I am trying to train a machine learning model where the loss function is binary cross entropy, because of gpu limitations i can only do batch size of 4 and i'm having lot of spikes in the loss graph. So I'm thinking to back-propagate after some predefined batch size(>4). So it's like i'll do 10 iterations of batch size 4 store the losses, after 10th iteration add the losses and back-propagate. will it be similar to batch size of 40.
TL;DR
f(a+b) = f(a)+f(b) is it true for binary cross entropy?
f(a+b) = f(a) + f(b) doesn't seem to be what you're after. This would imply that BCELoss is additive which it clearly isn't. I think what you really care about is if for some index i
# false
f(x, y) == f(x[:i], y[:i]) + f([i:], y[i:])
is true?
The short answer is no, because you're missing some scale factors. What you probably want is the following identity
# true
f(x, y) == (i / b) * f(x[:i], y[:i]) + (1.0 - i / b) * f(x[i:], y[i:])
where b is the total batch size.
This identity is used as motivation for the gradient accumulation method (see below). Also, this identity applies to any objective function which returns an average loss across each batch element, not just BCE.
Caveat/Pitfall: Keep in mind that batch norm will not behave exactly the same when using this approach since it updates its internal statistics based on batch size during the forward pass.
We can actually do a little better memory-wise than just computing the loss as a sum followed by backpropagation. Instead we can compute the gradient of each component in the equivalent sum individually and allow the gradients to accumulate. To better explain I'll give some examples of equivalent operations
Consider the following model
import torch
import torch.nn as nn
import torch.nn.functional as F
class MyModel(nn.Module):
def __init__(self):
super().__init__()
num_outputs = 5
# assume input shape is 10x10
self.conv_layer = nn.Conv2d(3, 10, 3, 1, 1)
self.fc_layer = nn.Linear(10*5*5, num_outputs)
def forward(self, x):
x = self.conv_layer(x)
x = F.max_pool2d(x, 2, 2, 0, 1, False, False)
x = F.relu(x)
x = self.fc_layer(x.flatten(start_dim=1))
x = torch.sigmoid(x) # or omit this and use BCEWithLogitsLoss instead of BCELoss
return x
# to ensure same results for this example
torch.manual_seed(0)
model = MyModel()
# the examples will work as long as the objective averages across batch elements
objective = nn.BCELoss()
# doesn't matter what type of optimizer
optimizer = torch.optim.SGD(model.parameters(), lr=0.001)
and lets say our data and targets for a single batch are
torch.manual_seed(1) # to ensure same results for this example
batch_size = 32
input_data = torch.randn((batch_size, 3, 10, 10))
targets = torch.randint(0, 1, (batch_size, 20)).float()
Full batch
The body of our training loop for an entire batch may look something like this
# entire batch
output = model(input_data)
loss = objective(output, targets)
optimizer.zero_grad()
loss.backward()
optimizer.step()
loss_value = loss.item()
print("Loss value: ", loss_value)
print("Model checksum: ", sum([p.sum().item() for p in model.parameters()]))
Weighted sum of loss on sub-batches
We could have computed this using the sum of multiple loss functions using
# This is simpler if the sub-batch size is a factor of batch_size
sub_batch_size = 4
assert (batch_size % sub_batch_size == 0)
# for this to work properly the batch_size must be divisible by sub_batch_size
num_sub_batches = batch_size // sub_batch_size
loss = 0
for sub_batch_idx in range(num_sub_batches):
start_idx = sub_batch_size * sub_batch_idx
end_idx = start_idx + sub_batch_size
sub_input = input_data[start_idx:end_idx]
sub_targets = targets[start_idx:end_idx]
sub_output = model(sub_input)
# add loss component for sub_batch
loss = loss + objective(sub_output, sub_targets) / num_sub_batches
optimizer.zero_grad()
loss.backward()
optimizer.step()
loss_value = loss.item()
print("Loss value: ", loss_value)
print("Model checksum: ", sum([p.sum().item() for p in model.parameters()]))
Gradient accumulation
The problem with the previous approach is that in order to apply back-propagation, pytorch needs to store intermediate results of layers in memory for every sub-batch. This ends up requiring a relatively large amount of memory and you may still run into memory consumption issues.
To alleviate this problem, instead of computing a single loss and performing back-propagation once, we could perform gradient accumulation. This gives equivalent results of the previous version. The difference here is that we instead perform a backward pass on each component of
the loss, only stepping the optimizer once all of them have been backpropagated. This way the computation graph is cleared after each sub-batch which will help with memory usage. Note that this works because .backward() actually accumulates (adds) the newly computed gradients to the existing .grad member of each model parameter. This is why optimizer.zero_grad() must be called only once, before the loop, and not during or after.
# This is simpler if the sub-batch size is a factor of batch_size
sub_batch_size = 4
assert (batch_size % sub_batch_size == 0)
# for this to work properly the batch_size must be divisible by sub_batch_size
num_sub_batches = batch_size // sub_batch_size
# Important! zero the gradients before the loop
optimizer.zero_grad()
loss_value = 0.0
for sub_batch_idx in range(num_sub_batches):
start_idx = sub_batch_size * sub_batch_idx
end_idx = start_idx + sub_batch_size
sub_input = input_data[start_idx:end_idx]
sub_targets = targets[start_idx:end_idx]
sub_output = model(sub_input)
# compute loss component for sub_batch
sub_loss = objective(sub_output, sub_targets) / num_sub_batches
# accumulate gradients
sub_loss.backward()
loss_value += sub_loss.item()
optimizer.step()
print("Loss value: ", loss_value)
print("Model checksum: ", sum([p.sum().item() for p in model.parameters()]))
I think 10 iterations of batch size 4 is same as one iteration of batch size 40, only here the time taken will be more. Across different training examples losses are added before backprop. But that doesn't make the function linear. BCELoss has a log component, and hence it is not a linear function. However what you said is correct. It will be similar to batch size 40.
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 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.