Logistic Regression on MNIST dataset - opencv

In this post you can find a very good tutorial on how to apply SVM classifier to MNIST dataset. I was wondering if I could use logistic regression instead of SVM classifier. So I searhed for Logistic regression in openCV, And I found that the syntax for both classifiers are almost identical. So I guessed that I could just comment out these parts:
cv::Ptr<cv::ml::SVM> svm = cv::ml::SVM::create();
svm->setType(cv::ml::SVM::C_SVC);
svm->setKernel(cv::ml::SVM::POLY);//LINEAR, RBF, SIGMOID, POLY
svm->setTermCriteria(cv::TermCriteria(cv::TermCriteria::MAX_ITER, 100, 1e-6));
svm->setGamma(3);
svm->setDegree(3);
svm->train( trainingMat , cv::ml::ROW_SAMPLE , labelsMat );
and replace it with:
cv::Ptr<cv::ml::LogisticRegression> lr1 = cv::ml::LogisticRegression::create();
lr1->setLearningRate(0.001);
lr1->setIterations(10);
lr1->setRegularization(cv::ml::LogisticRegression::REG_L2);
lr1->setTrainMethod(cv::ml::LogisticRegression::BATCH);
lr1->setMiniBatchSize(1);
lr1->train( trainingMat, cv::ml::ROW_SAMPLE, labelsMat);
But first I got this error:
OpenCV Error: Bad argument(data and labels must be a floating point matrix)
Then I changed
cv::Mat labelsMat(labels.size(), 1, CV_32S, labelsArray);
to:
cv::Mat labelsMat(labels.size(), 1, CV_32F, labelsArray);
And now I get this error: OpenCV Error: bad argument(data should have atleast two classes)
I have 10 classes (0,1,...,9) but I don't know why I get this error. My codes are almost identical with the ones in the mentioned tutorial.

In Python you could do something like this:
import matplotlib.pyplot as plt
# Import datasets, classifiers and performance metrics
from sklearn import datasets, svm, metrics
from sklearn.linear_models import LogisticRegression
# The digits dataset
digits = datasets.load_digits()
# The data that we are interested in is made of 8x8 images of digits, let's
# have a look at the first 3 images, stored in the `images` attribute of the
# dataset. If we were working from image files, we could load them using
# pylab.imread. Note that each image must have the same size. For these
# images, we know which digit they represent: it is given in the 'target' of
# the dataset.
images_and_labels = list(zip(digits.images, digits.target))
for index, (image, label) in enumerate(images_and_labels[:4]):
plt.subplot(2, 4, index + 1)
plt.axis('off')
plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
plt.title('Training: %i' % label)
# To apply a classifier on this data, we need to flatten the image, to
# turn the data in a (samples, feature) matrix:
n_samples = len(digits.images)
data = digits.images.reshape((n_samples, -1))
Choose which one of the classifiers you like below
# Create a classifier: a support vector classifier
classifier = svm.SVC(gamma=0.001)
# create a Logistic Regression Classifier
classifier = LogisticRegression(C=1.0)
# We learn the digits on the first half of the digits
classifier.fit(data[:n_samples / 2], digits.target[:n_samples / 2])
# Now predict the value of the digit on the second half:
expected = digits.target[n_samples / 2:]
predicted = classifier.predict(data[n_samples / 2:])
print("Classification report for classifier %s:\n%s\n"
% (classifier, metrics.classification_report(expected, predicted)))
print("Confusion matrix:\n%s" % metrics.confusion_matrix(expected, predicted))
images_and_predictions = list(zip(digits.images[n_samples / 2:], predicted))
for index, (image, prediction) in enumerate(images_and_predictions[:4]):
plt.subplot(2, 4, index + 5)
plt.axis('off')
plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
plt.title('Prediction: %i' % prediction)
plt.show()
You can see the whole code here

Related

How to overfit data with Keras?

