I'm using Pybrain to train a recurrent neural network. However, the average of the weights keeps climbing and after several iterations the train and test accuracy become lower. Now the highest performance on train data is about 55% and on test data is about 50%.
I think maybe the rnn have some training problems because of its high weights. How can I solve it? Thank you in advance.
The usual way to restrict the network parameters is to use a constrained error-functional which somehow penalizes the absolute magnitude of the parameters. Such is done in "weight decay" where you add to your sum-of-squares error the norm of the weights ||w||. Usually this is the Euclidian norm, but sometimes also the 1-norm in which case it is called "Lasso". Note that weight decay is also called ridge regression or Tikhonov regularization.
In PyBrain, according to this page in the documentation, there is available a Lasso-version of weight decay, which can be parametrized by the parameter wDecay.
Related
I'm training an FCN (Fully Convolutional Network) and using "Sigmoid Cross Entropy" as a loss function.
my measurements are F-measure and MAE.
The Train/Dev Loss w.r.t #iteration graph is something like the below:
Although Dev loss has a slight increase after #Iter=2200, my measurements on Dev set have been improved up to near #iter = 10000. I want to know is it possible in machine learning at all? If F-measure has been improved, should the loss also be decreased? How do you explain it?
Every answer would be appreciated.
Short answer, yes it's possible.
How I would explain it is by reasoning on the Cross-Entropy loss and how it differs from the metrics. Loss Functions for classification, generally speaking, are used to optimize models relying on probabilities (0.1/0.9), while metrics usually use the predicted labels. (0/1)
Assuming having strong confidence (close to 0 or to 1) in a model probability hypothesis, a wrong prediction will greatly increase the loss and have a small decrease in F-measure.
Likewise, in the opposite scenario, a model with low confidence (e.g. 0.49/0.51) would have a small impact on the loss function (from a numerical perspective) and a greater impact on the metrics.
Plotting the distribution of your predictions would help to confirm this hypothesis.
I have a model that I train using polynomial and radial basis functions, I split the data into train set and test set and I take a lot of samples from the train set. Now I'm at a loss for the next step, I know bias is the loss of the sample with the least loss. Do I calculate this on train data or test data? Is the variance just the variance of the losses on the test set?
The main goal of this tradeoff is to find the right amount of complexity for the decision boundary.
High complexity: (Could) Memorizes the past and (may) not generalize for the future (High variance problem)
Low complexity: (Could) not learn enough from the past because of very simple decision boundary and again (may) fail to have a good prediction as well (high bias problem)
This could be simply shown with a figure like the following,
I have the following:
rf = RandomForestClassifier(n_estimators=500, criterion='entropy', random_state=42)
rf.fit(X_train, y_train)
From this, I get:
1.0 accuracy on training set
0.6990116801437556 accuracy on test set
Since we're not setting the max_depth, it seems the trees are overfitting to the training data.
My question is: what does this tell us about the training data? Does the fact that it has reasonable accuracy imply that the test data is very like the training data and that's the only reason we're getting such an accuracy?
Since you don't specify the max_depth of the tree, it grows until you have all pure nodes. So it is natural to overfit and correct/expected to have 100% (or rather high if the min_number of samples for node is not too large) accuracy on the training set.
This fact in not very insightful about the training set.
The fact that you are having a "such good" accuracy on the test set could indeed point out a similarity in the distribution of training/test set (that a one point it is expected if they are drawn from the same phenomenon) and that the tree has some degree of generalizability.
As general rule I would say that it is wrong to infer conclusion from a single result and when the training set is over-fitting. Additionally considering 0.69 accuracy a "good" accuracy is relative to the problem at hand. 30% of difference between training set and test set could be a huge gap in many applications.
In order to have a better understanding of your problem and more robust results it would be better to use a cross validation approach and a random forest.
I have started recently with ML and TensorFlow. While going through the CIFAR10-tutorial on the website I came across a paragraph which is a bit confusing to me:
The usual method for training a network to perform N-way classification is multinomial logistic regression, aka. softmax regression. Softmax regression applies a softmax nonlinearity to the output of the network and calculates the cross-entropy between the normalized predictions and a 1-hot encoding of the label. For regularization, we also apply the usual weight decay losses to all learned variables. The objective function for the model is the sum of the cross entropy loss and all these weight decay terms, as returned by the loss() function.
I have read a few answers on what is weight decay on the forum and I can say that it is used for the purpose of regularization so that values of weights can be calculated to get the minimum losses and higher accuracy.
Now in the text above I understand that the loss() is made of cross-entropy loss(which is the difference in prediction and correct label values) and weight decay loss.
