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 am trying to compare multiple classifiers on a dataset that I have. To get accurate accuracy scores for the classifiers I am now performing 10 fold cross validation for each classifier. This goes well for all of them except SVM (both linear and rbf kernels). The data is loaded like this:
dataset = pd.read_csv("data/distance_annotated_indels.txt", delimiter="\t", header=None)
X = dataset.iloc[:, [5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]].values
y = dataset.iloc[:, 4].values
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2)
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)
Cross validation for for example a Random Forest works fine:
start = time.time()
classifier = RandomForestClassifier(n_estimators = 100, criterion = 'entropy')
classifier.fit(X_train, y_train)
y_pred = classifier.predict(X_test)
cv = ShuffleSplit(n_splits=10, test_size=0.2)
scores = cross_val_score(classifier, X, y, cv=10)
print(classification_report(y_test, y_pred))
print("Random Forest accuracy after 10 fold CV: %0.2f (+/- %0.2f)" % (scores.mean(), scores.std() * 2) + ", " + str(round(time.time() - start, 3)) + "s")
Output:
precision recall f1-score support
0 0.97 0.95 0.96 3427
1 0.95 0.97 0.96 3417
avg / total 0.96 0.96 0.96 6844
Random Forest accuracy after 10 fold CV: 0.92 (+/- 0.06), 90.842s
However for SVM this process takes ages (waited for 2 hours, still nothing). The sklearn website does not make me any wiser. Is there something I should be doing different for SVM classifiers? The SVM code is as follows:
start = time.time()
classifier = SVC(kernel = 'linear')
classifier.fit(X_train, y_train)
y_pred = classifier.predict(X_test)
scores = cross_val_score(classifier, X, y, cv=10)
print(classification_report(y_test, y_pred))
print("Linear SVM accuracy after 10 fold CV: %0.2f (+/- %0.2f)" % (scores.mean(), scores.std() * 2) + ", " + str(round(time.time() - start, 3)) + "s")
If you have a lot of samples the computational complexity of the problem gets in the way, see Training complexity of Linear SVM.
Consider playing with the verbose flag of cross_val_score to see more logs about progress. Also, with n_jobs set to a value > 1 (or even using all CPUs with n_jobs set to -1, if memory allows) you could speed up computation via parallelization. http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.cross_val_score.html can be useful to evaluate these options.
If performance is poor I'd consider reducing the value of cv (see https://stats.stackexchange.com/questions/27730/choice-of-k-in-k-fold-cross-validation for a discussion on this)
Also you can control the time with changing max_iter. If it set to -1 it can go forever according to soltion space. Set some integer value say 10000 as a stopping criteria.
alternatively you can try using optimized SVM implementation - for example with scikit-learn-intelex - https://github.com/intel/scikit-learn-intelex
First install package
pip install scikit-learn-intelex
And then add in your python script
from sklearnex import patch_sklearn
patch_sklearn()
I'm trying to train a CNN on the CIFAR-10 Dataset in Keras, but I'm only getting around 10% accuracy, essentially random. I'm training over 50 epochs, with a batch size of 32 and learning rate of 0.01. Is there anything in particular that I am doing wrong?
import os
import numpy as np
import pandas as pd
from PIL import Image
from keras.models import Model
from keras.layers import Input, Dense, Conv2D, MaxPool2D, Dropout, Flatten
from keras.optimizers import SGD
from keras.utils import np_utils
# trainingData = np.array([np.array(Image.open("train/" + f)) for f in os.listdir("train")]) #shape: 50k, 32, 32, 3
# testingData = np.array([np.array(Image.open("test/" + f)) for f in os.listdir("test")]) #shape: same as training
#
# trainingLabels = np.array(pd.read_csv("trainLabels.csv"))[:,1] #categorical labels ["dog", "cat", "etc"....]
# listOfLabels = sorted(list(set(trainingLabels)))
# trainingOutput = np.array([np.array([1.0 if label == ind else 0.0 for ind in listOfLabels]) for label in trainingLabels]) #converted to output
