Exponential Machines

Alexander Novikov, Mikhail Trofimov, Ivan Oseledets

Abstract: Modeling interactions between features improves the performance of machine learning solutions in many domains (e.g. recommender systems or sentiment analysis). In this paper, we introduce Exponential Machines (ExM), a predictor that models all interactions of every order. The key idea is to represent an exponentially large tensor of parameters in a factorized format called Tensor Train (TT). The Tensor Train format regularizes the model and lets you control the number of underlying parameters. To train the model, we develop a stochastic Riemannian optimization procedure, which allows us to fit tensors with 2^160 entries. We show that the model achieves state-of-the-art performance on synthetic data with high-order interactions and that it works on par with high-order factorization machines on a recommender system dataset MovieLens 100K.

Conflicts: phystech.edu, skoltech.ru, bayesgroup.ru, msu.ru, hse.ru

Community Implementations: [ 5 code implementations](https://www.catalyzex.com/paper/arxiv:1605.03795/code)