I'm trying to build a simple regression model using keras and tensorflow. In my problem I have data in the form (x, y), where x and y are simply numbers. I'd like to build a keras model in order to predict y using x as an input.
Since I think images better explains thing, these are my data:
We may discuss if they are good or not, but in my problem I cannot really cheat them.
My keras model is the following (data are splitted 30% test (X_test, y_test) and 70% training (X_train, y_train)):
model = tf.keras.Sequential()
model.add(tf.keras.layers.Dense(32, input_shape=() activation="relu", name="first_layer"))
model.add(tf.keras.layers.Dense(16, activation="relu", name="second_layer"))
model.add(tf.keras.layers.Dense(1, name="output_layer"))
model.compile(loss = "mean_squared_error", optimizer = "adam", metrics=["mse"] )
history = model.fit(X_train, y_train, epochs=500, batch_size=1, verbose=0, shuffle=False)
eval_result = model.evaluate(X_test, y_test)
print("\n\nTest loss:", eval_result, "\n")
predict_Y = model.predict(X)
note: X contains both X_test and X_train.
Plotting the prediction I get (blue squares are the prediction predict_Y)
I'm playing a lot with layers, activation funztions and other parameters. My goal is to find the best parameters to train the model, but the actual question, here, is slightly different: in fact I have hard times to force the model to overfit the data (as you can see from the above results).
Does anyone have some sort of idea about how to reproduce overfitting?
This is the outcome I would like to get:
(red dots are under blue squares!)
EDIT:
Here I provide you the data used in the example above: you can copy paste directly to a python interpreter:
X_train = [0.704619794270697, 0.6779457393024553, 0.8207082120250023, 0.8588819357831449, 0.8692320257603844, 0.6878750931810429, 0.9556331888763945, 0.77677964510883, 0.7211381534179618, 0.6438319113259414, 0.6478339581502052, 0.9710222750072649, 0.8952188423349681, 0.6303124926673513, 0.9640316662124185, 0.869691568491902, 0.8320164648420931, 0.8236399177660375, 0.8877334038470911, 0.8084042532069621, 0.8045680821762038]
y_train = [0.7766424210611557, 0.8210846773655833, 0.9996114311913593, 0.8041331063189883, 0.9980525368790883, 0.8164056182686034, 0.8925487603333683, 0.7758207470960685, 0.37345286573743475, 0.9325789202459493, 0.6060269037514895, 0.9319771743389491, 0.9990691225991941, 0.9320002808310418, 0.9992560731072977, 0.9980241561997089, 0.8882905258641204, 0.4678339275898943, 0.9312152374846061, 0.9542371205095945, 0.8885893668675711]
X_test = [0.9749191829308574, 0.8735366740730178, 0.8882783211709133, 0.8022891400991644, 0.8650601322313454, 0.8697902997857514, 1.0, 0.8165876695985228, 0.8923841531760973]
y_test = [0.975653685270635, 0.9096752789481569, 0.6653736469114154, 0.46367666660348744, 0.9991817903431941, 1.0, 0.9111205717076893, 0.5264993912088891, 0.9989199241685126]
X = [0.704619794270697, 0.77677964510883, 0.7211381534179618, 0.6478339581502052, 0.6779457393024553, 0.8588819357831449, 0.8045680821762038, 0.8320164648420931, 0.8650601322313454, 0.8697902997857514, 0.8236399177660375, 0.6878750931810429, 0.8923841531760973, 0.8692320257603844, 0.8877334038470911, 0.8735366740730178, 0.8207082120250023, 0.8022891400991644, 0.6303124926673513, 0.8084042532069621, 0.869691568491902, 0.9710222750072649, 0.9556331888763945, 0.8882783211709133, 0.8165876695985228, 0.6438319113259414, 0.8952188423349681, 0.9749191829308574, 1.0, 0.9640316662124185]
Y = [0.7766424210611557, 0.7758207470960685, 0.37345286573743475, 0.6060269037514895, 0.8210846773655833, 0.8041331063189883, 0.8885893668675711, 0.8882905258641204, 0.9991817903431941, 1.0, 0.4678339275898943, 0.8164056182686034, 0.9989199241685126, 0.9980525368790883, 0.9312152374846061, 0.9096752789481569, 0.9996114311913593, 0.46367666660348744, 0.9320002808310418, 0.9542371205095945, 0.9980241561997089, 0.9319771743389491, 0.8925487603333683, 0.6653736469114154, 0.5264993912088891, 0.9325789202459493, 0.9990691225991941, 0.975653685270635, 0.9111205717076893, 0.9992560731072977]
Where X contains the list of the x values and Y the corresponding y value. (X_test, y_test) and (X_train, y_train) are two (non overlapping) subset of (X, Y).