# #for example: training output for dog =
# #[1.0, 0.0, 0.0, ...]
# np.save("trainingInput.np", trainingData)
# np.save("testingInput.np", testingData)
# np.save("trainingOutput.np", trainingOutput)
trainingInput = np.load("trainingInput.npy") #shape = 50k, 32, 32, 3
testingInput = np.load("testingInput.npy") #shape = 10k, 32, 32, 3
listOfLabels = sorted(list(set(np.array(pd.read_csv("trainLabels.csv"))[:,1]))) #categorical list of labels as strings
trainingOutput = np.load("trainingOutput.npy") #shape = 50k, 10
#looks like [0.0, 1.0, 0.0 ... 0.0, 0.0]
print(listOfLabels)
print("Data loaded\n______________\n")
inp = Input(shape=(32, 32, 3))
conva1 = Conv2D(64, (3, 3), padding='same', activation='relu')(inp)
conva2 = Conv2D(64, (3, 3), padding='same', activation='relu')(conva1)
poola = MaxPool2D(pool_size=(3, 3))(conva2)
dropa = Dropout(0.1)(poola)
convb1 = Conv2D(128, (5, 5), padding='same', activation='relu')(dropa)
convb2 = Conv2D(128, (5, 5), padding='same', activation='relu')(convb1)
poolb = MaxPool2D(pool_size=(3, 3))(convb2)
dropb = Dropout(0.1)(poolb)
flat = Flatten()(dropb)
dropc = Dropout(0.5)(flat)
out = Dense(len(listOfLabels), activation='softmax')(dropc)
print(out.shape)
model = Model(inputs=inp, outputs=out)
lrSet = SGD(lr=0.01, clipvalue=0.5)
model.compile(loss='categorical_crossentropy', optimizer=lrSet, metrics=['accuracy'])
model.fit(trainingInput, trainingOutput, batch_size=32, epochs=50, verbose=1, validation_split=0.1)
print(model.predict(testingInput))
Is there anything in particular that I am doing wrong?
Not necessarily "wrong", but some pointers I can suggest are:
It is important that you rescale your data, in case you are not doing so. Instead of handling values ranging from [0,255] it is better to divide all by 255 and handle data with ranges [0,1]. This helps your model's weights converge faster, as each gradient update will be more significant compared to it's unscaled version.
I think that your dropout may be affecting your performance. Even more seeing that you are using CNNs and a strong (0.5) Dropout when passing data to your output. Quoting this great answer:
In the original paper that proposed dropout layers, by Hinton (2012), dropout (with p=0.5) was used on each of the fully connected (dense) layers before the output; it was not used on the convolutional layers. This became the most commonly used configuration.
More recent research has shown some value in applying dropout also to convolutional layers, although at much lower levels: p=0.1 or 0.2.
So perhaps reducing your dropout or playing with it a bit will yield better results. Do notice that you are doing consecutive dropouts on your data, which doesn't seem quite helpful in my opinion and could also be causing problem, so consider redesigning that part:
dropb = Dropout(0.1)(poolb) #drop
flat = Flatten()(dropb) #flatten
dropc = Dropout(0.5)(flat) #then drop again?
Your learning rate may be higher than what is normally used. Although that is SGD's default learning rate, with higher learning values you may be "rushing" your training and failing to find better minima that could yield better performance. Consider using a lower learning rate (0.001 or lower, adjust epochs as needed), or well adding weight decay on your SGD instance. This will prevent your model from getting stuck on local minima that give sub-optimal results.
I am new to machine learning and data science. Sorry, if it is a very stupid question.
I see there is an inbuilt function for cross-validation but not for a fixed validation set. I have a dataset with 50,000 samples labeled with years from 1990 to 2010. I need to train different classifiers on 1990-2008 samples, then validate on 2009 samples, and test on 2010 samples.
EDIT:
After #Quan Tran's answer, I tried this. This is how it should be?
