4,387 research outputs found
Exponential Machines
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.Comment: ICLR-2017 workshop track pape
Unsupervised Generative Modeling Using Matrix Product States
Generative modeling, which learns joint probability distribution from data
and generates samples according to it, is an important task in machine learning
and artificial intelligence. Inspired by probabilistic interpretation of
quantum physics, we propose a generative model using matrix product states,
which is a tensor network originally proposed for describing (particularly
one-dimensional) entangled quantum states. Our model enjoys efficient learning
analogous to the density matrix renormalization group method, which allows
dynamically adjusting dimensions of the tensors and offers an efficient direct
sampling approach for generative tasks. We apply our method to generative
modeling of several standard datasets including the Bars and Stripes, random
binary patterns and the MNIST handwritten digits to illustrate the abilities,
features and drawbacks of our model over popular generative models such as
Hopfield model, Boltzmann machines and generative adversarial networks. Our
work sheds light on many interesting directions of future exploration on the
development of quantum-inspired algorithms for unsupervised machine learning,
which are promisingly possible to be realized on quantum devices.Comment: 11 pages, 12 figures (not including the TNs) GitHub Page:
https://congzlwag.github.io/UnsupGenModbyMPS
- …