I am clear on cross entropy loss but what is this weight decay loss and why not just weight decay? How is this loss being calculated?
Weight decay is nothing but L2 regularisation of the weights, which can be achieved using tf.nn.l2_loss.
The loss function with regularisation is given by:
The second term of the above equation defines the L2-regularization of the weights (theta). It is generally added to avoid overfitting. This penalises peaky weights and makes sure that all the inputs are considered. (Few peaky weights means only those inputs connected to it are considered for decision making.)
During gradient descent parameter update, the above L2 regularization ultimately means that every weight is decayed linearly: W_new = (1 - lambda)* W_old + alpha*delta_J/delta_w. Thats why its generally called Weight decay.
Weight decay loss, because it adds to the cost function (the loss to be specific). Parameters are optimized from the loss. Using weight decay you want the effect to be visible to the entire network through the loss function.
TF L2 loss
Cost = Model_Loss(W) + decay_factor*L2_loss(W)
# In tensorflow it bascially computes half L2 norm
L2_loss = sum(W ** 2) / 2
What your tutorial is trying to say by "weight decay loss" is that compared to the cross-entropy cost you know from your unregularized models (i.e. how far off target were your model's predictions on training data), your new cost function penalizes not only prediction error but also the magnitude of the weights in your network. Whereas before you were optimizing only for correct prediction of the labels in your training set, now you are optimizing for correct label prediction as well as having small weights. The reason for this modification is that when a machine learning model trained by gradient descent yields large weights, it is likely they were arrived at in response to peculiarities (or, noise) in the training data. The model will not perform as well when exposed to held-out test data because it is overfit to the training set. The result of applying weight decay loss, more commonly called L2-regularization is that accuracy on training data will drop a bit but accuracy on test data can jump dramatically. And that's what you're after in the end: a model that generalizes well to data it did not see during training.
So you can get a firmer grasp on the mechanics of weight decay, let's look at the learning rule for weights in a L2-regularized network:
where eta and lambda are user-defined learning rate and regularization parameter, respectively and n is the number of training examples (you'll have to look up those Greek letters if you're not familiar). Since the values eta and (eta*lambda)/n both are constants for a given iteration of training, it's enough to interpret the learning rule for weight decay as "for a given weight, subract a small multiple of the derivative of the cost function with respect to that weight, and subtract a small multiple of the weight itself."
Let's look at four weights in an imaginary network and how the above learning rule affects them. As you can see, the regularization term shown in red pushes weights toward zero no matter what. It is designed to minimize the magnitude of the weight matrix, which it does by minimizing the absolute values of individual weights. Some key things to notice in these plots:
When the sign of the cost derivative and the sign are the weight are the same, the regularization term accelerates the weight's path to its optimum!
The amount that the regularization term affects the weight update is proportional to the current value of that weight. I've shown this in the plots with tiny red arrows showing contributions of weights with current values close to zero, and larger red arrows for weights with larger current magnitudes.
I implement the ResNet for the cifar 10 in accordance with this document https://arxiv.org/pdf/1512.03385.pdf
But my accuracy is significantly different from the accuracy obtained in the document
My - 86%
Pcs daughter - 94%
What's my mistake?
https://github.com/slavaglaps/ResNet_cifar10
Your question is a little bit too generic, my opinion is that the network is over fitting to the training data set, as you can see the training loss is quite low, but after the epoch 50 the validation loss is not improving anymore.
I didn't read the paper in deep so I don't know how did they solved the problem but increasing regularization might help. The following link will point you in the right direction http://cs231n.github.io/neural-networks-3/
below I copied the summary of the text:
Summary
To train a Neural Network:
Gradient check your implementation with a small batch of data and be aware of the pitfalls.
As a sanity check, make sure your initial loss is reasonable, and that you can achieve 100% training accuracy on a very small portion of
the data
During training, monitor the loss, the training/validation accuracy, and if you’re feeling fancier, the magnitude of updates in relation to
parameter values (it should be ~1e-3), and when dealing with ConvNets,
the first-layer weights.
The two recommended updates to use are either SGD+Nesterov Momentum or Adam.
Decay your learning rate over the period of the training. For example, halve the learning rate after a fixed number of epochs, or
whenever the validation accuracy tops off.
Search for good hyperparameters with random search (not grid search). Stage your search from coarse (wide hyperparameter ranges,
training only for 1-5 epochs), to fine (narrower rangers, training for
many more epochs)
Form model ensembles for extra performance
I would argue that the difference in data pre processing makes the difference in performance. He is using padding and random crops, which in essence increases the amount of training samples and decreases the generalization error. Also as the previous poster said you are missing regularization features, such as the weight decay.
You should take another look at the paper and make sure you implement everything like they did.