1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
|
#!/usr/bin/env python3
import logging
import numpy as np
logger = logging.getLogger(__name__)
def _xv_partitions_kfold(length, k=10):
"""
Return k pairs of training and validation sets for k-fold cross-validation on `length` items.
In k-fold cross-validation, every k-th item is used for validation and the remainder is used for training.
As there are k ways to do this (items 0, k, 2k, ... vs. items 1, k+1, 2k+1, ... etc), this function returns k pairs of training and validation set.
Note that this function operates on indices, not data.
"""
pairs = []
num_slices = k
indexes = np.arange(length)
for i in range(num_slices):
training = np.delete(indexes, slice(i, None, num_slices))
validation = indexes[i::num_slices]
pairs.append((training, validation))
return pairs
def _xv_partition_montecarlo(length):
"""
Return training and validation set for Monte Carlo cross-validation on `length` items.
This function operates on indices, not data. It randomly partitions range(length) into a list of training indices and a list of validation indices.
The training set contains 2/3 of all indices; the validation set consits of the remaining 1/3.
Example: 9 items -> training = [7, 3, 8, 0, 4, 2], validation = [ 1, 6, 5]
"""
shuffled = np.random.permutation(np.arange(length))
border = int(length * float(2) / 3)
training = shuffled[:border]
validation = shuffled[border:]
return (training, validation)
class CrossValidator:
"""
Cross-Validation helper for model generation.
Given a set of measurements and a model class, it will partition the
data into training and validation sets, train the model on the training
set, and assess its quality on the validation set. This is repeated
several times depending on cross-validation algorithm and configuration.
Reports the mean model error over all cross-validation runs.
"""
def __init__(self, model_class, by_name, parameters, arg_count):
"""
Create a new CrossValidator object.
Does not perform cross-validation yet.
arguments:
model_class -- model class/type used for model synthesis,
e.g. PTAModel or AnalyticModel. model_class must have a
constructor accepting (by_name, parameters, arg_count)
and provide an `assess` method.
by_name -- measurements aggregated by state/transition/function/... name.
Layout: by_name[name][attribute] = list of data. Additionally,
by_name[name]['attributes'] must be set to the list of attributes,
e.g. ['power'] or ['duration', 'energy'].
"""
self.model_class = model_class
self.by_name = by_name
self.names = sorted(by_name.keys())
self.parameters = sorted(parameters)
self.arg_count = arg_count
def kfold(self, model_getter, k=10):
"""
Perform k-fold cross-validation and return average model quality.
The by_name data is divided into 1-1/k training and 1/k validation in a deterministic manner.
After creating a model for the training set, the
model type returned by model_getter is evaluated on the validation set.
This is repeated k times; the average of all measures is returned to the user.
arguments:
model_getter -- function with signature (model_object) -> model,
e.g. lambda m: m.get_fitted()[0] to evaluate the parameter-aware
model with automatic parameter detection.
k -- step size for k-fold cross-validation. The validation set contains 100/k % of data.
return value:
dict of model quality measures.
{
'by_name' : {
for each name: {
for each attribute: {
'mae' : mean of all mean absolute errors
'mae_list' : list of the individual MAE values encountered during cross-validation
'smape' : mean of all symmetric mean absolute percentage errors
'smape_list' : list of the individual SMAPE values encountered during cross-validation
}
}
}
}
"""
# training / validation subsets for each state and transition
subsets_by_name = dict()
training_and_validation_sets = list()
for name in self.names:
sample_count = len(self.by_name[name]["param"])
subsets_by_name[name] = list()
subsets_by_name[name] = _xv_partitions_kfold(sample_count, k)
for i in range(k):
training_and_validation_sets.append(dict())
for name in self.names:
training_and_validation_sets[i][name] = subsets_by_name[name][i]
return self._generic_xv(model_getter, training_and_validation_sets)
def montecarlo(self, model_getter, count=200):
"""
Perform Monte Carlo cross-validation and return average model quality.
The by_name data is randomly divided into 2/3 training and 1/3
validation. After creating a model for the training set, the
model type returned by model_getter is evaluated on the validation set.
This is repeated count times (defaulting to 200); the average of all
measures is returned to the user.
arguments:
model_getter -- function with signature (model_object) -> model,
e.g. lambda m: m.get_fitted()[0] to evaluate the parameter-aware
model with automatic parameter detection.
count -- number of validation runs to perform, defaults to 200
return value:
dict of model quality measures.
{
'by_name' : {
for each name: {
for each attribute: {
'mae' : mean of all mean absolute errors
'mae_list' : list of the individual MAE values encountered during cross-validation
'smape' : mean of all symmetric mean absolute percentage errors
'smape_list' : list of the individual SMAPE values encountered during cross-validation
}
}
}
}
"""
# training / validation subsets for each state and transition
subsets_by_name = dict()
training_and_validation_sets = list()
for name in self.names:
sample_count = len(self.by_name[name]["param"])
subsets_by_name[name] = list()
for _ in range(count):
subsets_by_name[name].append(_xv_partition_montecarlo(sample_count))
for i in range(count):
training_and_validation_sets.append(dict())
for name in self.names:
training_and_validation_sets[i][name] = subsets_by_name[name][i]
return self._generic_xv(model_getter, training_and_validation_sets)
def _generic_xv(self, model_getter, training_and_validation_sets):
ret = {"by_name": dict()}
for name in self.names:
ret["by_name"][name] = dict()
for attribute in self.by_name[name]["attributes"]:
ret["by_name"][name][attribute] = {
"mae_list": list(),
"smape_list": list(),
}
for training_and_validation_by_name in training_and_validation_sets:
res = self._single_xv(model_getter, training_and_validation_by_name)
for name in self.names:
for attribute in self.by_name[name]["attributes"]:
ret["by_name"][name][attribute]["mae_list"].append(
res["by_name"][name][attribute]["mae"]
)
ret["by_name"][name][attribute]["smape_list"].append(
res["by_name"][name][attribute]["smape"]
)
for name in self.names:
for attribute in self.by_name[name]["attributes"]:
ret["by_name"][name][attribute]["mae"] = np.mean(
ret["by_name"][name][attribute]["mae_list"]
)
ret["by_name"][name][attribute]["smape"] = np.mean(
ret["by_name"][name][attribute]["smape_list"]
)
return ret
def _single_xv(self, model_getter, tv_set_dict):
training = dict()
validation = dict()
for name in self.names:
training[name] = {"attributes": self.by_name[name]["attributes"]}
validation[name] = {"attributes": self.by_name[name]["attributes"]}
if "isa" in self.by_name[name]:
training[name]["isa"] = self.by_name[name]["isa"]
validation[name]["isa"] = self.by_name[name]["isa"]
training_subset, validation_subset = tv_set_dict[name]
for attribute in self.by_name[name]["attributes"]:
self.by_name[name][attribute] = np.array(self.by_name[name][attribute])
training[name][attribute] = self.by_name[name][attribute][
training_subset
]
validation[name][attribute] = self.by_name[name][attribute][
validation_subset
]
# We can't use slice syntax for 'param', which may contain strings and other odd values
training[name]["param"] = list()
validation[name]["param"] = list()
for idx in training_subset:
training[name]["param"].append(self.by_name[name]["param"][idx])
for idx in validation_subset:
validation[name]["param"].append(self.by_name[name]["param"][idx])
training_data = self.model_class(training, self.parameters, self.arg_count)
training_model = model_getter(training_data)
validation_data = self.model_class(validation, self.parameters, self.arg_count)
return validation_data.assess(training_model)
|
