Обучение полносвязной многослойной нейросети на исправленных данных¶
В данном примере будет рассмотрена обработка данных и обучение на их основе нейросетевой модели. Будет продемонстрирован метод скользящего окна - для разделения обучающей и тестовой выборки на наборы данных для обучения, а также будут определены параметры модели, для получения наиболее точных прогнозных значений.
Запуск необходимых библиотек:
Resolving package versions...
No Changes to `~/.project/Project.toml`
No Changes to `~/.project/Manifest.toml`
Подготовка обучающей и тестовой выборки:¶
Загрузка данных для обучения модели:
Данные были сохранены после выполнения примера /start/examples/data_analysis/data_processing.ipynb.
Формирование обучающего набора данных:¶
Весь датасет был разделён на обучающую и тестовую выборку. Обучающая выборка составила 0,8 от всего датасета, а тестовая 0,2.
Out[0]:
1 | 1 | 747.7 | 19.7 |
2 | 2 | 744.2 | 22.1 |
3 | 3 | 748.6 | 23.0 |
4 | 4 | 754.5 | 23.4 |
5 | 5 | 754.6 | 21.9 |
Разделение вектора T на батчи длиной в 100 наблюдений:
Батч - небольшой набор данных, который может служить обучающим множеством для построения модели прогнозирования. Взят из первоначального обучающего набора T с помощью метода скользящего окна.
Метод скользящего окна:

где x - наблюдение, а y1 - прогнозное значение.
Преобразование полученного набора в вектор-строку:
Out[0]:
1×136000 adjoint(::Vector{Any}) with eltype Any:
19.7 22.1 23.0 23.4 21.9 23.35 … 26.4 18.8 19.7 16.3 16.8 20.5
Изменение формы массива для соответствия длине батча, указанной выше:
Out[0]:
100×1360 reshape(adjoint(::Vector{Any}), 100, 1360) with eltype Any:
19.7 22.1 23.0 23.4 21.9 23.35 … -4.4 -2.9 -4.0 -4.7 -4.2
22.1 23.0 23.4 21.9 23.35 24.8 -2.9 -4.0 -4.7 -4.2 -7.8
23.0 23.4 21.9 23.35 24.8 26.25 -4.0 -4.7 -4.2 -7.8 1.7
23.4 21.9 23.35 24.8 26.25 27.7 -4.7 -4.2 -7.8 1.7 2.8
21.9 23.35 24.8 26.25 27.7 28.0 -4.2 -7.8 1.7 2.8 2.9
23.35 24.8 26.25 27.7 28.0 27.4 … -7.8 1.7 2.8 2.9 5.8
24.8 26.25 27.7 28.0 27.4 25.1 1.7 2.8 2.9 5.8 3.1
26.25 27.7 28.0 27.4 25.1 25.6 2.8 2.9 5.8 3.1 4.1
27.7 28.0 27.4 25.1 25.6 24.5 2.9 5.8 3.1 4.1 5.1
28.0 27.4 25.1 25.6 24.5 21.9 5.8 3.1 4.1 5.1 4.4
27.4 25.1 25.6 24.5 21.9 15.5 … 3.1 4.1 5.1 4.4 4.3
25.1 25.6 24.5 21.9 15.5 22.7 4.1 5.1 4.4 4.3 7.5
25.6 24.5 21.9 15.5 22.7 23.1 5.1 4.4 4.3 7.5 6.9
⋮ ⋮ ⋱ ⋮
22.1 18.9 17.9 15.5 20.9 20.3 19.9917 19.7 15.3 20.5 19.5
18.9 17.9 15.5 20.9 20.3 16.7 19.7 15.3 20.5 19.5 19.3
17.9 15.5 20.9 20.3 16.7 15.5 … 15.3 20.5 19.5 19.3 21.6
15.5 20.9 20.3 16.7 15.5 12.7 20.5 19.5 19.3 21.6 21.1
20.9 20.3 16.7 15.5 12.7 9.7 19.5 19.3 21.6 21.1 23.8
20.3 16.7 15.5 12.7 9.7 6.7 19.3 21.6 21.1 23.8 23.6
16.7 15.5 12.7 9.7 6.7 4.3 21.6 21.1 23.8 23.6 26.4
15.5 12.7 9.7 6.7 4.3 5.6 … 21.1 23.8 23.6 26.4 18.8
12.7 9.7 6.7 4.3 5.6 12.2 23.8 23.6 26.4 18.8 19.7
9.7 6.7 4.3 5.6 12.2 12.8 23.6 26.4 18.8 19.7 16.3
6.7 4.3 5.6 12.2 12.8 12.3 26.4 18.8 19.7 16.3 16.8
4.3 5.6 12.2 12.8 12.3 9.8 18.8 19.7 16.3 16.8 20.5
Out[0]:
100×1360 reshape(adjoint(::Vector{Any}), 100, 1360) with eltype Any:
19.7 22.1 23.0 23.4 21.9 23.35 … -4.4 -2.9 -4.0 -4.7 -4.2
22.1 23.0 23.4 21.9 23.35 24.8 -2.9 -4.0 -4.7 -4.2 -7.8
23.0 23.4 21.9 23.35 24.8 26.25 -4.0 -4.7 -4.2 -7.8 1.7
23.4 21.9 23.35 24.8 26.25 27.7 -4.7 -4.2 -7.8 1.7 2.8
21.9 23.35 24.8 26.25 27.7 28.0 -4.2 -7.8 1.7 2.8 2.9
23.35 24.8 26.25 27.7 28.0 27.4 … -7.8 1.7 2.8 2.9 5.8
24.8 26.25 27.7 28.0 27.4 25.1 1.7 2.8 2.9 5.8 3.1
26.25 27.7 28.0 27.4 25.1 25.6 2.8 2.9 5.8 3.1 4.1
27.7 28.0 27.4 25.1 25.6 24.5 2.9 5.8 3.1 4.1 5.1
28.0 27.4 25.1 25.6 24.5 21.9 5.8 3.1 4.1 5.1 4.4
27.4 25.1 25.6 24.5 21.9 15.5 … 3.1 4.1 5.1 4.4 4.3
25.1 25.6 24.5 21.9 15.5 22.7 4.1 5.1 4.4 4.3 7.5
25.6 24.5 21.9 15.5 22.7 23.1 5.1 4.4 4.3 7.5 6.9
⋮ ⋮ ⋱ ⋮
22.1 18.9 17.9 15.5 20.9 20.3 19.9917 19.7 15.3 20.5 19.5
18.9 17.9 15.5 20.9 20.3 16.7 19.7 15.3 20.5 19.5 19.3
17.9 15.5 20.9 20.3 16.7 15.5 … 15.3 20.5 19.5 19.3 21.6
15.5 20.9 20.3 16.7 15.5 12.7 20.5 19.5 19.3 21.6 21.1
20.9 20.3 16.7 15.5 12.7 9.7 19.5 19.3 21.6 21.1 23.8
20.3 16.7 15.5 12.7 9.7 6.7 19.3 21.6 21.1 23.8 23.6
16.7 15.5 12.7 9.7 6.7 4.3 21.6 21.1 23.8 23.6 26.4
15.5 12.7 9.7 6.7 4.3 5.6 … 21.1 23.8 23.6 26.4 18.8
12.7 9.7 6.7 4.3 5.6 12.2 23.8 23.6 26.4 18.8 19.7
9.7 6.7 4.3 5.6 12.2 12.8 23.6 26.4 18.8 19.7 16.3
6.7 4.3 5.6 12.2 12.8 12.3 26.4 18.8 19.7 16.3 16.8
4.3 5.6 12.2 12.8 12.3 9.8 18.8 19.7 16.3 16.8 20.5
Определение массива целевых значений:
Out[0]:
1×1360 adjoint(::Vector{Float64}) with eltype Float64:
5.6 12.2 12.8 12.3 9.8 11.0 8.7 … 18.8 19.7 16.3 16.8 20.5 19.2
Преобразование в формат приемлемый для обработки нейросетью:
Out[0]:
1×1360 Matrix{Float32}:
5.6 12.2 12.8 12.3 9.8 11.0 8.7 … 18.8 19.7 16.3 16.8 20.5 19.2
Формирование тестового набора данных:¶
Разделение тестовой выборки на батчи длиной 100 наблюдений:
Out[0]:
100×261 Matrix{Float32}:
23.1 18.9 17.2 12.4 15.0 23.3 … -9.7 -8.8 -7.4 -5.2 -3.1 -2.0
18.9 17.2 12.4 15.0 23.3 20.7 -8.8 -7.4 -5.2 -3.1 -2.0 -1.3
17.2 12.4 15.0 23.3 20.7 15.0 -7.4 -5.2 -3.1 -2.0 -1.3 -0.5
12.4 15.0 23.3 20.7 15.0 13.2 -5.2 -3.1 -2.0 -1.3 -0.5 -2.4
15.0 23.3 20.7 15.0 13.2 11.2 -3.1 -2.0 -1.3 -0.5 -2.4 -0.9
23.3 20.7 15.0 13.2 11.2 15.5 … -2.0 -1.3 -0.5 -2.4 -0.9 -0.2
20.7 15.0 13.2 11.2 15.5 13.4 -1.3 -0.5 -2.4 -0.9 -0.2 -3.9
15.0 13.2 11.2 15.5 13.4 14.1 -0.5 -2.4 -0.9 -0.2 -3.9 2.0
13.2 11.2 15.5 13.4 14.1 10.9 -2.4 -0.9 -0.2 -3.9 2.0 1.3
11.2 15.5 13.4 14.1 10.9 14.5 -0.9 -0.2 -3.9 2.0 1.3 1.0
15.5 13.4 14.1 10.9 14.5 15.2 … -0.2 -3.9 2.0 1.3 1.0 0.3
13.4 14.1 10.9 14.5 15.2 25.0 -3.9 2.0 1.3 1.0 0.3 1.4
14.1 10.9 14.5 15.2 25.0 26.5 2.0 1.3 1.0 0.3 1.4 -0.5
⋮ ⋮ ⋱ ⋮ ⋮
16.7 16.4 21.4 17.1 17.1 20.0 21.5 22.2 23.3 21.8 22.4 26.3
16.4 21.4 17.1 17.1 20.0 18.0 22.2 23.3 21.8 22.4 26.3 28.0
21.4 17.1 17.1 20.0 18.0 24.2 … 23.3 21.8 22.4 26.3 28.0 27.9
17.1 17.1 20.0 18.0 24.2 14.7 21.8 22.4 26.3 28.0 27.9 27.7
17.1 20.0 18.0 24.2 14.7 16.0 22.4 26.3 28.0 27.9 27.7 26.6
20.0 18.0 24.2 14.7 16.0 24.6 26.3 28.0 27.9 27.7 26.6 25.1
