Vector-valued output from Predict

Question

I have a list of 3D points, and I'd like to run a Predict on them just to test. It should be fairly straightforward. Here's a simple example:

trains = {{1, 2, 3} -> {4, 5, 6}, {2, 3, 4} -> {7, 8, 9}};

p = Predict[trains];

ERROR:
Predict: Incompatible variable type (Numerical) and variable value ({4,5,6}).

I'm not sure what I'm doing wrong. Any advise?

Answer 1

In Mathematica 11 you can create such a neural network architecture (seq2seq learning). Desktop version of Mathematica 11 is not available yet, so I have experimented in the Wolfram Cloud.

$Version
11.0.0 for Linux x86 (64-bit) (July 28, 2016)

net=NetChain[{16,3},"Input"->3,"Output"->3]

trains = {{1, 2, 3} -> {4, 5, 6}, {2, 3, 4} -> {7, 8, 9}};

net = NetTrain[net, trains];

net[{1,2,3}]

{4.00003,4.99999,5.99999}

Documentation: http://reference.wolfram.com/language/guide/NeuralNetworks.html

Answer 2

What the best approach is depends heavily on what you are trying to do. It could be that you don't even need machine learning.

You could construct your own neural network to deal with this kind of input-output. But if you want to use predict you'd have to construct a separate predictor for each component as Mikado comments.

trains = {{1, 2, 3} -> {4, 5, 6}, {2, 3, 4} -> {7, 8, 9}};

t = Transpose@(Table[First@# -> (Last@#)[[i]], {i, 1, 3}] & /@ trains);
p = Predict[#] & /@ t;
f[x_]  := #[x] & /@ p;

Use by calling f, e.g: f[{1,2,3}]:

{4., 5., 6.}

Whether this is a good approach for your problem is impossible to tell due to the lack of information.