作者: JacoVerster
创建日期 2021/05/20
上次修改日期 2021/06/06
描述:对训练集大小与模型准确率之间的关系进行建模。
在许多现实场景中,用于训练深度学习模型的图像数据量有限。这在医学影像领域尤其常见,因为数据集的创建成本很高。在解决新问题时,通常首先出现的问题之一是:“我们需要多少图像才能训练出一个足够好的机器学习模型?”
在大多数情况下,只有少量样本可用,我们可以利用这些样本对训练数据量与模型性能之间的关系进行建模。这种模型可用于估算图像的最佳数量,从而达到能够实现所需模型性能的样本量。
Balki 等人发表的关于样本量确定方法的系统综述提供了多种样本量确定方法的示例。在本示例中,使用了一种平衡的子采样方案来确定模型的最佳样本量。具体方法是:选择包含 Y 个图像的随机子样本,并使用该子样本训练模型。然后,在独立的测试集上评估模型。对于每个子样本,重复此过程 N 次(并进行替换),以便能够构建观测性能的均值和置信区间。
import os
os.environ["KERAS_BACKEND"] = "tensorflow"
import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
import keras
from keras import layers
import tensorflow_datasets as tfds
# Define seed and fixed variables
seed = 42
keras.utils.set_random_seed(seed)
AUTO = tf.data.AUTOTUNE
我们将使用TF Flowers 数据集。
# Specify dataset parameters
dataset_name = "tf_flowers"
batch_size = 64
image_size = (224, 224)
# Load data from tfds and split 10% off for a test set
(train_data, test_data), ds_info = tfds.load(
dataset_name,
split=["train[:90%]", "train[90%:]"],
shuffle_files=True,
as_supervised=True,
with_info=True,
)
# Extract number of classes and list of class names
num_classes = ds_info.features["label"].num_classes
class_names = ds_info.features["label"].names
print(f"Number of classes: {num_classes}")
print(f"Class names: {class_names}")
# Convert datasets to NumPy arrays
def dataset_to_array(dataset, image_size, num_classes):
images, labels = [], []
for img, lab in dataset.as_numpy_iterator():
images.append(tf.image.resize(img, image_size).numpy())
labels.append(tf.one_hot(lab, num_classes))
return np.array(images), np.array(labels)
img_train, label_train = dataset_to_array(train_data, image_size, num_classes)
img_test, label_test = dataset_to_array(test_data, image_size, num_classes)
num_train_samples = len(img_train)
print(f"Number of training samples: {num_train_samples}")
Number of classes: 5
Class names: ['dandelion', 'daisy', 'tulips', 'sunflowers', 'roses']
Number of training samples: 3303
plt.figure(figsize=(16, 12))
for n in range(30):
ax = plt.subplot(5, 6, n + 1)
plt.imshow(img_test[n].astype("uint8"))
plt.title(np.array(class_names)[label_test[n] == True][0])
plt.axis("off")
使用 Keras 预处理层定义图像增强,并将其应用于训练集。
# Define image augmentation model
image_augmentation = keras.Sequential(
[
layers.RandomFlip(mode="horizontal"),
layers.RandomRotation(factor=0.1),
layers.RandomZoom(height_factor=(-0.1, -0)),
layers.RandomContrast(factor=0.1),
],
)
# Apply the augmentations to the training images and plot a few examples
img_train = image_augmentation(img_train).numpy()
plt.figure(figsize=(16, 12))
for n in range(30):
ax = plt.subplot(5, 6, n + 1)
plt.imshow(img_train[n].astype("uint8"))
plt.title(np.array(class_names)[label_train[n] == True][0])
plt.axis("off")
我们创建了一些方便的函数来构建迁移学习模型,编译和训练模型,以及解冻层以进行微调。
def build_model(num_classes, img_size=image_size[0], top_dropout=0.3):
"""Creates a classifier based on pre-trained MobileNetV2.