To predict and show the model results I simply use matplotlib (imported as plt):
predict_Y = model.predict(X)
plt.plot(X, Y, "ro", X, predict_Y, "bs")
plt.show()
Overfitted models are rarely useful in real life. It appears to me that OP is well aware of that but wants to see if NNs are indeed capable of fitting (bounded) arbitrary functions or not. On one hand, the input-output data in the example seems to obey no discernible pattern. On the other hand, both input and output are scalars in [0, 1] and there are only 21 data points in the training set.
Based on my experiments and results, we can indeed overfit as requested. See the image below.
Numerical results:
x y_true y_pred error
0 0.704620 0.776642 0.773753 -0.002889
1 0.677946 0.821085 0.819597 -0.001488
2 0.820708 0.999611 0.999813 0.000202
3 0.858882 0.804133 0.805160 0.001026
4 0.869232 0.998053 0.997862 -0.000190
5 0.687875 0.816406 0.814692 -0.001714
6 0.955633 0.892549 0.893117 0.000569
7 0.776780 0.775821 0.779289 0.003469
8 0.721138 0.373453 0.374007 0.000554
9 0.643832 0.932579 0.912565 -0.020014
10 0.647834 0.606027 0.607253 0.001226
11 0.971022 0.931977 0.931549 -0.000428
12 0.895219 0.999069 0.999051 -0.000018
13 0.630312 0.932000 0.930252 -0.001748
14 0.964032 0.999256 0.999204 -0.000052
15 0.869692 0.998024 0.997859 -0.000165
16 0.832016 0.888291 0.887883 -0.000407
17 0.823640 0.467834 0.460728 -0.007106
18 0.887733 0.931215 0.932790 0.001575
19 0.808404 0.954237 0.960282 0.006045
20 0.804568 0.888589 0.906829 0.018240
{'me': -0.00015776709314323828,
'mae': 0.00329163070145315,
'mse': 4.0713782563067185e-05,
'rmse': 0.006380735268216915}
OP's code seems good to me. My changes were minor:
Use deeper networks. It may not actually be necessary to use a depth of 30 layers but since we just want to overfit, I didn't experiment too much with what's the minimum depth needed.
Each Dense layer has 50 units. Again, this may be overkill.
Added batch normalization layer every 5th dense layer.
Decreased learning rate by half.
Ran optimization for longer using the all 21 training examples in a batch.
Used MAE as objective function. MSE is good but since we want to overfit, I want to penalize small errors the same way as large errors.
Random numbers are more important here because data appears to be arbitrary. Though, you should get similar results if you change random number seed and let the optimizer run long enough. In some cases, optimization does get stuck in a local minima and it would not produce overfitting (as requested by OP).
The code is below.
import numpy as np
import pandas as pd
import tensorflow as tf
from tensorflow.keras.layers import Input, Dense, BatchNormalization
from tensorflow.keras.models import Model
from tensorflow.keras.optimizers import Adam
import matplotlib.pyplot as plt
# Set seed just to have reproducible results
np.random.seed(84)
tf.random.set_seed(84)
# Load data from the post
# https://stackoverflow.com/questions/61252785/how-to-overfit-data-with-keras
X_train = np.array([0.704619794270697, 0.6779457393024553, 0.8207082120250023,
0.8588819357831449, 0.8692320257603844, 0.6878750931810429,
0.9556331888763945, 0.77677964510883, 0.7211381534179618,
0.6438319113259414, 0.6478339581502052, 0.9710222750072649,
0.8952188423349681, 0.6303124926673513, 0.9640316662124185,
0.869691568491902, 0.8320164648420931, 0.8236399177660375,
0.8877334038470911, 0.8084042532069621,
0.8045680821762038])
Y_train = np.array([0.7766424210611557, 0.8210846773655833, 0.9996114311913593,
0.8041331063189883, 0.9980525368790883, 0.8164056182686034,
0.8925487603333683, 0.7758207470960685,
0.37345286573743475, 0.9325789202459493,
0.6060269037514895, 0.9319771743389491, 0.9990691225991941,
0.9320002808310418, 0.9992560731072977, 0.9980241561997089,
0.8882905258641204, 0.4678339275898943, 0.9312152374846061,
0.9542371205095945, 0.8885893668675711])
X_test = np.array([0.9749191829308574, 0.8735366740730178, 0.8882783211709133,
0.8022891400991644, 0.8650601322313454, 0.8697902997857514,
1.0, 0.8165876695985228, 0.8923841531760973])
Y_test = np.array([0.975653685270635, 0.9096752789481569, 0.6653736469114154,
0.46367666660348744, 0.9991817903431941, 1.0,