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

Seq2Seq for string reversal

If I have a string, say "abc" and target of that string in reverse, say "cba".
Can a neural network, in particular an encoder-decoder model, learn this mapping? If so, what is the best model to accomplish this.
I ask, as this is a structural translation rather than a simple character mapping as in normal machine translation
If your network is an old-fashioned encoder-decoder model (without attention), then, as #Prune said, it has memory bottleneck (encoder dimensionality). Thus, such a network cannot learn to reverse strings of arbitrary size. However, you can train such an RNN to reverse strings of limited size. For example, the following toy seq2seq LSTM is able to reverse sequences of digits with length up to 10. Here is how you train it:
from keras.models import Model
from keras.layers import Input, LSTM, Dense, Embedding
import numpy as np
emb_dim = 20
latent_dim = 100 # Latent dimensionality of the encoding space.
vocab_size = 12 # digits 0-9, 10 is for start token, 11 for end token
encoder_inputs = Input(shape=(None, ), name='enc_inp')
common_emb = Embedding(input_dim=vocab_size, output_dim=emb_dim)
encoder_emb = common_emb(encoder_inputs)
encoder = LSTM(latent_dim, return_state=True)
encoder_outputs, state_h, state_c = encoder(encoder_emb)
encoder_states = [state_h, state_c]
decoder_inputs = Input(shape=(None,), name='dec_inp')
decoder_emb = common_emb(decoder_inputs)
decoder_lstm = LSTM(latent_dim, return_sequences=True, return_state=True)
decoder_outputs, _, _ = decoder_lstm(decoder_emb, initial_state=encoder_states)
decoder_dense = Dense(vocab_size, activation='softmax')
decoder_outputs = decoder_dense(decoder_outputs)
model = Model([encoder_inputs, decoder_inputs], decoder_outputs)
def generate_batch(length=4, batch_size=64):
x = np.random.randint(low=0, high=10, size=(batch_size, length))
y = x[:, ::-1]
start = np.ones((batch_size, 1), dtype=int) * 10
end = np.ones((batch_size, 1), dtype=int) * 11
enc_x = np.concatenate([start, x], axis=1)
dec_x = np.concatenate([start, y], axis=1)
dec_y = np.concatenate([y, end], axis=1)
dec_y_onehot = np.zeros(shape=(batch_size, length+1, vocab_size), dtype=int)
for row in range(batch_size):
for col in range(length+1):
dec_y_onehot[row, col, dec_y[row, col]] = 1
return [enc_x, dec_x], dec_y_onehot
def generate_batches(batch_size=64, max_length=10):
while True:
length = np.random.randint(low=1, high=max_length)
yield generate_batch(length=length, batch_size=batch_size)
model.compile(optimizer='rmsprop', loss='categorical_crossentropy', metrics=['categorical_accuracy'])
model.fit_generator(generate_batches(), steps_per_epoch=1000, epochs=20)
Now you can apply it to reverse a sequence (my decoder is very inefficient, but it does illustrate the principle)
input_seq = np.array([[10, 2, 1, 2, 8, 5, 0, 6]])
result = np.array([[10]])
next_digit = -1
for i in range(100):
next_digit = model.predict([input_seq, result])[0][-1].argmax()
if next_digit == 11:
break
result = np.concatenate([result, [[next_digit]]], axis=1)
print(result[0][1:])
Hoorray, it prints [6 0 5 8 2 1 2] !
Generally, you can think of such a model as a weird autoencoder (with a reversal side-effect), and choose architecture and training procedure suitable for autoencoders. And there is quite a vast literature about text autoencoders.
Moreover, if you make an encoder-decoder model with attention, then, it will have no memory bottleneck, so, in principle, it is possible to reverse a sequence of any length with a neural network. However, attention requires quadratic computational time, so in practice even neural networks with attention will be very inefficient for long sequences.
I doubt that a NN will learn the abstract structural transformation. Since the string is of unbounded input length, the finite NN won't have the info necessary. NLP processes generally work with identifying small blocks and simple context-sensitive shifts. I don't think they'd identify the end-to-end swaps needed.
However, I expect that an image processor, adapted to a single dimension, would learn this quite quickly. Some can learn how to rotate a sub-image.

