Variable time units LSTM

Question

I am working with data that requires classifying if a patient will develop cancer or not in the future, based on medical tests done over time. The tests have a sequential relationship. A, then B, then C, etc. For example:

| Patient ID | Test ID | RBC Count | WBC Count | Label
|     1      |    A    |     4.2   |    7000   |   0
|     1      |    B    |     5.3   |    12000  |   0
|     1      |    C    |     2.4   |    15000  |   1
|     2      |    A    |     7.6   |    8000   |   0
|     2      |    B    |     7.4   |    7500   |   0

Each point is not taken at a regular time interval, so this may not be considered a time-series data. How can I apply Keras Sequential model to this? Especially since each patient can have a different number of tests, up to 5, eg. Patient ID 1 has 3 tests, and Patient ID 2 has 2 tests.

Answer 1

[Wow.A Great problem]

Possible solution:(Personal opinion)

First Opinion is: Use SVM or KNN instead of a neural net as your data is trivial like 2D vector.

Second Opinion is:

As you aren't trying to predict the next text possibility of a particular patient so in this case RNN(LSTM,GRU) might not help you. So a simple solution is Autoencoder to compress the data and then run a simple logistic regression or svm or may be a neural net.

How?

1.As your Patient numbers are not same in all cases so you should represent his/her all medical test data into a single vector.That is where Autoencoder comes into play.example:

Suppose we have 3 patient: First-3 test , second-2 test ,three-5 test. Our goal is to compress each patient data into 2 dimension vector(as your features are RBC and WBC , 2 features , so it will learn well if we compress it into 2D vector).

(inside asterik sign(*) your data goes)

First Patient=[[*],[*],[*]] # three test
Second Patient=[[*],[*]] # two test
Third Patient=[[*],[*],[*],[*],[*]] # five test

Now you compress the data via Variational autoencoder.

scale your data as wbc>>rbc

then use variational autoencoder to get the latent space vector

use dimesion=2 in latent space via Dense(2)

now when you get the vectors just add the vectors of test for each patient

Like : For First patient you got three vector in latent space like-

[2.33,4.2]+[5.11,9.22]+[0.21,6.32]=result..and You got the representaion for First patient.

after you got all of them a trivial svm/polynomial regression would be just fine.

Let me know how you solved it.

Answer 2

This most certainly sounds like a problem for a Phased LSTM https://arxiv.org/abs/1610.09513

It's designed to process inputs that arrive at irregular time intervals, for example, from two sensors working at different frequencies. As a cool bonus, it's able to process much longer sequences, where a usual LSTM would freak out.

Its derivatives and Backprop is described here: Gradient derivation reference for Phased LSTM

Also, make sure to read "heads up" and notes of the author on his github, before you start implementing it: https://github.com/dannyneil/public_plstm