Biostat 203B
Display system information for reproducibility.
import IPython
print(IPython.sys_info()){'commit_hash': '8b1204b6c',
'commit_source': 'installation',
'default_encoding': 'utf-8',
'ipython_path': '/opt/venv/lib/python3.10/site-packages/IPython',
'ipython_version': '8.21.0',
'os_name': 'posix',
'platform': 'Linux-6.6.12-linuxkit-aarch64-with-glibc2.35',
'sys_executable': '/opt/venv/bin/python',
'sys_platform': 'linux',
'sys_version': '3.10.12 (main, Nov 20 2023, 15:14:05) [GCC 11.4.0]'}sessionInfo()R version 4.3.2 (2023-10-31)
Platform: aarch64-unknown-linux-gnu (64-bit)
Running under: Ubuntu 22.04.3 LTS
Matrix products: default
BLAS: /usr/lib/aarch64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/aarch64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
loaded via a namespace (and not attached):
[1] digest_0.6.34 fastmap_1.1.1 xfun_0.42 Matrix_1.6-1.1
[5] lattice_0.21-9 reticulate_1.35.0 knitr_1.45 htmltools_0.5.7
[9] png_0.1-8 rmarkdown_2.25 cli_3.6.2 grid_4.3.2
[13] compiler_4.3.2 rstudioapi_0.15.0 tools_4.3.2 evaluate_0.23
[17] Rcpp_1.0.12 yaml_2.3.8 rlang_1.1.3 jsonlite_1.8.8
[21] htmlwidgets_1.6.4Load some libraries.
# Load the pandas library
import pandas as pd
# Load numpy for array manipulation
import numpy as np
# Load seaborn plotting library
import seaborn as sns
import matplotlib.pyplot as plt
# Set font sizes in plots
sns.set(font_scale = 1.2)
# Display all columns
pd.set_option('display.max_columns', None)
# Load Tensorflow and Keras
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layerslibrary(keras)
library(jpeg)In this example, we train a CNN (convolution neural network) on the CIFAR100 data set. Achieve testing accuracy 44.5% after 30 epochs. Random guess would have an accuracy of about 1%.
The CIFAR100 database is a large database of \(32 \times 32\) color images that is commonly used for training and testing machine learning algorithms.
50,000 training images, 10,000 testing images.
Acquire data:
# Load the data and split it between train and test sets
(x_train, y_train), (x_test, y_test) = keras.datasets.cifar100.load_data()Downloading data from https://www.cs.toronto.edu/~kriz/cifar-100-python.tar.gz
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169001437/169001437 [==============================] - 6s 0us/step# Training set
x_train.shape(50000, 32, 32, 3)y_train.shape(50000, 1)# Test set
x_test.shape(10000, 32, 32, 3)y_test.shape(10000, 1)cifar100 <- dataset_cifar100()
x_train <- cifar100$train$x
y_train <- cifar100$train$y
x_test <- cifar100$test$x
y_test <- cifar100$test$yTraining set:
dim(x_train)[1] 50000 32 32 3dim(y_train)[1] 50000 1Testing set:
dim(y_train)[1] 50000 1dim(y_test)[1] 10000 1For CNN, we keep the \(32 \times 32 \times 3\) tensor structure, instead of vectorizing into a long vector.