0.9111205717076893, 0.5264993912088891, 0.9989199241685126])
X = np.array([0.704619794270697, 0.77677964510883, 0.7211381534179618,
0.6478339581502052, 0.6779457393024553, 0.8588819357831449,
0.8045680821762038, 0.8320164648420931, 0.8650601322313454,
0.8697902997857514, 0.8236399177660375, 0.6878750931810429,
0.8923841531760973, 0.8692320257603844, 0.8877334038470911,
0.8735366740730178, 0.8207082120250023, 0.8022891400991644,
0.6303124926673513, 0.8084042532069621, 0.869691568491902,
0.9710222750072649, 0.9556331888763945, 0.8882783211709133,
0.8165876695985228, 0.6438319113259414, 0.8952188423349681,
0.9749191829308574, 1.0, 0.9640316662124185])
Y = np.array([0.7766424210611557, 0.7758207470960685, 0.37345286573743475,
0.6060269037514895, 0.8210846773655833, 0.8041331063189883,
0.8885893668675711, 0.8882905258641204, 0.9991817903431941, 1.0,
0.4678339275898943, 0.8164056182686034, 0.9989199241685126,
0.9980525368790883, 0.9312152374846061, 0.9096752789481569,
0.9996114311913593, 0.46367666660348744, 0.9320002808310418,
0.9542371205095945, 0.9980241561997089, 0.9319771743389491,
0.8925487603333683, 0.6653736469114154, 0.5264993912088891,
0.9325789202459493, 0.9990691225991941, 0.975653685270635,
0.9111205717076893, 0.9992560731072977])
# Reshape all data to be of the shape (batch_size, 1)
X_train = X_train.reshape((-1, 1))
Y_train = Y_train.reshape((-1, 1))
X_test = X_test.reshape((-1, 1))
Y_test = Y_test.reshape((-1, 1))
X = X.reshape((-1, 1))
Y = Y.reshape((-1, 1))
# Is data scaled? NNs do well with bounded data.
assert np.all(X_train >= 0) and np.all(X_train <= 1)
assert np.all(Y_train >= 0) and np.all(Y_train <= 1)
assert np.all(X_test >= 0) and np.all(X_test <= 1)
assert np.all(Y_test >= 0) and np.all(Y_test <= 1)
assert np.all(X >= 0) and np.all(X <= 1)
assert np.all(Y >= 0) and np.all(Y <= 1)
# Build a model with variable number of hidden layers.
# We will use Keras functional API.
# https://www.perfectlyrandom.org/2019/06/24/a-guide-to-keras-functional-api/
n_dense_layers = 30 # increase this to get more complicated models
# Define the layers first.
input_tensor = Input(shape=(1,), name='input')
layers = []
for i in range(n_dense_layers):
layers += [Dense(units=50, activation='relu', name=f'dense_layer_{i}')]
if (i > 0) & (i % 5 == 0):
# avg over batches not features
layers += [BatchNormalization(axis=1)]
sigmoid_layer = Dense(units=1, activation='sigmoid', name='sigmoid_layer')
# Connect the layers using Keras Functional API
mid_layer = input_tensor
for dense_layer in layers:
mid_layer = dense_layer(mid_layer)
output_tensor = sigmoid_layer(mid_layer)
model = Model(inputs=[input_tensor], outputs=[output_tensor])
optimizer = Adam(learning_rate=0.0005)
model.compile(optimizer=optimizer, loss='mae', metrics=['mae'])
model.fit(x=[X_train], y=[Y_train], epochs=40000, batch_size=21)
# Predict on various datasets
Y_train_pred = model.predict(X_train)
# Create a dataframe to inspect results manually
train_df = pd.DataFrame({
'x': X_train.reshape((-1)),
'y_true': Y_train.reshape((-1)),
'y_pred': Y_train_pred.reshape((-1))
})
train_df['error'] = train_df['y_pred'] - train_df['y_true']
print(train_df)
# A dictionary to store all the errors in one place.
train_errors = {
'me': np.mean(train_df['error']),
'mae': np.mean(np.abs(train_df['error'])),
'mse': np.mean(np.square(train_df['error'])),
'rmse': np.sqrt(np.mean(np.square(train_df['error']))),
}
print(train_errors)
# Make a plot to visualize true vs predicted
plt.figure(1)
plt.clf()
plt.plot(train_df['x'], train_df['y_true'], 'r.', label='y_true')
plt.plot(train_df['x'], train_df['y_pred'], 'bo', alpha=0.25, label='y_pred')
plt.grid(True)
plt.xlabel('x')
plt.ylabel('y')
plt.title(f'Train data. MSE={np.round(train_errors["mse"], 5)}.')
plt.legend()
plt.show(block=False)
plt.savefig('true_vs_pred.png')
A problem you may encountering is that you don't have enough training data for the model to be able to fit well. In your example, you only have 21 training instances, each with only 1 feature. Broadly speaking with neural network models, you need on the order of 10K or more training instances to produce a decent model.