18.0 24.2 14.7 16.0 24.6 23.3 28.0 27.9 27.7 26.6 25.1 21.0
24.2 14.7 16.0 24.6 23.3 19.4 … 27.9 27.7 26.6 25.1 21.0 18.7
14.7 16.0 24.6 23.3 19.4 11.6 27.7 26.6 25.1 21.0 18.7 17.8
16.0 24.6 23.3 19.4 11.6 13.7 26.6 25.1 21.0 18.7 17.8 21.3
24.6 23.3 19.4 11.6 13.7 8.3 25.1 21.0 18.7 17.8 21.3 21.6
23.3 19.4 11.6 13.7 8.3 13.9 21.0 18.7 17.8 21.3 21.6 21.9
Построение и обучение нейросети:¶
Определение архитектуры нейросети:
Out[0]:
Chain(
Dense(100 => 50, elu), # 5_050 parameters
Dense(50 => 25, elu), # 1_275 parameters
Dense(25 => 5, elu), # 130 parameters
Dense(5 => 1), # 6 parameters
) # Total: 8 arrays, 6_461 parameters, 25.738 KiB.
Определение параметров обучения:
Out[0]:
loss (generic function with 1 method)
Epoch 1: Loss = 147.93127
Epoch 10: Loss = 40.457306
Epoch 20: Loss = 34.76956
Epoch 30: Loss = 26.913574
Epoch 40: Loss = 24.001925
Epoch 50: Loss = 20.977661
Epoch 60: Loss = 18.199791
Epoch 70: Loss = 16.144032
Epoch 80: Loss = 14.6047535
Epoch 90: Loss = 13.4236555
Epoch 100: Loss = 12.447013
Epoch 110: Loss = 11.691035
Epoch 120: Loss = 11.081361
Epoch 130: Loss = 10.575395
Epoch 140: Loss = 10.132528
Epoch 150: Loss = 9.736594
Epoch 160: Loss = 9.365963
Epoch 170: Loss = 9.002684
Epoch 180: Loss = 8.6449375
Epoch 190: Loss = 8.312174
Epoch 200: Loss = 7.997946
Визуализация изменения функции потерь:
Получение прогнозных значений:
Out[0]:
5-element Vector{Float64}:
19.431472778320312
20.471216201782227
18.861164093017578
13.53215217590332
14.286093711853027
Визуализация предсказанных значений:¶
Out[0]:
5-element Vector{Int64}:
1
2
3
4
5
Подключение бэкэнда - метода отображения графики:
Формирование набора данных из начального датасета для сравнения:
Out[0]:
5-element Vector{Float64}:
19.7
22.1
23.0
23.4
21.9
Построение графика зависимости температуры от времени по исходным и спрогнозированным данным:
Так как исходный датасет имеет участки, в которых пропущенные значения были заменены линейной интерполяцией, то сложно оценить работу обученной нейросетевой модели на прямой.
Для этого были загружены реальные данные без пропусков:
Построение графика зависимости температуры от времени по реальным и спрогнозированным данным:
Проверим взаимосвязь полученных величин с помощью корреляции Пирсона, таким образом оценив точность полученной модели:
Коэффициент корреляции Пирсона может принимать значения от -1 до 1, где 0 будет означать отсутствие связи между переменными, а -1 и 1 - тесную связь (обратная и прямая зависимость соответственно).
В данном примере были предобработаны данные температурных наблюдений за последние пять лет, а также определена архитектура нейросети, параметры оптимизатора и функция потерь.
Модель была обучена и показала достаточно высокую, но не идеальную сходимость предсказанных значений с реальными данными. Для улучшения качества прогноза нейросеть может быть модифицирована путём изменения архитектуры слоёв и увеличения обучающей выборки.
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