 0.000045 0.000058 50 (0, 1, 3, 2) (12, 13, 15, 18) 0.820821 4 0.000000 -4.837787e-05 4.837787e-05 -1.000000
2 0.000049 0.000003 0.000045 0.000062 50 (3, 0, 1, 2) (12, 13, 15, 18) 0.823070 4 0.000000 -4.851040e-05 4.851040e-05 -1.000000
120 0.005918 0.001085 0.004598 0.008312 15 (1, 0, 3, 2) (3, 244, 244, 6) 1.597357 4 0.008259 2.341673e-03 2.341673e-03 0.395716
128 0.010677 0.001457 0.008504 0.014070 15 (2, 3, 1, 0) (3, 244, 244, 6) 2.882191 4 0.008132 -2.545011e-03 2.545011e-03 -0.238356
121 0.006106 0.000556 0.005619 0.007305 15 (2, 0, 3, 1) (3, 244, 244, 6) 1.648325 4 0.008700 2.593662e-03 2.593662e-03 0.424746
118 0.003780 0.000882 0.002701 0.005402 15 (3, 0, 1, 2) (3, 244, 244, 6) 1.020432 4 0.006488 2.707333e-03 2.707333e-03 0.716171
115 0.003653 0.000874 0.002567 0.005244 15 (1, 2, 3, 0) (3, 244, 244, 6) 0.986071 4 0.006488 2.834624e-03 2.834624e-03 0.775972
129 0.012421 0.003052 0.007818 0.018106 15 (3, 2, 1, 0) (3, 244, 244, 6) 3.352770 4 0.009386 -3.034652e-03 3.034652e-03 -0.244323
119 0.004938 0.000367 0.004532 0.005844 15 (1, 3, 0, 2) (3, 244, 244, 6) 1.333061 4 0.008700 3.761588e-03 3.761588e-03 0.761694
127 0.010339 0.002789 0.005878 0.018301 15 (0, 3, 2, 1) (3, 244, 244, 6) 2.790823 4 0.005271 -5.068171e-03 5.068171e-03 -0.490205
130 0.013432 0.004496 0.006536 0.021250 15 (3, 2, 0, 1) (3, 244, 244, 6) 3.625680 4 0.008132 -5.299336e-03 5.299336e-03 -0.394540
131 0.014579 0.004026 0.007144 0.020739 15 (3, 0, 2, 1) (3, 244, 244, 6) 3.935483 4 0.008259 -6.320138e-03 6.320138e-03 -0.433499

All big errors are negative. The model seems to give a lower value for all big errors. These errors may be outliers, the processor was busy doing something else at that time.

```s = data_err.sort_values('predict')
```
average deviation min_exec max_exec number perm shape ratio dim predict err abserr rel
20 0.000158 0.000021 0.000127 0.000192 50 (3, 0, 2, 1) (12, 13, 15, 18) 2.684876 4 0.000000 -0.000158 0.000158 -1.000000
42 0.000147 0.000017 0.000106 0.000175 50 (0, 1, 3, 2) (3, 244, 244, 1) 1.369978 4 0.000000 -0.000147 0.000147 -1.000000
34 0.000151 0.000016 0.000136 0.000197 50 (1, 2, 0) (3, 244, 244) 1.438446 3 0.000000 -0.000151 0.000151 -1.000000
33 0.000124 0.000017 0.000108 0.000171 50 (2, 0, 1) (3, 244, 244) 1.185666 3 0.000000 -0.000124 0.000124 -1.000000
44 0.000189 0.000044 0.000142 0.000265 50 (1, 2, 3, 0) (3, 244, 244, 1) 1.766905 4 0.000000 -0.000189 0.000189 -1.000000
27 0.000097 0.000004 0.000083 0.000110 50 (2, 0, 1) (43, 44, 45) 1.300915 3 0.000000 -0.000097 0.000097 -1.000000
25 0.000074 0.000009 0.000065 0.000109 50 (0, 1, 2) (43, 44, 45) 1.000000 3 0.000000 -0.000074 0.000074 -1.000000
24 0.000073 0.000009 0.000062 0.000094 50 (1, 2, 0) (43, 44, 45) 0.985513 3 0.000000 -0.000073 0.000073 -1.000000
22 0.000214 0.000060 0.000136 0.000295 50 (1, 0, 3, 2) (12, 13, 15, 18) 3.627240 4 0.000000 -0.000214 0.000214 -1.000000
21 0.000164 0.000045 0.000124 0.000231 50 (3, 1, 2, 0) (12, 13, 15, 18) 2.778193 4 0.000000 -0.000164 0.000164 -1.000000
128 0.010677 0.001457 0.008504 0.014070 15 (2, 3, 1, 0) (3, 244, 244, 6) 2.882191 4 0.008132 -0.002545 0.002545 -0.238356
130 0.013432 0.004496 0.006536 0.021250 15 (3, 2, 0, 1) (3, 244, 244, 6) 3.625680 4 0.008132 -0.005299 0.005299 -0.394540
122 0.006722 0.001807 0.005067 0.011245 15 (1, 3, 2, 0) (3, 244, 244, 6) 1.814552 4 0.008259 0.001537 0.001537 0.228654
125 0.007815 0.001757 0.005932 0.010779 15 (2, 1, 3, 0) (3, 244, 244, 6) 2.109489 4 0.008259 0.000444 0.000444 0.056871
120 0.005918 0.001085 0.004598 0.008312 15 (1, 0, 3, 2) (3, 244, 244, 6) 1.597357 4 0.008259 0.002342 0.002342 0.395716
123 0.007071 0.000982 0.005454 0.008559 15 (3, 1, 0, 2) (3, 244, 244, 6) 1.908667 4 0.008259 0.001188 0.001188 0.168070
131 0.014579 0.004026 0.007144 0.020739 15 (3, 0, 2, 1) (3, 244, 244, 6) 3.935483 4 0.008259 -0.006320 0.006320 -0.433499
121 0.006106 0.000556 0.005619 0.007305 15 (2, 0, 3, 1) (3, 244, 244, 6) 1.648325 4 0.008700 0.002594 0.002594 0.424746
119 0.004938 0.000367 0.004532 0.005844 15 (1, 3, 0, 2) (3, 244, 244, 6) 1.333061 4 0.008700 0.003762 0.003762 0.761694
129 0.012421 0.003052 0.007818 0.018106 15 (3, 2, 1, 0) (3, 244, 244, 6) 3.352770 4 0.009386 -0.003035 0.003035 -0.244323