Arguments:
num_classes: Int, number of classese to use in the softmax layer.
img_size: Int, square size of input images (defaults is 224).
top_dropout: Int, value for dropout layer (defaults is 0.3).
Returns:
Uncompiled Keras model.
"""
# Create input and pre-processing layers for MobileNetV2
inputs = layers.Input(shape=(img_size, img_size, 3))
x = layers.Rescaling(scale=1.0 / 127.5, offset=-1)(inputs)
model = keras.applications.MobileNetV2(
include_top=False, weights="imagenet", input_tensor=x
)
# Freeze the pretrained weights
model.trainable = False
# Rebuild top
x = layers.GlobalAveragePooling2D(name="avg_pool")(model.output)
x = layers.Dropout(top_dropout)(x)
outputs = layers.Dense(num_classes, activation="softmax")(x)
model = keras.Model(inputs, outputs)
print("Trainable weights:", len(model.trainable_weights))
print("Non_trainable weights:", len(model.non_trainable_weights))
return model
def compile_and_train(
model,
training_data,
training_labels,
metrics=[keras.metrics.AUC(name="auc"), "acc"],
optimizer=keras.optimizers.Adam(),
patience=5,
epochs=5,
):
"""Compiles and trains the model.
Arguments:
model: Uncompiled Keras model.
training_data: NumPy Array, training data.
training_labels: NumPy Array, training labels.
metrics: Keras/TF metrics, requires at least 'auc' metric (default is
`[keras.metrics.AUC(name='auc'), 'acc']`).
optimizer: Keras/TF optimizer (defaults is `keras.optimizers.Adam()).
patience: Int, epochsfor EarlyStopping patience (defaults is 5).
epochs: Int, number of epochs to train (default is 5).
Returns:
Training history for trained Keras model.
"""
stopper = keras.callbacks.EarlyStopping(
monitor="val_auc",
mode="max",
min_delta=0,
patience=patience,
verbose=1,
restore_best_weights=True,
)
model.compile(loss="categorical_crossentropy", optimizer=optimizer, metrics=metrics)
history = model.fit(
x=training_data,
y=training_labels,
batch_size=batch_size,
epochs=epochs,
validation_split=0.1,
callbacks=[stopper],
)
return history
def unfreeze(model, block_name, verbose=0):
"""Unfreezes Keras model layers.
Arguments:
model: Keras model.
block_name: Str, layer name for example block_name = 'block4'.
Checks if supplied string is in the layer name.
verbose: Int, 0 means silent, 1 prints out layers trainability status.
Returns:
Keras model with all layers after (and including) the specified
block_name to trainable, excluding BatchNormalization layers.
"""
# Unfreeze from block_name onwards
set_trainable = False
for layer in model.layers:
if block_name in layer.name:
set_trainable = True
if set_trainable and not isinstance(layer, layers.BatchNormalization):
layer.trainable = True
if verbose == 1:
print(layer.name, "trainable")
else:
if verbose == 1:
print(layer.name, "NOT trainable")
print("Trainable weights:", len(model.trainable_weights))
print("Non-trainable weights:", len(model.non_trainable_weights))
return model
为了在多个子样本集上训练模型,我们需要创建一个迭代训练函数。
def train_model(training_data, training_labels):
"""Trains the model as follows:
- Trains only the top layers for 10 epochs.
- Unfreezes deeper layers.
- Train for 20 more epochs.
Arguments:
training_data: NumPy Array, training data.
training_labels: NumPy Array, training labels.
Returns:
Model accuracy.
