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What is out of bag error in Random Forests?
Is it the optimal parameter for finding the right number of trees in a Random Forest?
I will take an attempt to explain:
Suppose our training data set is represented by T and suppose data set has M features (or attributes or variables).
T = {(X1,y1), (X2,y2), ... (Xn, yn)}
and
Xi is input vector {xi1, xi2, ... xiM}
yi is the label (or output or class).
summary of RF:
Random Forests algorithm is a classifier based on primarily two methods -
Bagging
Random subspace method.
Suppose we decide to have S number of trees in our forest then we first create S datasets of "same size as original" created from random resampling of data in T with-replacement (n times for each dataset). This will result in {T1, T2, ... TS} datasets. Each of these is called a bootstrap dataset. Due to "with-replacement" every dataset Ti can have duplicate data records and Ti can be missing several data records from original datasets. This is called Bootstrapping. (en.wikipedia.org/wiki/Bootstrapping_(statistics))
Bagging is the process of taking bootstraps & then aggregating the models learned on each bootstrap.
Now, RF creates S trees and uses m (=sqrt(M) or =floor(lnM+1)) random subfeatures out of M possible features to create any tree. This is called random subspace method.
So for each Ti bootstrap dataset you create a tree Ki. If you want to classify some input data D = {x1, x2, ..., xM} you let it pass through each tree and produce S outputs (one for each tree) which can be denoted by Y = {y1, y2, ..., ys}. Final prediction is a majority vote on this set.
Out-of-bag error:
After creating the classifiers (S trees), for each (Xi,yi) in the original training set i.e. T, select all Tk which does not include (Xi,yi). This subset, pay attention, is a set of boostrap datasets which does not contain a particular record from the original dataset. This set is called out-of-bag examples. There are n such subsets (one for each data record in original dataset T). OOB classifier is the aggregation of votes ONLY over Tk such that it does not contain (xi,yi).
Out-of-bag estimate for the generalization error is the error rate of the out-of-bag classifier on the training set (compare it with known yi's).
Why is it important?
The study of error estimates for bagged classifiers in Breiman
[1996b], gives empirical evidence to show that the out-of-bag estimate
is as accurate as using a test set of the same size as the training
set. Therefore, using the out-of-bag error estimate removes the need
for a set aside test set.1
(Thanks #Rudolf for corrections. His comments below.)
In Breiman's original implementation of the random forest algorithm, each tree is trained on about 2/3 of the total training data. As the forest is built, each tree can thus be tested (similar to leave one out cross validation) on the samples not used in building that tree. This is the out of bag error estimate - an internal error estimate of a random forest as it is being constructed.
Related
First of all, thank you in advance for the answers to come. I am confused about the use of K-Fold Cross Validation (CV) with CNN.
When working with CV under normal conditions, as seen in the link below, the original dataset is first split as test and training.
https://miro.medium.com/max/875/1*pJ5jQHPfHDyuJa4-7LR11Q.png
Then, the training dataset is divided into training and validation in the K cycle according to the determined K value. In short, if we say K = 5, our training is repeated 5 times, and each time a newly trained model is formed.
Question 1: How can we calculate the overall training-validation accuracy and loss values of 5 different models. Do we need to add up and average the success of all models?
Question 2: We separated the TEST data set from the original data set at the beginning of the training. How can we test the TEST data set on 5 different models? Should we test on 5 models then get their average accuracy or should we test only on the most successful model?
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I am quite new to pytorch and deep learning. Here is my question. I have two different datasets with the same feature domain sharing one neural network for a regression problem. The input is the features and the output is the target value. The first dataset uses a normal loss while the second dataset, I am trying to create a new loss for it.
I have searched multi-loss problems, people usually have two loss summed up for the backward process. But I want to use the loss in turn. (When I train the first dataset, the nn uses the first loss and when I train the second dataset, the nn uses the other loss)
Is this possible to do? Appreciate if anyone has some idea.