high variance with Randomforest learner

I'm using Random Forest Regressor to fit a 10-dimensional regression problem with around 300 thousand samples. Although not necessary when dealing with Random Forest I started by putting the data on the same scale (by using preprocessing of sklearn) and then I did a randomised search over the following parameter space:
n_estimators=[int(x) for x in linspace (start=100, stop= 2000, num=11)]
max_features= auto, sqrt
max_depth= from 1- to 150 with step =11
min_sampl_split=2,5,10,12
min_samples_leaf=1,2,4,6
Bootstrap true or false
Moreover, after getting the best parameters I did a second narrower search.
Though I am using a 10-Fold cross validation scheme with the random search I'm still getting a serious overfitting problem!
Moreover, I have also tried using DBSCAN algorithm to check for outliers. After excluding some parts of the dataset I got even worse results!
Should I include other parameters of the Random Forest in the randomised search? or should I apply some more preprocessing techniques on the data set before fitting?
For convenience, this is my implementation I wrote:
from sklearn.model_selection import ShuffleSplit
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import RandomizedSearchCV
n_estimators = [int(x) for x in np.linspace(start = 1, stop =
15, num = 15)]
max_features = ['auto', 'sqrt']
max_depth = [int(x) for x in np.linspace(10, 110, num = 11)]
max_depth.append(None)
min_samples_split = [2, 5, 10,12]
min_samples_leaf = [1, 2, 4,6]
bootstrap = [True, False]
cv = ShuffleSplit(n_splits=10, test_size=0.01, random_state=0)
random_grid = {'n_estimators': n_estimators,
'max_features': max_features,
'max_depth': max_depth,
'min_samples_split': min_samples_split,
'min_samples_leaf': min_samples_leaf,
'bootstrap': bootstrap}
rf = RandomForestRegressor()
rf_random = RandomizedSearchCV(estimator = rf, param_distributions
= random_grid, n_iter = 50, cv = cv, verbose=2, random_state=42,
n_jobs = 32)
rf_random.fit(x_train, y_train)
the best parameters returned by the randomizedsearch function:
bootstrap: Fasle. Min_samples_leaf=2. n_estimators= 1647. Max_features: sqrt. min_samples_split=3. Max_depth: None.
The range of the target is from 0 to 10000 [unit]. This model is resulting in 6.98 [unit] RMSE accuracy on the training set and and average of 67.54 [unit] RMSE accuracy on the test sets.
that line
max_depth= from 1- to 150 with step =11
For a 10 feature problem, the optimum depth is under 10. You are overfitting like crazy beacause of that. consider putting max_depth from 1 to 15 with step 1
min_sampl_split=2,5,10,12
min_samples_leaf=1,2,4,6
This should help reduce the variance, however, the step of 11 for max_depth is killing all the efforts you could possibly make

TensorFlow - Classification with thousands of labels

I'm very new to TensorFlow. I've been trying use TensorFlow to create a function where I give it a vector with 6 features and get back a label.
I have a training data set in the form of 6 features and 1 label. The label is in the first column:
309,3,0,2,4,0,6
309,12,0,2,4,0,6
309,0,4,17,2,0,6
318,0,660,414,58,3,12
311,0,0,414,58,0,2
298,0,53,355,5,0,2
60,16,14,381,30,4,2
312,0,8,8,13,0,3
...
I have the index for the labels which is a list of thousand and thousands of names:
309,Joe
318,Joey
311,Bruce
...
How do I create a model and train it using TensorFlow to be able to predict the label, given a vector without the first column?
--
This is what I tried:
from __future__ import print_function
import tflearn
name_count = sum(1 for line in open('../../names.csv')) # this comes out to 24260
# Load CSV file, indicate that the first column represents labels
from tflearn.data_utils import load_csv
data, labels = load_csv('../../data.csv', target_column=0,
categorical_labels=True, n_classes=name_count)
# Build neural network
net = tflearn.input_data(shape=[None, 6])
net = tflearn.fully_connected(net, 32)
net = tflearn.fully_connected(net, 32)
net = tflearn.fully_connected(net, 2, activation='softmax')
net = tflearn.regression(net)
# Define model
model = tflearn.DNN(net)
# Start training (apply gradient descent algorithm)
model.fit(data, labels, n_epoch=10, batch_size=16, show_metric=True)
# Predict
pred = model.predict([[218,5,124,26,0,3]]) # 326
print("Name:", pred[0][1])
It's based on https://github.com/tflearn/tflearn/blob/master/tutorials/intro/quickstart.md
I get the error:
ValueError: Cannot feed value of shape (16, 24260) for Tensor u'TargetsData/Y:0', which has shape '(?, 2)'
24260 is the number of lines in names.csv
Thank you!
net = tflearn.fully_connected(net, 2, activation='softmax')
looks to be saying you have 2 output classes, but in reality you have 24260. 16 is the size of your minibatch, so you have 16 rows of 24260 columns (one of these 24260 will be a 1, the others will be all 0s).

Under what parameters are SVC and LinearSVC in scikit-learn equivalent?

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.

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