# Fit a decision tree
estimator1 = DecisionTreeClassifier( max_depth = 9, max_leaf_nodes=9)
estimator1.fit(X_train, y_train)
print estimator1
# validate using validation set
acc = np.zeros((20,20)) # store accuracy
for i in range(20):
for j in range(20):
estimator1 = DecisionTreeClassifier(max_depth = i+1, max_leaf_nodes=j+2)
estimator1.fit(X_valid, y_valid)
y_pred = estimator1.predict(X_valid)
acc[i,j] = accuracy_score(y_valid, y_pred)
best_mod = np.where(acc == acc.max())
print best_mod
print acc[best_mod]
# Predict target values
estimator1 = DecisionTreeClassifier(max_depth = int(best_mod[0]) + 1, max_leaf_nodes= int(best_mod[1]) + 2)
estimator1.fit(X_valid, y_valid)
y_pred = estimator1.predict(X_test)
confusion = metrics.confusion_matrix(y_test, y_pred)
TP = confusion[1, 1]
TN = confusion[0, 0]
FP = confusion[0, 1]
FN = confusion[1, 0]
# Classification Accuracy
print "======= ACCURACY ========"
print((TP + TN) / float(TP + TN + FP + FN))
print accuracy_score(y_valid, y_pred)
# store the predicted probabilities for class
y_pred_prob = estimator1.predict_proba(X_test)[:, 1]
# plot a ROC curve for y_test and y_pred_prob
fpr, tpr, thresholds = metrics.roc_curve(y_test, y_pred_prob)
plt.plot(fpr, tpr)
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.0])
plt.title('ROC curve for DecisionTreeClassifier')
plt.xlabel('False Positive Rate (1 - Specificity)')
plt.ylabel('True Positive Rate (Sensitivity)')
plt.grid(True)
print("======= AUC ========")
print(metrics.roc_auc_score(y_test, y_pred_prob))
I get this answer, which is not the best accuracy.
DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=9,
max_features=None, max_leaf_nodes=9, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
presort=False, random_state=None, splitter='best')
(array([5]), array([19]))
[ 0.8489011]
======= ACCURACY ========
0.574175824176
0.538461538462
======= AUC ========
0.547632099893
In this case, there are three separate sets. The train set, the test set and the validation set.
The train set is used to fit the parameters of the classifier. For example:
clf = DecisionTreeClassifier(max_depth=2)
clf.fit(trainfeatures, labels)
The validation set is used to tune the hyper parameters of the classifier or find the cutoff point for the training procedure. For example, in the case of Decision tree, max_depth is a hyper parameter. You will need to find a good set of hyper parameters by experimenting with different values of hyper parameters (tuning) and compare the performance measures (accuracy/precision,..) on the validation set.
The test set is used to estimate the error rate on unseen data. After having the performance measures on the test set, the model must not be trained/tuned any further.
I read this thread about the difference between SVC() and LinearSVC() in scikit-learn.
Now I have a data set of binary classification problem(For such a problem, the one-to-one/one-to-rest strategy difference between both functions could be ignore.)
I want to try under what parameters would these 2 functions give me the same result. First of all, of course, we should set kernel='linear' for SVC()
However, I just could not get the same result from both functions. I could not find the answer from the documents, could anybody help me to find the equivalent parameter set I am looking for?
Updated:
I modified the following code from an example of the scikit-learn website, and apparently they are not the same:
import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2] # we only take the first two features. We could
# avoid this ugly slicing by using a two-dim dataset
y = iris.target
for i in range(len(y)):
if (y[i]==2):
y[i] = 1
h = .02 # step size in the mesh
# we create an instance of SVM and fit out data. We do not scale our
# data since we want to plot the support vectors
C = 1.0 # SVM regularization parameter
svc = svm.SVC(kernel='linear', C=C).fit(X, y)
lin_svc = svm.LinearSVC(C=C, dual = True, loss = 'hinge').fit(X, y)
# create a mesh to plot in
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
# title for the plots
titles = ['SVC with linear kernel',
'LinearSVC (linear kernel)']
for i, clf in enumerate((svc, lin_svc)):
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, m_max]x[y_min, y_max].
plt.subplot(1, 2, i + 1)
plt.subplots_adjust(wspace=0.4, hspace=0.4)
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Paired)
plt.xlabel('Sepal length')
plt.ylabel('Sepal width')
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.xticks(())
plt.yticks(())
plt.title(titles[i])
plt.show()
Result:
Output Figure from previous code
In mathematical sense you need to set:
SVC(kernel='linear', **kwargs) # by default it uses RBF kernel
and
LinearSVC(loss='hinge', **kwargs) # by default it uses squared hinge loss
Another element, which cannot be easily fixed is increasing intercept_scaling in LinearSVC, as in this implementation bias is regularized (which is not true in SVC nor should be true in SVM - thus this is not SVM) - consequently they will never be exactly equal (unless bias=0 for your problem), as they assume two different models
SVC : 1/2||w||^2 + C SUM xi_i
LinearSVC: 1/2||[w b]||^2 + C SUM xi_i
Personally I consider LinearSVC one of the mistakes of sklearn developers - this class is simply not a linear SVM.
After increasing intercept scaling (to 10.0)
However, if you scale it up too much - it will also fail, as now tolerance and number of iterations are crucial.
To sum up: LinearSVC is not linear SVM, do not use it if do not have to.