# Rescale
x_train = x_train / 255
x_test = x_test / 255
# Train
x_train.shape(50000, 32, 32, 3)# Test
x_test.shape(10000, 32, 32, 3)# rescale
x_train <- x_train / 255
x_test <- x_test / 255
dim(x_train)[1] 50000 32 32 3dim(x_test)[1] 10000 32 32 3Encode \(y\) as binary class matrix:
y_train = keras.utils.to_categorical(y_train, 100)
y_test = keras.utils.to_categorical(y_test, 100)
# Train
y_train.shape(50000, 100)# Test
y_test.shape(10000, 100)# First train instance
y_train[0]array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
dtype=float32)y_train <- to_categorical(y_train, 100)
y_test <- to_categorical(y_test, 100)
dim(y_train)[1] 50000 100dim(y_test)[1] 10000 100# head(y_train)Show a few images:
import matplotlib.pyplot as plt
# Feature: 32x32 color image
for i in range(25):
plt.figure()
plt.imshow(x_train[i]);
plt.show()
par(mar = c(0, 0, 0, 0), mfrow = c(5, 5))
index <- sample(seq(50000), 25)
for (i in index) plot(as.raster(x_train[i,,, ]))
Define a sequential model (a linear stack of layers) with 2 fully-connected hidden layers (256 and 128 neurons):
model = keras.Sequential(
[
keras.Input(shape = (32, 32, 3)),
layers.Conv2D(
filters = 32,
kernel_size = (3, 3),
padding = 'same',
activation = 'relu',
# input_shape = (32, 32, 3)
),
layers.MaxPooling2D(pool_size = (2, 2)),
layers.Conv2D(
filters = 64,
kernel_size = (3, 3),
padding = 'same',
activation = 'relu'
),
layers.MaxPooling2D(pool_size = (2, 2)),
layers.Conv2D(
filters = 128,
kernel_size = (3, 3),
padding = 'same',
activation = 'relu'
),
layers.MaxPooling2D(pool_size = (2, 2)),
layers.Conv2D(
filters = 256,
kernel_size = (3, 3),
padding = 'same',
activation = 'relu'
),
layers.MaxPooling2D(pool_size = (2, 2)),
layers.Flatten(),
layers.Dropout(rate = 0.5),
layers.Dense(units = 512, activation = 'relu'),
layers.Dense(units = 100, activation = 'softmax')
]
)
model.summary()Model: "sequential"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
conv2d (Conv2D) (None, 32, 32, 32) 896
max_pooling2d (MaxPooling2 (None, 16, 16, 32) 0
D)
conv2d_1 (Conv2D) (None, 16, 16, 64) 18496
max_pooling2d_1 (MaxPoolin (None, 8, 8, 64) 0
g2D)
conv2d_2 (Conv2D) (None, 8, 8, 128) 73856
max_pooling2d_2 (MaxPoolin (None, 4, 4, 128) 0
g2D)
conv2d_3 (Conv2D) (None, 4, 4, 256) 295168
max_pooling2d_3 (MaxPoolin (None, 2, 2, 256) 0
g2D)
flatten (Flatten) (None, 1024) 0
dropout (Dropout) (None, 1024) 0
dense (Dense) (None, 512) 524800
dense_1 (Dense) (None, 100) 51300
=================================================================
Total params: 964516 (3.68 MB)
Trainable params: 964516 (3.68 MB)
Non-trainable params: 0 (0.00 Byte)
_________________________________________________________________Plot the model:
tf.keras.utils.plot_model(
model,
to_file = "model.png",
show_shapes = True,
show_dtype = False,
show_layer_names = True,
rankdir = "TB",
expand_nested = False,
dpi = 96,
layer_range = None,
show_layer_activations = False,
)You must install pydot (`pip install pydot`) and install graphviz (see instructions at https://graphviz.gitlab.io/download/) for plot_model to work.
model <- keras_model_sequential() %>%
layer_conv_2d(
filters = 32,
kernel_size = c(3, 3),
padding = "same",
activation = "relu",
input_shape = c(32, 32, 3)
) %>%
layer_max_pooling_2d(pool_size = c(2, 2)) %>%
layer_conv_2d(
filters = 64,
kernel_size = c(3, 3),
padding = "same",
activation = "relu"
) %>%
layer_max_pooling_2d(pool_size = c(2, 2)) %>%
layer_conv_2d(
filters = 128,
kernel_size = c(3, 3),
padding = "same",
activation = "relu"
) %>%
layer_max_pooling_2d(pool_size = c(2, 2)) %>%
layer_conv_2d(
filters = 256,
kernel_size = c(3, 3),
padding = "same",
activation = "relu"
) %>%
layer_max_pooling_2d(pool_size = c(2, 2)) %>%
layer_flatten() %>%
layer_dropout(rate = 0.5) %>%
layer_dense(units = 512, activation = "relu") %>%
layer_dense(units = 100, activation = "softmax")
summary(model)Model: "sequential_1"
________________________________________________________________________________
Layer (type) Output Shape Param #
================================================================================
conv2d_7 (Conv2D) (None, 32, 32, 32) 896
max_pooling2d_7 (MaxPooling2D) (None, 16, 16, 32) 0
conv2d_6 (Conv2D) (None, 16, 16, 64) 18496
max_pooling2d_6 (MaxPooling2D) (None, 8, 8, 64) 0
conv2d_5 (Conv2D) (None, 8, 8, 128) 73856
max_pooling2d_5 (MaxPooling2D) (None, 4, 4, 128) 0
conv2d_4 (Conv2D) (None, 4, 4, 256) 295168
max_pooling2d_4 (MaxPooling2D) (None, 2, 2, 256) 0
flatten_1 (Flatten) (None, 1024) 0
dropout_1 (Dropout) (None, 1024) 0
dense_3 (Dense) (None, 512) 524800
dense_2 (Dense) (None, 100) 51300
================================================================================
Total params: 964516 (3.68 MB)
Trainable params: 964516 (3.68 MB)
Non-trainable params: 0 (0.00 Byte)
________________________________________________________________________________Compile the model with appropriate loss function, optimizer, and metrics:
model.compile(
loss = "categorical_crossentropy",
optimizer = "rmsprop",
metrics = ["accuracy"]
)model %>% compile(
loss = 'categorical_crossentropy',
optimizer = optimizer_rmsprop(),
metrics = c('accuracy')
)80%/20% split for the train/validation set. On my laptop, each epoch takes about half minute.
