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Optimizing conditional multiclass softmax objective function in XGBoost

I have successfully implemented a custom multiclass softmax function function in XGBoost based on this tutorial. The reason for customization is that the classes I want to predict are conditional on some data inputs - i.e. of the 24 possible classes being predicted, only a certain subset are valid. valid_transitions are lists of indices corresponding to classes we want to make predictions on and invalid_transitions are the inverse set of indices.
I have implemented .fit() and .predict_proba() such that they take valid_transitions and invalid_transitions as arguments which tells softprob_obj() and softmax()which classes to null out during training and prediction.
def softmax(x, valid_transitions, invalid_transitions):
for i in range(len(x)):
e = np.exp(x[i,valid_transitions[i]])
x[i, valid_transitions[i]] = e/np.sum(e)
x[i, invalid_transitions[i]] = 0
return x
def softprob_obj(labels, predt, data, valid_transitions, invalid_transitions):
'''Loss function. Computing the gradient and approximated hessian (diagonal).
Reimplements the `multi:softprob` inside XGBoost.
'''
kRows = len(data)
kClasses = len(np.unique(labels))
# The prediction is of shape (rows, classes), each element in a row
# represents a raw prediction (leaf weight, hasn't gone through softmax
# yet). In XGBoost 1.0.0, the prediction is transformed by a softmax
# function, fixed in later versions.
assert predt.shape == (kRows, kClasses)
eps = 1e-6
# compute the gradient and hessian, slow iterations in Python, only
# suitable for demo. Also the one in native XGBoost core is more robust to
# numeric overflow as we don't do anything to mitigate the `exp` in
# `softmax` here.
probs = softmax(predt, valid_transitions, invalid_transitions)
labels = labels.astype(int)
hess = np.maximum((2.0 * probs * (1.0 - probs)), eps)
probs[np.arange(len(probs)),labels] -= 1
# Right now (XGBoost 1.0.0), reshaping is necessary
grad = probs.reshape((kRows * kClasses, 1))
hess = hess.reshape((kRows * kClasses, 1))
return grad, hess
This works, but is pretty slow in training, presumably because the core xgboost functions I'm replacing are not written in python. I made some attempts to try to vectorize the calculation in numpy to avoid the for loop in softmax(), but ran into some issues with the ragged arrays that valid_transition and invalid_transition create. Was wondering if anyone had any ideas on how to optimize this within python. Thanks!

PyTorch: Is retain_graph=True necessary in alternating optimization?

I'm trying to optimize two models in an alternating fashion using PyTorch. The first is a neural network that is changing the representation of my data (ie a map f(x) on my input data x, parameterized by some weights W). The second is a Gaussian mixture model that is operating on the f(x) points, ie in the neural network space (rather than clustering points in the input space. I am optimizing the GMM using expectation maximization, so the parameter updates are analytically derived, rather than using gradient descent.
I have two loss functions here: the first is a function of the distances ||f(x) - f(y)||, and the second is the loss function of the Gaussian mixture model (ie how 'clustered' everything looks in the NN representation space). What I want to do is take a step in the NN optimization using both of the above loss functions (since it depends on both), and then do an expectation-maximization step for the GMM. The code looks like this (I have removed a lot since there is a ton of code):
data, labels = load_dataset()
net = NeuralNetwork()
net_optim = torch.optim.Adam(net.parameters(), lr=0.05, weight_decay=1)
# initialize weights, means, and covariances for the Gaussian clusters
concentrations, means, covariances, precisions = initialization(net.forward_one(data))
for i in range(1000):
net_optim.zero_grad()
pairs, pair_labels = pairGenerator(data, labels) # samples some pairs of datapoints
outputs = net(pairs[:, 0, :], pairs[:, 1, :]) # computes pairwise distances
net_loss = NeuralNetworkLoss(outputs, pair_labels) # loss function based on pairwise dist.
embedding = net.forward_one(data) # embeds all data in the NN space
log_prob, log_likelihoods = expectation_step(embedding, means, precisions, concentrations)
concentrations, means, covariances, precisions = maximization_step(embedding, log_likelihoods)
gmm_loss = GMMLoss(log_likelihoods, log_prob, precisions, concentrations)
net_loss.backward(retain_graph=True)
gmm_loss.backward(retain_graph=True)
net_optim.step()
Essentially, this is what is happening:
Sample some pairs of points from the dataset
Push pairs of points through the NN and compute network loss based on those outputs
Embed all datapoints using the NN and perform a clustering EM step in that embedding space
Compute variational loss (ELBO) based on clustering parameters
Update neural network parameters using both the variational loss and the network loss
However, to perform (5), I am required to add the flag retain_graph=True, otherwise I get the error:
RuntimeError: Trying to backward through the graph a second time, but the buffers have already been freed. Specify retain_graph=True when calling backward the first time.
It seems like having two loss functions means that I need to retain the computational graph?
I am not sure how to work around this, as with retain_graph=True, around iteration 400, each iteration is taking ~30 minutes to complete. Does anyone know how I might fix this? I apologize in advance – I am still very new to automatic differentiation.

