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#Tensor machines for learning target-specific polynomial features

Jiyan Yang ([email protected])

Alex Gittens ([email protected])

##About Tensor machines find a parsimonious set of polynomial features in a target-specific manner. See the paper Tensor machines for learning target-specific polynomial features for more details.

This repository contains a collection of codes used to train tensor machines on a given dataset and evaluate their generalization performance.

##Codes The usage of each code is documented in the corresponding .m file. In particular,

• tensor_machines.m is the main file that implements tensor machines;
• tm_fg.m and tm_fg0.m evaluate the function objective and compute the gradient of the underlying optimization problem;
• get_tm_pred.m calculates prediction on a new dataset using a learned model after training;
• cv_tensor_machines.m uses grid search to tune hyper-parameters for tensor machines;
• tm_solver.m serves as an interface that allows one to train tensor machines and evaluate the generalization performance of tensor machines on a test set.

##Solvers The underlying optimization solver is central in training tensor machines. We considered two solvers: minFunc and SFO.

• SFO is included in this package.
• minFunc can be downloaded via this link.

For the parameters used in these two solvers, see tensor_machines.m.

##Datasets In datasets/, two publicly available datasets from UCI repository are included.

• adult.mat: the Adult dataset;
• forest_small.mat: a subset of the Forest dataset; this has the test set of the original Forest dataset and a subset of 50000 training examples chosen randomly from the original training set.

##Examples

• main.m demonstrates how to use our code to fit and evaluate TMs on a real dataset.
• main2.m is similar to main.m but here the target is artificial, to allow us to test TMs performance on known polynomial targets

##Reference Jiyan Yang and Alex Gittens, Tensor machines for learning target-specific polynomial features.

##License The MIT License (MIT)

Copyright (c) 2015 Jiyan Yang and Alex Gittens

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.