"""
model = build_model(num_classes)
# Compile and train top layers
history = compile_and_train(
model,
training_data,
training_labels,
metrics=[keras.metrics.AUC(name="auc"), "acc"],
optimizer=keras.optimizers.Adam(),
patience=3,
epochs=10,
)
# Unfreeze model from block 10 onwards
model = unfreeze(model, "block_10")
# Compile and train for 20 epochs with a lower learning rate
fine_tune_epochs = 20
total_epochs = history.epoch[-1] + fine_tune_epochs
history_fine = compile_and_train(
model,
training_data,
training_labels,
metrics=[keras.metrics.AUC(name="auc"), "acc"],
optimizer=keras.optimizers.Adam(learning_rate=1e-4),
patience=5,
epochs=total_epochs,
)
# Calculate model accuracy on the test set
_, _, acc = model.evaluate(img_test, label_test)
return np.round(acc, 4)
现在我们有了模型构建函数和支持的迭代函数,就可以在多个子样本分割上训练模型了。
请注意,这将训练 20 个模型,需要一些时间。请确保您已启用 GPU 运行时。
为了使本示例保持轻量级,提供了先前训练运行的样本数据。
def train_iteratively(sample_splits=[0.05, 0.1, 0.25, 0.5], iter_per_split=5):
"""Trains a model iteratively over several sample splits.
Arguments:
sample_splits: List/NumPy array, contains fractions of the trainins set
to train over.
iter_per_split: Int, number of times to train a model per sample split.
Returns:
Training accuracy for all splits and iterations and the number of samples
used for training at each split.
"""
# Train all the sample models and calculate accuracy
train_acc = []
sample_sizes = []
for fraction in sample_splits:
print(f"Fraction split: {fraction}")
# Repeat training 3 times for each sample size
sample_accuracy = []
num_samples = int(num_train_samples * fraction)
for i in range(iter_per_split):
print(f"Run {i+1} out of {iter_per_split}:")
# Create fractional subsets
rand_idx = np.random.randint(num_train_samples, size=num_samples)
train_img_subset = img_train[rand_idx, :]
train_label_subset = label_train[rand_idx, :]
# Train model and calculate accuracy
accuracy = train_model(train_img_subset, train_label_subset)
print(f"Accuracy: {accuracy}")
sample_accuracy.append(accuracy)
train_acc.append(sample_accuracy)
sample_sizes.append(num_samples)
return train_acc, sample_sizes
# Running the above function produces the following outputs
train_acc = [
[0.8202, 0.7466, 0.8011, 0.8447, 0.8229],
[0.861, 0.8774, 0.8501, 0.8937, 0.891],
[0.891, 0.9237, 0.8856, 0.9101, 0.891],
[0.8937, 0.9373, 0.9128, 0.8719, 0.9128],
]
sample_sizes = [165, 330, 825, 1651]
现在,我们通过在平均准确率点拟合指数曲线来绘制学习曲线。我们使用 TF 在数据上拟合指数函数。
然后,我们外推学习曲线以预测在整个训练集上训练的模型的准确率。
def fit_and_predict(train_acc, sample_sizes, pred_sample_size):
"""Fits a learning curve to model training accuracy results.
Arguments:
train_acc: List/Numpy Array, training accuracy for all model
training splits and iterations.
sample_sizes: List/Numpy array, number of samples used for training at
each split.
pred_sample_size: Int, sample size to predict model accuracy based on
fitted learning curve.
"""
x = sample_sizes
mean_acc = tf.convert_to_tensor([np.mean(i) for i in train_acc])
error = [np.std(i) for i in train_acc]
# Define mean squared error cost and exponential curve fit functions
mse = keras.losses.MeanSquaredError()
def exp_func(x, a, b):
return a * x**b
# Define variables, learning rate and number of epochs for fitting with TF
a = tf.Variable(0.0)
b = tf.Variable(0.0)
learning_rate = 0.01
training_epochs = 5000
# Fit the exponential function to the data
for epoch in range(training_epochs):
with tf.GradientTape() as tape:
y_pred = exp_func(x, a, b)
cost_function = mse(y_pred, mean_acc)
# Get gradients and compute adjusted weights
gradients = tape.gradient(cost_function, [a, b])
a.assign_sub(gradients[0] * learning_rate)
b.assign_sub(gradients[1] * learning_rate)
print(f"Curve fit weights: a = {a.numpy()} and b = {b.numpy()}.")