I would recommend doing
total_loss = net_loss + gmm_loss
total_loss.backward()
Note that the gradient of net_loss w.r.t gmm weights is 0 thus summing the losses won't have any effect.
Here is a good thread on pytorch regarding the retain_graph. https://discuss.pytorch.org/t/what-exactly-does-retain-variables-true-in-loss-backward-do/3508/24

SKlearn prediction on test dataset with different shape from training dataset shape

I'm new to ML and would be grateful for any assistance provided. I've run a linear regression prediction using test set A and training set A. I saved the linear regression model and would now like to use the same model to predict a test set A target using features from test set B. Each time I run the model it throws up the error below
How can I successfully predict a test data set from features and a target with different shapes?
Input
print(testB.shape)
print(testA.shape)
Output
(2480, 5)
(1315, 6)
Input
saved_model = joblib.load(filename)
testB_result = saved_model.score(testB_features, testA_target)
print(testB_result)
Output
ValueError: Found input variables with inconsistent numbers of samples: [1315, 2480]
Thanks again

They are inconsistent shapes which is why the error is being thrown. Have you tried to reshape the data so one of them are same shape? From a quick look, it seems that you have more samples and one less feature in testA.
Think about it, if you have trained your model with 5 features you cannot then ask the same model to make a prediction given 6 features. You speak of using a Linear Regressor, the equation is roughly:
y = b + w0*x0 + w1*x1 + w2*x2 + .. + wN-1*xN-1
Where {
y is your output/label
N is the number of features
b is the bias term
w(i) is the ith weight
x(i) is the ith feature value
}
You have trained a linear regressor with 5 features, effectively producing the following
y (your output/label) = b + w0*x0 + w1*x1 + w2*x2 + w3*x3 + w4*x4
You then ask it to make a prediction given 6 features but it only knows how to deal with 5.
Aside from that issue, you also have too many samples, testB has 2480 and testA has 1315. These need to match, as the model wants to make 2480 predictions, but you only give it 1315 outputs to compare it to. How can you get a score for 1165 missing samples? Do you now see why the data has to be reshaped?
EDIT
Assuming you have datasets with an equal amount of features as discussed above, you may now look at reshaping (removing data) testB like so:
testB = testB[0:1314, :]
testB.shape
(1315, 5)
Or, if you would prefer a solution using the numpy API:
testB = np.delete(testB, np.s_[0:(len(testB)-len(testA))], axis=0)
testB.shape
(1315, 5)
Keep in mind, when doing this you slice out a number of samples. If this is important to you (which it can be) then it may be better to introduce a pre-processing step to help out with the missing values, namely imputing them like this. It is worth noting that the data you are reshaping should be shuffled (unless it is already), as you may be removing parts of the data the model should be learning about. Neglecting to do this could result in a model that may not generalise as well as you hoped.