batch_size = 128
epochs = 30
history = model.fit(
x_train,
y_train,
batch_size = batch_size,
epochs = epochs,
validation_split = 0.2
)Plot training history:
hist = pd.DataFrame(history.history)
hist['epoch'] = np.arange(1, epochs + 1)
hist = hist.melt(
id_vars = ['epoch'],
value_vars = ['loss', 'accuracy', 'val_loss', 'val_accuracy'],
var_name = 'type',
value_name = 'value'
)
hist['split'] = np.where(['val' in s for s in hist['type']], 'validation', 'train')
hist['metric'] = np.where(['loss' in s for s in hist['type']], 'loss', 'accuracy')
# Accuracy trace plot
plt.figure()
sns.relplot(
data = hist[hist['metric'] == 'accuracy'],
kind = 'scatter',
x = 'epoch',
y = 'value',
hue = 'split'
).set(
xlabel = 'Epoch',
ylabel = 'Accuracy'
);
plt.show()
# Loss trace plot
plt.figure()
sns.relplot(
data = hist[hist['metric'] == 'loss'],
kind = 'scatter',
x = 'epoch',
y = 'value',
hue = 'split'
).set(
xlabel = 'Epoch',
ylabel = 'Loss'
);
plt.show()
system.time({
history <- model %>% fit(
x_train, y_train,
epochs = 30, batch_size = 128,
validation_split = 0.2
)
})Epoch 1/30
313/313 - 12s - loss: 4.2324 - accuracy: 0.0479 - val_loss: 3.8928 - val_accuracy: 0.1007 - 12s/epoch - 37ms/step
Epoch 2/30
313/313 - 11s - loss: 3.6810 - accuracy: 0.1334 - val_loss: 3.4087 - val_accuracy: 0.1859 - 11s/epoch - 36ms/step
Epoch 3/30
313/313 - 11s - loss: 3.3213 - accuracy: 0.1960 - val_loss: 3.3177 - val_accuracy: 0.2009 - 11s/epoch - 36ms/step
Epoch 4/30
313/313 - 11s - loss: 3.0629 - accuracy: 0.2442 - val_loss: 2.9877 - val_accuracy: 0.2666 - 11s/epoch - 36ms/step
Epoch 5/30
313/313 - 11s - loss: 2.8499 - accuracy: 0.2852 - val_loss: 2.9542 - val_accuracy: 0.2652 - 11s/epoch - 36ms/step
Epoch 6/30
313/313 - 11s - loss: 2.6751 - accuracy: 0.3219 - val_loss: 2.7540 - val_accuracy: 0.3177 - 11s/epoch - 37ms/step
Epoch 7/30
313/313 - 12s - loss: 2.5119 - accuracy: 0.3538 - val_loss: 2.5667 - val_accuracy: 0.3526 - 12s/epoch - 39ms/step
Epoch 8/30
313/313 - 12s - loss: 2.3687 - accuracy: 0.3819 - val_loss: 2.5618 - val_accuracy: 0.3470 - 12s/epoch - 38ms/step
Epoch 9/30
313/313 - 11s - loss: 2.2353 - accuracy: 0.4117 - val_loss: 2.4659 - val_accuracy: 0.3695 - 11s/epoch - 37ms/step
Epoch 10/30
313/313 - 12s - loss: 2.1188 - accuracy: 0.4354 - val_loss: 2.4559 - val_accuracy: 0.3791 - 12s/epoch - 38ms/step
Epoch 11/30
313/313 - 12s - loss: 2.0101 - accuracy: 0.4614 - val_loss: 2.3046 - val_accuracy: 0.4076 - 12s/epoch - 37ms/step
Epoch 12/30
313/313 - 12s - loss: 1.9032 - accuracy: 0.4827 - val_loss: 2.3713 - val_accuracy: 0.3998 - 12s/epoch - 37ms/step
Epoch 13/30
313/313 - 12s - loss: 1.7979 - accuracy: 0.5089 - val_loss: 2.2715 - val_accuracy: 0.4226 - 12s/epoch - 37ms/step
Epoch 14/30