### Correlation between predictors#

```cc = DataFrame(dict([(c['name'], numpy.maximum(c['model'].predict(X), 0)) for c in coefs]))
cc['yt'] = yt
cc
```
reg med Lasso-0.010000 Lasso-0.100000 Lasso-0.200000 pos medpos yt
0 0.298789 0.052436 0.000000 0.000000 0.000000 0.000000 0.000000 0.044222
1 0.000000 0.071575 0.000000 0.000000 0.000000 0.000000 0.000000 0.048378
2 0.000000 0.048393 0.000000 0.000000 0.000000 0.000000 0.000000 0.048510
3 0.000000 0.048393 0.000000 0.000000 0.000000 0.000000 0.000000 0.048954
4 0.248089 0.050781 0.000000 0.000000 0.000000 0.000000 0.000000 0.050805
... ... ... ... ... ... ... ... ...
127 5.270700 4.177012 4.917105 4.615490 4.464429 4.837032 4.251381 10.338870
128 8.132342 7.354799 8.107191 7.646966 7.334861 7.858363 6.706548 10.677354
129 9.386005 8.186190 8.991256 8.082431 7.397300 8.771040 6.896204 12.420657
130 8.132342 7.354799 8.107191 7.646966 7.334861 7.858363 6.706548 13.431679
131 8.259236 7.561004 7.962160 7.605605 7.334861 7.829728 6.738972 14.579374

132 rows × 8 columns

```cc.corr()
```
reg med Lasso-0.010000 Lasso-0.100000 Lasso-0.200000 pos medpos yt
reg 1.000000 0.994124 0.996922 0.985715 0.979826 0.988323 0.980433 0.903528
med 0.994124 1.000000 0.995863 0.989990 0.987374 0.990341 0.988401 0.894833
Lasso-0.010000 0.996922 0.995863 1.000000 0.992689 0.987930 0.994420 0.988358 0.899384
Lasso-0.100000 0.985715 0.989990 0.992689 1.000000 0.998564 0.998756 0.997985 0.886902
Lasso-0.200000 0.979826 0.987374 0.987930 0.998564 1.000000 0.995092 0.999385 0.880614
pos 0.988323 0.990341 0.994420 0.998756 0.995092 1.000000 0.995169 0.890093
medpos 0.980433 0.988401 0.988358 0.997985 0.999385 0.995169 1.000000 0.881208
yt 0.903528 0.894833 0.899384 0.886902 0.880614 0.890093 0.881208 1.000000

## Standalone predictions#

```def get_coef(pipe, names):
c1 = pipe.steps[0][-1].scale_
c2 = pipe.steps[1][-1].coef_
return dict(zip(names, c2 / c1))

get_coef(coefs[-1]["model"], X.columns)
```
```{'CST_': 0.829481835464256,
'begin': 0.0,
'dbegin': 0.0,
'dend': 0.0,
'dim': 0.08294721851224843,
'discont': 0.07025394222472751,
'edit': 0.03782977428195987,
'end': 0.0,
'end16': 0.0,
'end32': 0.0,
'ibegin16': 0.0,
'ibegin2': 0.0,
'ibegin32': 0.0,
'ibegin4': 0.0,
'ibegin64': 0.0,
'ibegin8': 0.0,
'iend16': 0.0,
'iend2': 0.0,
'iend32': 0.0,
'iend4': 0.0,
'iend64': 0.0,
'iend8': 0.0,
'middle': 3.42896339670081e-06,
'rbegin': 0.0,
'rdiscont': 0.0,
'redit': 0.0,
'rend': 0.0,
'rend16': 0.0,
'rend32': 0.0,
'rev': 0.11940214295823245,
'rmiddle': 0.0,
'rot': 0.023189032947793925,
'size': 3.021302183272755e-06}
```
```def predict(coefs, shape, perm):
feat = compute_features(shape, perm)
res = 0
for k, v in feat.items():
res += v * coefs[k]
return res / 1000

def predict_model(model, shape, perm, names):
feat = compute_features(shape, perm)
a = numpy.zeros((1, len(names)), dtype=numpy.float64)
for i, n in enumerate(names):
a[0, i] = feat[n]
return model.predict(a) / 1000

coef = get_coef(coefs[-1]["model"], X.columns)
(predict(coef, (3, 224, 224, 6), (3, 0, 1, 2)),
predict_model(coefs[-1]["model"], (3, 224, 224, 6), (3, 0, 1, 2), X.columns))
```
```(0.005450704959759156, array([0.0054507]))
```