3darray training/testing TensorFlow RNN LSTM

(I am testing my abilities to write short but effective questions so let me know how I do here)
I am trying to train/test a TensorFlow recurrent neural network, specifically an LSTM, with some trials of time-series data in the following ndarray format:
[[[time_step_trial_0, feature, feature, ...]
[time_step_trial_0, feature, feature, ...]]
[[time_step_trial_1, feature, feature, ...]
[time_step_trial_1, feature, feature, ...]]
[[time_step_trial_2, feature, feature, ...]
[time_step_trial_2, feature, feature, ...]]]
The the 1d portion of this 3darray holds the a time step and all feature values that were observed at that time step. The 2d block contains all 1d arrays (time steps) that were observed in one trial. The 3d block contains all 2d blocks (trials) recorded for the time-series dataset. For each trial, the time step frequency is constant and the window interval is the same across all trials (0 to 50 seconds, 0 to 50 seconds, etc.).
For example, I am given data for Formula 1 race cars such as torque, speed, acceleration, rotational velocity, etc. Over a certain time interval recording time steps every 0.5 seconds, I form 1d arrays with each time step versus the recorded features recorded at that time step. Then I form a 2D array around all time steps corresponding to one Formula 1 race car's run on the track. I create a final 3D array holding all F1 cars and their time-series data. I want to train and test a model to detect anomalies in the F1 common trajectories on the course for new cars.
I am currently aware that the TensorFlow models support 2d arrays for training and testing. I was wondering what procedures I would have to go through in order the be able to train and test the model on all of the independent trials (2d) contained in this 3darray. In addition, I will be adding more trials in the future. So what are the proper procedures to go through in order to constantly be updating my model with the new data/trials to strengthen my LSTM.
Here is the model I was trying to initially replicate for a different purpose other than human activity: https://github.com/guillaume-chevalier/LSTM-Human-Activity-Recognition. Another more feasible model would be this which I would much rather look at for anomaly detection in the time-series data: https://arxiv.org/abs/1607.00148. I want to build a anomaly detection model that given the set of non-anomalous time-series training data, we can detect anomalies in the test data where parts of the data over time is defined as "out of family."

I think for most LSTM's you're going to want to think of your data in this way (as it will be easy to use as input for the networks).
You'll have 3 dimension measurements:
feature_size = the number of different features (torque, velocity, etc.)
number_of_time_steps = the number of time steps collected for a single car
number_of_cars = the number of cars
It will most likely be easiest to read your data in as a set of matrices, where each matrix corresponds to one full sample (all the time steps for a single car).
You can arrange these matrices so that each row is an observation and each column is a different parameter (or the opposite, you may have to transpose the matrices, look at how your network input is formatted).
So each matrix is of size:
number_of_time_steps x feature_size (#rows x #columns). You will have number_of_cars different matrices. Each matrix is a sample.
To convert your array to this format, you can use this block of code (note, you can already access a single sample in your array with A[n], but this makes it so the shape of the accessed elements are what you expect):
import numpy as np
A = [[['car1', 'timefeatures1'],['car1', 'timefeatures2']],
[['car2', 'timefeatures1'],['car2', 'timefeatures2']],
[['car3', 'timefeatures1'],['car3', 'timefeatures2']]
]
easy_format = np.array(A)
Now you can get an individual sample with easy_format[n], where n is the sample you want.
easy_format[1] prints
array([['car2', 'timefeatures1'],
['car2', 'timefeatures2']],
dtype='|S12')
easy_format[1].shape = (2,2)
Now that you can do that, you can format them however you need for the network you're using (transposing rows and columns if necessary, presenting a single sample at a time or all of them at once, etc.)
What you're looking to do (if I'm reading that second paper correctly) most likely requires a sequence to sequence lstm or rnn. Your original sequence is your time series for a given trial, and you're generating an intermediate set of weights (an embedding) that can recreate that original sequence with a low amount of error. You're doing this for all the trials. You will train this lstm on a series of reasonably normal trials and get it to perform well (reconstruct the sequence accurately). You can then use this same set of embeddings to try to reconstruct a new sequence, and if it has a high reconstruction error, you can assume it's anomalous.
Check this repo for a sample of what you'd want along with explanations of how to use it and what the code is doing (it only maps a sequence of integers to another sequence of integers, but can easily be extended to map a sequence of vectors to a sequence of vectors): https://github.com/ichuang/tflearn_seq2seq The pattern you'd define is just your original sequence. You might also take a look at autoencoders for this problem.
Final Edit: Check this repository: https://github.com/beld/Tensorflow-seq2seq-autoencoder/blob/master/simple_seq2seq_autoencoder.py
I have modified the code in it very slightly to work on the newest version of tensorflow and to make some of the variable names clearer. You should be able to modify it to run on your dataset. Right now I'm just having it autoencode a randomly generated array of 1's and 0's. You would do this for a large subset of your data and then see if other data was reconstructed accurately or not (much higher error than average might imply an anomaly).
import numpy as np
import tensorflow as tf
learning_rate = 0.001
training_epochs = 30000
display_step = 100
hidden_state_size = 100
samples = 10
time_steps = 20
step_dims = 5
test_data = np.random.choice([ 0, 1], size=(time_steps, samples, step_dims))
initializer = tf.random_uniform_initializer(-1, 1)
seq_input = tf.placeholder(tf.float32, [time_steps, samples, step_dims])
encoder_inputs = [tf.reshape(seq_input, [-1, step_dims])]
decoder_inputs = ([tf.zeros_like(encoder_inputs[0], name="GO")]
+ encoder_inputs[:-1])
targets = encoder_inputs
weights = [tf.ones_like(targets_t, dtype=tf.float32) for targets_t in targets]
cell = tf.contrib.rnn.BasicLSTMCell(hidden_state_size)
_, enc_state = tf.contrib.rnn.static_rnn(cell, encoder_inputs, dtype=tf.float32)
cell = tf.contrib.rnn.OutputProjectionWrapper(cell, step_dims)
dec_outputs, dec_state = tf.contrib.legacy_seq2seq.rnn_decoder(decoder_inputs, enc_state, cell)
y_true = [tf.reshape(encoder_input, [-1]) for encoder_input in encoder_inputs]
y_pred = [tf.reshape(dec_output, [-1]) for dec_output in dec_outputs]
loss = 0
for i in range(len(y_true)):
loss += tf.reduce_sum(tf.square(tf.subtract(y_pred[i], y_true[i])))
optimizer = tf.train.AdamOptimizer(learning_rate).minimize(loss)
init = tf.initialize_all_variables()
with tf.Session() as sess:
sess.run(init)
x = test_data
for epoch in range(training_epochs):
#x = np.arange(time_steps * samples * step_dims)
#x = x.reshape((time_steps, samples, step_dims))
feed = {seq_input: x}
_, cost_value = sess.run([optimizer, loss], feed_dict=feed)
if epoch % display_step == 0:
print "logits"
a = sess.run(y_pred, feed_dict=feed)
print a
print "labels"
b = sess.run(y_true, feed_dict=feed)
print b
print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(cost_value))
print("Optimization Finished!")