313/313 - 12s - loss: 1.7050 - accuracy: 0.5266 - val_loss: 2.3203 - val_accuracy: 0.4111 - 12s/epoch - 37ms/step
Epoch 15/30
313/313 - 11s - loss: 1.6266 - accuracy: 0.5452 - val_loss: 2.2828 - val_accuracy: 0.4242 - 11s/epoch - 37ms/step
Epoch 16/30
313/313 - 11s - loss: 1.5506 - accuracy: 0.5646 - val_loss: 2.2076 - val_accuracy: 0.4397 - 11s/epoch - 37ms/step
Epoch 17/30
313/313 - 11s - loss: 1.4676 - accuracy: 0.5815 - val_loss: 2.3869 - val_accuracy: 0.4154 - 11s/epoch - 36ms/step
Epoch 18/30
313/313 - 11s - loss: 1.4044 - accuracy: 0.5954 - val_loss: 2.2411 - val_accuracy: 0.4457 - 11s/epoch - 36ms/step
Epoch 19/30
313/313 - 12s - loss: 1.3215 - accuracy: 0.6185 - val_loss: 2.3227 - val_accuracy: 0.4362 - 12s/epoch - 37ms/step
Epoch 20/30
313/313 - 11s - loss: 1.2654 - accuracy: 0.6323 - val_loss: 2.3015 - val_accuracy: 0.4403 - 11s/epoch - 36ms/step
Epoch 21/30
313/313 - 11s - loss: 1.2092 - accuracy: 0.6478 - val_loss: 2.2746 - val_accuracy: 0.4444 - 11s/epoch - 36ms/step
Epoch 22/30
313/313 - 11s - loss: 1.1527 - accuracy: 0.6573 - val_loss: 2.3165 - val_accuracy: 0.4467 - 11s/epoch - 36ms/step
Epoch 23/30
313/313 - 11s - loss: 1.1081 - accuracy: 0.6709 - val_loss: 2.3376 - val_accuracy: 0.4478 - 11s/epoch - 36ms/step
Epoch 24/30
313/313 - 11s - loss: 1.0640 - accuracy: 0.6835 - val_loss: 2.3923 - val_accuracy: 0.4321 - 11s/epoch - 36ms/step
Epoch 25/30
313/313 - 11s - loss: 1.0223 - accuracy: 0.6936 - val_loss: 2.5082 - val_accuracy: 0.4384 - 11s/epoch - 36ms/step
Epoch 26/30
313/313 - 11s - loss: 0.9673 - accuracy: 0.7070 - val_loss: 2.4766 - val_accuracy: 0.4387 - 11s/epoch - 36ms/step
Epoch 27/30
313/313 - 11s - loss: 0.9430 - accuracy: 0.7146 - val_loss: 2.3742 - val_accuracy: 0.4426 - 11s/epoch - 36ms/step
Epoch 28/30
313/313 - 11s - loss: 0.9014 - accuracy: 0.7236 - val_loss: 2.4442 - val_accuracy: 0.4514 - 11s/epoch - 36ms/step
Epoch 29/30
313/313 - 11s - loss: 0.8834 - accuracy: 0.7289 - val_loss: 2.6080 - val_accuracy: 0.4310 - 11s/epoch - 36ms/step
Epoch 30/30
313/313 - 11s - loss: 0.8477 - accuracy: 0.7383 - val_loss: 2.5085 - val_accuracy: 0.4524 - 11s/epoch - 36ms/step user system elapsed
2887.588 126.822 345.324 plot(history)
Evaluate model performance on the test data:
score = model.evaluate(x_test, y_test, verbose = 0)
print("Test loss:", score[0])Test loss: 2.5904178619384766print("Test accuracy:", score[1])Test accuracy: 0.43849998712539673
model %>% evaluate(x_test, y_test)313/313 - 1s - loss: 2.4325 - accuracy: 0.4631 - 1s/epoch - 4ms/step loss accuracy
2.432508 0.463100 Generate predictions on new data:
model %>% predict(x_test) %>% k_argmax()313/313 - 1s - 1s/epoch - 4ms/steptf.Tensor([95 80 55 ... 51 42 26], shape=(10000), dtype=int64)