# We can now estimate the accuracy for pred_sample_size
max_acc = exp_func(pred_sample_size, a, b).numpy()
# Print predicted x value and append to plot values
print(f"A model accuracy of {max_acc} is predicted for {pred_sample_size} samples.")
x_cont = np.linspace(x[0], pred_sample_size, 100)
# Build the plot
fig, ax = plt.subplots(figsize=(12, 6))
ax.errorbar(x, mean_acc, yerr=error, fmt="o", label="Mean acc & std dev.")
ax.plot(x_cont, exp_func(x_cont, a, b), "r-", label="Fitted exponential curve.")
ax.set_ylabel("Model classification accuracy.", fontsize=12)
ax.set_xlabel("Training sample size.", fontsize=12)
ax.set_xticks(np.append(x, pred_sample_size))
ax.set_yticks(np.append(mean_acc, max_acc))
ax.set_xticklabels(list(np.append(x, pred_sample_size)), rotation=90, fontsize=10)
ax.yaxis.set_tick_params(labelsize=10)
ax.set_title("Learning curve: model accuracy vs sample size.", fontsize=14)
ax.legend(loc=(0.75, 0.75), fontsize=10)
ax.xaxis.grid(True)
ax.yaxis.grid(True)
plt.tight_layout()
plt.show()
# The mean absolute error (MAE) is calculated for curve fit to see how well
# it fits the data. The lower the error the better the fit.
mae = keras.losses.MeanAbsoluteError()
print(f"The mae for the curve fit is {mae(mean_acc, exp_func(x, a, b)).numpy()}.")
# We use the whole training set to predict the model accuracy
fit_and_predict(train_acc, sample_sizes, pred_sample_size=num_train_samples)
Curve fit weights: a = 0.6445642113685608 and b = 0.048097413033246994.
A model accuracy of 0.9517362117767334 is predicted for 3303 samples.
The mae for the curve fit is 0.016098767518997192.
从外推曲线可以看出,3303 张图像将产生约 95% 的估计准确率。
现在,让我们使用所有数据(3303 张图像)并训练模型,看看我们的预测是否准确!
# Now train the model with full dataset to get the actual accuracy
accuracy = train_model(img_train, label_train)
print(f"A model accuracy of {accuracy} is reached on {num_train_samples} images!")
/var/folders/8n/8w8cqnvj01xd4ghznl11nyn000_93_/T/ipykernel_30919/1838736464.py:16: UserWarning: `input_shape` is undefined or non-square, or `rows` is not in [96, 128, 160, 192, 224]. Weights for input shape (224, 224) will be loaded as the default.
model = keras.applications.MobileNetV2(
Trainable weights: 2
Non_trainable weights: 260
Epoch 1/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 18s 338ms/step - acc: 0.4305 - auc: 0.7221 - loss: 1.4585 - val_acc: 0.8218 - val_auc: 0.9700 - val_loss: 0.5043
Epoch 2/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 15s 326ms/step - acc: 0.7666 - auc: 0.9504 - loss: 0.6287 - val_acc: 0.8792 - val_auc: 0.9838 - val_loss: 0.3733
Epoch 3/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 16s 332ms/step - acc: 0.8252 - auc: 0.9673 - loss: 0.5039 - val_acc: 0.8852 - val_auc: 0.9880 - val_loss: 0.3182
Epoch 4/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 16s 348ms/step - acc: 0.8458 - auc: 0.9768 - loss: 0.4264 - val_acc: 0.8822 - val_auc: 0.9893 - val_loss: 0.2956
Epoch 5/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 16s 350ms/step - acc: 0.8661 - auc: 0.9812 - loss: 0.3821 - val_acc: 0.8912 - val_auc: 0.9903 - val_loss: 0.2755