Your input shape and the corresponding model depends on why type of Anomaly you want to detect. You can consider:
1. Feature only Anomaly:
Here you consider individual features and decide whether any of them is Anomalous, without considering when its measured. In your example,the feature [torque, speed, acceleration,...] is an anomaly if one or more is an outlier with respect to the other features. In this case your inputs should be of form [batch, features].
2. Time-feature Anomaly:
Here your inputs are dependent on when you measure the feature. Your current feature may depend on the previous features measured over time. For example there may be a feature whose value is an outlier if it appears at time 0 but not outlier if it appears furture in time. In this case you divide each of your trails with overlapping time windows and form a feature set of form [batch, time_window, features].
It should be very simple to start with (1) using an autoencoder where you train an auto-encoder and on the error between input and output, you can choose a threshold like 2-standard devations from the mean to determine whether its an outlier or not.
For (2), you can follow the second paper you mentioned using a seq2seq model, where your decoder error will determine which features are outliers. You can check on this for the implementation of such a model.

How does sklearn.svm.svc's function predict_proba() work internally?

I am using sklearn.svm.svc from scikit-learn to do binary classification. I am using its predict_proba() function to get probability estimates. Can anyone tell me how predict_proba() internally calculates the probability?

Scikit-learn uses LibSVM internally, and this in turn uses Platt scaling, as detailed in this note by the LibSVM authors, to calibrate the SVM to produce probabilities in addition to class predictions.
Platt scaling requires first training the SVM as usual, then optimizing parameter vectors A and B such that
P(y|X) = 1 / (1 + exp(A * f(X) + B))
where f(X) is the signed distance of a sample from the hyperplane (scikit-learn's decision_function method). You may recognize the logistic sigmoid in this definition, the same function that logistic regression and neural nets use for turning decision functions into probability estimates.
Mind you: the B parameter, the "intercept" or "bias" or whatever you like to call it, can cause predictions based on probability estimates from this model to be inconsistent with the ones you get from the SVM decision function f. E.g. suppose that f(X) = 10, then the prediction for X is positive; but if B = -9.9 and A = 1, then P(y|X) = .475. I'm pulling these numbers out of thin air, but you've noticed that this can occur in practice.
Effectively, Platt scaling trains a probability model on top of the SVM's outputs under a cross-entropy loss function. To prevent this model from overfitting, it uses an internal five-fold cross validation, meaning that training SVMs with probability=True can be quite a lot more expensive than a vanilla, non-probabilistic SVM.

Actually I found a slightly different answer that they used this code to convert decision value to probability
'double fApB = decision_value*A+B;
if (fApB >= 0)
return Math.exp(-fApB)/(1.0+Math.exp(-fApB));
else
return 1.0/(1+Math.exp(fApB)) ;'
Here A and B values can be found in the model file (probA and probB).
It offers a way to convert probability to decision value and thus to hinge loss.
Use that ln(0) = -200.