The loss function does not necessarily have to do with network topology. You can use the corresponding loss with each dataset you use, e.g.
if first_task:
dataloader = torch.utils.data.DataLoader(first_dataset)
loss_fn = first_loss_fn
else:
dataloader = torch.utils.data.Dataloader(second_dataset)
loss_fn = second_loss_fn
# The pytorch training loop, very roughly
for batch in dataloader:
x, y = batch
optimizer.zero_grad()
loss = loss_fn(network.forward(x), y) # calls the corresponding loss function
loss.backward()
optimizer.step()
You can do this for the two datasets sequentially (meaning you interleave by epochs):
for batch in dataloader_1:
...
loss = first_loss_fn(...)
for batch in dataloader_2:
...
loss = second_loss_fn(...)
or better
dataset = torch.utils.data.ChainDataset([first_dataset, second_dataset])
dataloader = torch.utils.data.DataLoader(dataset)
You can also do simultaneously (interleave by examples). The standard way I think would be to use torch.utils.data.ConcatDataset
dataset = torch.utils.data.ConcatDataset([first_dataset, second_dataset])
dataloader = torch.utils.data.DataLoader(dataset)
Note that here you need each sample to store information about the dataset it comes from so you can determine which cost to apply.
A simpler way would be to interleave by batches (then you apply the same cost to the entire batch). For this case one way proposed here is to use separate dataloaders (this way you get flexibility on how often to sample each of them).
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Image of Bags and how to choose from them
Imagine I have 10 bags,Ordered one after other.ie Bag 1 , Bag 2 ......... Bag n.
Each bag has distinct set of words.
In order to understand what a bag is,
Consider we have a vocabulary of 10,000 words.
The first bag contains words Hello , India , Manager.
ie Bag 1 will have 1's at the words index present in the bag.
ex:Bag 1 will be of size 10000*1
if Hello's index was 1 India's index was 2 and Manager's was 4
It will be
[0 , 1, 1, 0 , 1 ,0,0,0,0.........]
*I dont have a model yet.
*I'm thinking to use story books,But its still kind of abstract for me.
A word has to chosen from each bag and assigned a number word 1(word from bag 1)
word 2(word from bag 2) and they must form a MEANINGFULL sentence in their numerical order.!
First, we need a way that the computer can recognise a word otherwise it cannot pick the correct one. That means at this stage, we need to decide what we are teaching the computer to begin with (ie what is a verb, noun, grammar) but I will assume we will dump a dictionary into it and give no information except the words themselves.
So that the computer can compute what sentences are, we need to convert them to numbers (one way would be to work alphabetically starting at 1, using them as keys for a dictionary (digital this time(!)) and the word as the value). Now we can apply the same linear algebra techniques to this problem as any other problem.
So we need to make generations of matrices of weights to multiply into the keys of the dictionary, then remove all the weights beyond the range of dictionary keys, the rest can be used to get the value in the dictionary and make a sentence. Optionally, you can also use a threshold value to take off of all the outputs of the matrix multiplication
Now for the hard part: learning. Once you have a few (say 100) matrices, we need to "breed" the best ones (this is where human intervention is needed) and you need to pick the 50 most meaningful sentences (might be hard at first) and use them to base your next 100 of (easiest way would be to weight the 50 matrices randomly for a weighted mean 100 times).
And the boring bit, keep running the generations over and over until you get to a point where your sentences are meaningful most of the time (of course there is no guarantee that it will always be meaningful but that's the nature of ANN's)
If you find it doesn't work, you can use more layers (more matrices) and/or I recently heard of a different technique that dynamically changed the network but I can't really help with that.
Have a database with thousands/millions of valid sentences.
Create a dictionary where each word represents a number (reserve 0 for "nothing", 1 for "start of sentence" and 2 for "end of sentence").
word_dic = { "_nothing_": 0, "_start_": 1, "_end_": 2, "word1": 3, "word2": 4, ...}
reverse_dic = {v:k for k,v in word_dic.items()}
Remember to add "_start_" and "_end_" at the beginning and end of all sentences in the database, and "_nothing_" after the end to complete the desired length capable of containing all sentences. (Ideally, work with sentences with 10 or less words, so your model wont't try to create bigger sentences).
Transform all your sentences into sequences of indices:
#supposing you have an array of shape (sentences, length) as string:
indices = []
for word in database.reshape((-1,)):
indices.append(word_dic[word])
indices = np.array(indices).reshape((sentences,length))
Transform this into categorical words with the keras function to_categorical()
cat_sentences = to_categorical(indices) #shape (sentences,length,dictionary_size)
Hint: keras has lots of useful text preprocessing functions here.