Consider the following code that generates a noisy sine wave and tries to train a densely-connected feed-forward neural network to fit the data. My model has two linear layers, each with 50 hidden units and a ReLU activation function. The experiments are parameterized with the variable num_points which I will increase.
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
import numpy as np
import matplotlib.pyplot as plt
np.random.seed(7)
def generate_data(num_points=100):
X = np.linspace(0.0 , 2.0 * np.pi, num_points).reshape(-1, 1)
noise = np.random.normal(0, 1, num_points).reshape(-1, 1)
y = 3 * np.sin(X) + noise
return X, y
def run_experiment(X_train, y_train, X_test, batch_size=64):
num_points = X_train.shape[0]
model = keras.Sequential()
model.add(layers.Dense(50, input_shape=(1, ), activation='relu'))
model.add(layers.Dense(50, activation='relu'))
model.add(layers.Dense(1, activation='linear'))
model.compile(loss = "mse", optimizer = "adam", metrics=["mse"] )
history = model.fit(X_train, y_train, epochs=10,
batch_size=batch_size, verbose=0)
yhat = model.predict(X_test, batch_size=batch_size)
plt.figure(figsize=(5, 5))
plt.plot(X_train, y_train, "ro", markersize=2, label='True')
plt.plot(X_train, yhat, "bo", markersize=1, label='Predicted')
plt.ylim(-5, 5)
plt.title('N=%d points' % (num_points))
plt.legend()
plt.grid()
plt.show()
Here is how I invoke the code:
num_points = 100
X, y = generate_data(num_points)
run_experiment(X, y, X)
Now, if I run the experiment with num_points = 100, the model predictions (in blue) do a terrible job at fitting the true noisy sine wave (in red).
Now, here is num_points = 1000:
Here is num_points = 10000:
And here is num_points = 100000:
As you can see, for my chosen NN architecture, adding more training instances allows the neural network to better (over)fit the data.
If you do have a lot of training instances, then if you want to purposefully overfit your data, you can either increase the neural network capacity or reduce regularization. Specifically, you can control the following knobs:
increase the number of layers
increase the number of hidden units
increase the number of features per data instance
reduce regularization (e.g. by removing dropout layers)
use a more complex neural network architecture (e.g. transformer blocks instead of RNN)
You may be wondering if neural networks can fit arbitrary data rather than just a noisy sine wave as in my example. Previous research says that, yes, a big enough neural network can fit any data. See:
Universal approximation theorem. https://en.wikipedia.org/wiki/Universal_approximation_theorem
Zhang 2016, "Understanding deep learning requires rethinking generalization". https://arxiv.org/abs/1611.03530
As discussed in the comments, you should make a Python array (with NumPy) like this:-
Myarray = [[0.65, 1], [0.85, 0.5], ....]
Then you would just call those specific parts of the array whom you need to predict. Here the first value is the x-axis value. So you would call it to obtain the corresponding pair stored in Myarray
There are many resources to learn these types of things. some of them are ===>
https://www.geeksforgeeks.org/python-using-2d-arrays-lists-the-right-way/
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=2&cad=rja&uact=8&ved=0ahUKEwjGs-Oxne3oAhVlwTgGHfHnDp4QtwIILTAB&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DQgfUT7i4yrc&usg=AOvVaw3LympYRszIYi6_OijMXH72
I have generated a data set using EMNIST that has one character per image or two characters per image.The image is sized at 28x56(hxw)
I basically want to predict the one or two characters in a given image. I am not sure on which architecture to follow to implement this. There are 62 character classes.
ex:-single character two characters
For single character y= [23]
For two characters y= [35,11]
I tried the following.
I tried implementing this thorough a CTC but I got stuck in a infinite loss that I couldn't fix.