Epoch 6/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 16s 336ms/step - acc: 0.8656 - auc: 0.9836 - loss: 0.3555 - val_acc: 0.9003 - val_auc: 0.9906 - val_loss: 0.2701
Epoch 7/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 16s 331ms/step - acc: 0.8800 - auc: 0.9846 - loss: 0.3430 - val_acc: 0.8943 - val_auc: 0.9914 - val_loss: 0.2548
Epoch 8/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 16s 333ms/step - acc: 0.8917 - auc: 0.9871 - loss: 0.3143 - val_acc: 0.8973 - val_auc: 0.9917 - val_loss: 0.2494
Epoch 9/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 15s 320ms/step - acc: 0.9003 - auc: 0.9891 - loss: 0.2906 - val_acc: 0.9063 - val_auc: 0.9908 - val_loss: 0.2463
Epoch 10/10
47/47 ━━━━━━━━━━━━━━━━━━━━ 15s 324ms/step - acc: 0.8997 - auc: 0.9895 - loss: 0.2839 - val_acc: 0.9124 - val_auc: 0.9912 - val_loss: 0.2394
Trainable weights: 24
Non-trainable weights: 238
Epoch 1/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 27s 537ms/step - acc: 0.8457 - auc: 0.9747 - loss: 0.4365 - val_acc: 0.9094 - val_auc: 0.9916 - val_loss: 0.2692
Epoch 2/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 24s 502ms/step - acc: 0.9223 - auc: 0.9932 - loss: 0.2198 - val_acc: 0.9033 - val_auc: 0.9891 - val_loss: 0.2826
Epoch 3/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 25s 534ms/step - acc: 0.9499 - auc: 0.9972 - loss: 0.1399 - val_acc: 0.9003 - val_auc: 0.9910 - val_loss: 0.2804
Epoch 4/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 26s 554ms/step - acc: 0.9590 - auc: 0.9983 - loss: 0.1130 - val_acc: 0.9396 - val_auc: 0.9968 - val_loss: 0.1510
Epoch 5/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 25s 533ms/step - acc: 0.9805 - auc: 0.9996 - loss: 0.0538 - val_acc: 0.9486 - val_auc: 0.9914 - val_loss: 0.1795
Epoch 6/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 24s 516ms/step - acc: 0.9949 - auc: 1.0000 - loss: 0.0226 - val_acc: 0.9124 - val_auc: 0.9833 - val_loss: 0.3186
Epoch 7/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 25s 534ms/step - acc: 0.9900 - auc: 0.9999 - loss: 0.0297 - val_acc: 0.9275 - val_auc: 0.9881 - val_loss: 0.3017
Epoch 8/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 25s 536ms/step - acc: 0.9910 - auc: 0.9999 - loss: 0.0228 - val_acc: 0.9426 - val_auc: 0.9927 - val_loss: 0.1938
Epoch 9/29
47/47 ━━━━━━━━━━━━━━━━━━━━ 0s 489ms/step - acc: 0.9995 - auc: 1.0000 - loss: 0.0069Restoring model weights from the end of the best epoch: 4.
47/47 ━━━━━━━━━━━━━━━━━━━━ 25s 527ms/step - acc: 0.9995 - auc: 1.0000 - loss: 0.0068 - val_acc: 0.9426 - val_auc: 0.9919 - val_loss: 0.2957
Epoch 9: early stopping
12/12 ━━━━━━━━━━━━━━━━━━━━ 2s 170ms/step - acc: 0.9641 - auc: 0.9972 - loss: 0.1264
A model accuracy of 0.9964 is reached on 3303 images!
我们看到,使用 3303 张图像可以达到约 94-96%* 的模型准确率。这与我们的估计非常接近!
即使我们只使用了 50% 的数据集(1651 张图像),我们也能够对模型的训练行为进行建模,并预测给定图像数量下的模型准确率。同样的方法可用于预测达到所需准确率所需的图像数量。当可用数据量较少时,这非常有用,并且已证明深度学习模型可以收敛,但需要更多图像。图像数量预测可用于规划和预算进一步的图像收集工作。