Separate training input and output data:
#input is the sentences except for the last word
x_train = cat_sentences[:,:-1,:]
y_train = cat_sentences[:,1:,:]
Let's create an LSTM based model that will predict the next words from the previous words:
model = Sequential()
model.add(LSTM(dontKnow,return_sequences=True,input_shape=(None,dictionary_size)))
model.add(.....)
model.add(LSTM(dictionary_size,return_sequences=True,activation='sigmoid'))
#or a Dense(dictionary_size,activation='sigmoid')
Compile and fit this model with x_train and y_train:
model.compile(....)
model.fit(x_train,y_train,....)
Create an identical model using stateful=True in all LSTM layers:
newModel = ......
Transfer the weights from the trained model:
newModel.set_weights(model.get_weights())
Create your bags in a categorical way, shape (10, dictionary_size).
Use the model to predict one word from the _start_ word.
#reset the states of the stateful model before you start a 10 word prediction:
newModel.reset_states()
firstWord = newModel.predict(startWord) #startword is shaped as (1,1,dictionary_size)
The firstWord will be a vector with size dictionary_size telling (sort of) the probabilities of each existing word. Compare to the words in the bag. You can choose the highest probability, or use some random selecting if the probabilities of other words in the bag are also good.
#example taking the most probable word:
firstWord = np.array(firstWord == firstWord.max(), dtype=np.float32)
Do the same again, but now input firstWord in the model:
secondWord = newModel.predict(firstWord) #respect the shapes
Repeat the process until you get a sentence. Notice that you may find _end_ before the 10 words in the bag are satisfied. You may decide to finish the process with a shorter sentence then, especially if other word probabilities are low.
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I'm going through this tutorial on RNNs/LSTMs and I'm having quite a hard time understanding stateful LSTMs. My questions are as follows :
1. Training batching size
In the Keras docs on RNNs, I found out that the hidden state of the sample in i-th position within the batch will be fed as input hidden state for the sample in i-th position in the next batch. Does that mean that if we want to pass the hidden state from sample to sample we have to use batches of size 1 and therefore perform online gradient descent? Is there a way to pass the hidden state within a batch of size >1 and perform gradient descent on that batch ?
2. One-Char Mapping Problems
In the tutorial's paragraph 'Stateful LSTM for a One-Char to One-Char Mapping' were given a code that uses batch_size = 1 and stateful = True to learn to predict the next letter of the alphabet given a letter of the alphabet. In the last part of the code (line 53 to the end of the complete code), the model is tested starting with a random letter ('K') and predicts 'B' then given 'B' it predicts 'C', etc. It seems to work well except for 'K'. However, I tried the following tweak to the code (last part too, I kept lines 52 and above):
# demonstrate a random starting point
letter1 = "M"
seed1 = [char_to_int[letter1]]
x = numpy.reshape(seed, (1, len(seed), 1))
x = x / float(len(alphabet))
prediction = model.predict(x, verbose=0)
index = numpy.argmax(prediction)
print(int_to_char[seed1[0]], "->", int_to_char[index])
letter2 = "E"
seed2 = [char_to_int[letter2]]
seed = seed2
print("New start: ", letter1, letter2)
for i in range(0, 5):
x = numpy.reshape(seed, (1, len(seed), 1))
x = x / float(len(alphabet))
prediction = model.predict(x, verbose=0)
index = numpy.argmax(prediction)
print(int_to_char[seed[0]], "->", int_to_char[index])
seed = [index]
model.reset_states()
and these outputs:
M -> B
New start: M E
E -> C
C -> D
D -> E
E -> F
It looks like the LSTM did not learn the alphabet but just the positions of the letters, and that regardless of the first letter we feed in, the LSTM will always predict B since it's the second letter, then C and so on.
Therefore, how does keeping the previous hidden state as initial hidden state for the current hidden state help us with the learning given that during test if we start with the letter 'K' for example, letters A to J will not have been fed in before and the initial hidden state won't be the same as during training ?