Padded the single character ground truths with 62 to note a blank character and trained a CNN with following layers.
print()
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
y_train = sequence.pad_sequences(y_train, padding='post', value = 62)
y_test = sequence.pad_sequences(y_test,padding='post', value = 62)
X_train = X_train/255.0
X_test = X_test/255.0
input_shape = (28, 56, 1)
model = Sequential()
model.add(Conv2D(filters=72, kernel_size=(11,11), padding = 'same', activation='relu',input_shape=input_shape))
model.add(MaxPooling2D(pool_size=(2,2),strides=2))
model.add(Conv2D(filters=144, kernel_size=(7,7) , padding = 'same', activation='relu'))
model.add(Conv2D(filters=144, kernel_size=(3,3) , padding = 'same', activation='relu'))
model.add(MaxPooling2D(pool_size=(2,2)))
model.add(Flatten())
model.add(Dense(units=1024, activation='relu'))
model.add(Dropout(.5))
model.add(Dense(512, activation='relu'))
model.add(Dense(units=2, activation='relu'))
model.compile(loss='mse', optimizer='adam', metrics=['accuracy'])
model.summary()
batch_size = 128
steps = math.ceil(X_train.shape[0]/batch_size)
datagen = ImageDataGenerator(
featurewise_center=False, # set input mean to 0 over the dataset
samplewise_center=False, # set each sample mean to 0
featurewise_std_normalization=False, # divide inputs by std of the dataset
samplewise_std_normalization=False, # divide each input by its std
zca_whitening=False, # apply ZCA whitening
rotation_range=0, # randomly rotate images in the range (degrees, 0 to 180)
zoom_range = 0.2, # Randomly zoom image
width_shift_range=0.2, # randomly shift images horizontally (fraction of total width)
height_shift_range=0.1, # randomly shift images vertically (fraction of total height)
horizontal_flip=False, # randomly flip images
vertical_flip=False)
history = model.fit_generator(datagen.flow(X_train,y_train, batch_size=batch_size),
epochs = 6, validation_data = (X_test, y_test),
verbose = 1,steps_per_epoch=steps)
I was able to reach an accuracy of around 90% for validation set. However when I feed a generated image to see it's prediction it's a few characters off from the correct classification. Is there something wrong in the way I have created the model or pre-processed the data?
I have recognized my error. I have tried to tackle the problem using regression method wheres the problem is a classification problem.
I'm trying to build OneClass classifier for image recognition. I found this article, but because I have no full source code I don't exactly understand what am i doing.
X_train, X_test, y_train, y_test = train_test_split(x, y, random_state=42)
# X_train (2250, 200, 200, 3)
resnet_model = ResNet50(input_shape=(200, 200, 3), weights='imagenet', include_top=False)
features_array = resnet_model.predict(X_train)
# features_array (2250, 7, 7, 2048)
pca = PCA(svd_solver='randomized', n_components=450, whiten=True, random_state=42)
svc = SVC(kernel='rbf', class_weight='balanced')
model = make_pipeline(pca, svc)
param_grid = {'svc__C': [1, 5, 10, 50], 'svc__gamma': [0.0001, 0.0005, 0.001, 0.005]}
grid = GridSearchCV(model, param_grid)
grid.fit(X_train, y_train)
I have 2250 images (food and not food) 200x200px size, I send this data to predict method of ResNet50 model. Result is (2250, 7, 7, 2048) tensor, any one know what this dimensionality does it mean?
When I try to run grid.fit method i get an error:
ValueError: Found array with dim 4. Estimator expected <= 2.
These are the findings I could make.
You are getting the output tensor above the global average pooling layer. (See resnet_model.summary() to know about how input dimension changes to output dimension)
For a simple fix, add an Average pooling 2d Layer on top of resnet_model.
(So that output shape becomes (2250,1,1, 2048))
resnet_model = ResNet50(input_shape=(200, 200, 3), weights='imagenet', include_top=False)
resnet_op = AveragePooling2D((7, 7), name='avg_pool_app')(resnet_model.output)
resnet_model = Model(resnet_model.input, resnet_op, name="ResNet")
This generally is present in the source code of ResNet50 itself. Basically we are appending an AveragePooling2D layer to the resnet50 model. The last line combines the layer (2nd line) and the base line model into a model object.
Now the output dimension (feature_array) will be (2250, 1, 1, 2048) (because of added average pooling layer).
To avoid the ValueError you ought to reshape this feature_array to (2250, 2048)
feature_array = np.reshape(feature_array, (-1, 2048))
In the last line of the program in the question,
grid.fit(X_train, y_train)
you have fit with X_train (which are images in this case). The correct variable here is features_array (This is considered to be summary of the image). Entering this line will rectify the error,
grid.fit(features_array, y_train)
For more finetuning in this fashion by extracting feature vectors do look here (training with neural nets instead of using PCA and SVM).
Hope this helps!!