Support Vector Regression with High Dimensional Output using python's libsvm

Support Vector Machines as a mathematical framework is formulated in terms of a single prediction variable. Hence most libraries implementing them will reflect this as using one single target variable in their API.

What you could do is train a single SVM model for each target dimension in your data.

• on the plus side, you can train them in // on a cluster as each model is independent of one another

• on the minus side, sub-models will share nothing and won't benefit from what they individually discovered in the structure of the input data and potentially need a lot of memory to store the model as they will have no shared intermediate representation

Variant of SVMs can probably be devised in a multi-task learning setting to learn some common kernel-based intermediate representation suitable for reuse to predict multi-dimensional targets however this is not implemented in libsvm AFAIK. Google for multi task learning SVM if you want to learn more.

Alternatively, multi-layer perceptrons (a kind of feed forward neural networks) can naturally deal with multi-dimensional outcomes and hence should be better at sharing intermediate representations of the data reused across targets, especially if they are deep enough with the first layers pre-trained in an unsupervised manner using an autoencoder objective function.

You might want to have a look at http://deeplearning.net/tutorial/ for a nice introduction to various neural network architectures and practical tools and examples to implement them efficiently.