3. Training an LSTM on a book for sentence generation
I want to train my LSTM on a whole book to learn how to generate sentences and perhaps learn the authors style too, how can I naturally train my LSTM on that text (input the whole text and let the LSTM figure out the dependencies between the words) instead of having to 'artificially' create batches of sentences from that book myself to train my LSTM on? I believe I should use stateful LSTMs could help but I'm not sure how.
Having a stateful LSTM in Keras means that a Keras variable will be used to store and update the state, and in fact you could check the value of the state vector(s) at any time (that is, until you call reset_states()). A non-stateful model, on the other hand, will use an initial zero state every time it processes a batch, so it is as if you always called reset_states() after train_on_batch, test_on_batch and predict_on_batch. The explanation about the state being reused for the next batch on stateful models is just about that difference with non-stateful; of course the state will always flow within each sequence in the batch and you do not need to have batches of size 1 for that to happen. I see two scenarios where stateful models are useful:
You want to train on split sequences of data because these are very long and it would not be practical to train on their whole length.
On prediction time, you want to retrieve the output for each time point in the sequence, not just at the end (either because you want to feed it back into the network or because your application needs it). I personally do that in the models that I export for later integration (which are "copies" of the training model with batch size of 1).
I agree that the example of an RNN for the alphabet does not really seem very useful in practice; it will only work when you start with the letter A. If you want to learn to reproduce the alphabet starting at any letter, you would need to train the network with that kind of examples (subsequences or rotations of the alphabet). But I think a regular feed-forward network could learn to predict the next letter of the alphabet training on pairs like (A, B), (B, C), etc. I think the example is meant for demonstrative purposes more than anything else.
You may have probably already read it, but the popular post The Unreasonable Effectiveness of Recurrent Neural Networks shows some interesting results along the lines of what you want to do (although it does not really dive into implementation specifics). I don't have personal experience training RNN with textual data, but there is a number of approaches you can research. You can build character-based models (like the ones in the post), where your input and receive one character at a time. A more advanced approach is to do some preprocessing on the texts and transform them into sequences of numbers; Keras includes some text preprocessing functions to do that. Having one single number as feature space is probably not going to work all that well, so you could simply turn each word into a vector with one-hot encoding or, more interestingly, have the network learn the best vector representation for each for, which is what they call en embedding. You can go even further with the preprocessing and look into something like NLTK, specially if you want to remove stop words, punctuation and things like that. Finally, if you have sequences of different sizes (e.g. you are using full texts instead of excerpts of a fixed size, which may or may not be important for you) you will need to be a bit more careful and use masking and/or sample weighting. Depending on the exact problem, you can set up the training accordingly. If you want to learn to generate similar text, the "Y" would be the similar to the "X" (one-hot encoded), only shifted by one (or more) positions (in this case you may need to use return_sequences=True and TimeDistributed layers). If you want to determine the autor, your output could be a softmax Dense layer.
Hope that helps.
Below is the exercise question posed on this page https://www.tensorflow.org/versions/0.6.0/tutorials/deep_cnn/index.html
EXERCISE: The output of inference are un-normalized logits. Try
editing the network architecture to return normalized predictions
using tf.softmax().
In the spirit of the exercise, I want to know if I'm on the right-track (not looking for the coded-up answer).
Here's my proposed solution.
Step 1: The last layer (of the inference) in the example is a "softmax_linear", i.e., it simply does the unnormalized WX+b transformation. As stipulated, we apply the tf.nn.softmax operation with softmax_linear as input. This normalizes the output as probabilities on the range [0, 1].
Step 2: The next step is to modify the cross-entropy calculation in the loss-function. Since we already have normalized output, we need to replace the tf.nn.softmax_cross_entropy_with_logits operation with a plain cross_entropy(normalized_softmax, labels) function (that does not further normalize the output before calculating the loss). I believe this function is not available in the tensorflow library; it needs to be written.
That's it. Feedback is kindly solicited.
Step 1 is more then sufficient if you insert the tf.nn.softmax() in cifar10_eval.py (and not in cifar10.py). For example:
logits = cifar10.inference(images)
normalized_logits = tf.nn.softmax(logits)
top_k_op = tf.nn.in_top_k(normalized_logits, labels, 1)