Reverse Annealing for Nonnegative/Binary Matrix Factorization

非负/二进制矩阵分解上的松弛辅助反向退火

Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization

本文针对非负/二进制矩阵分解，提出用线性规划松弛解初始化反向退火，在人脸和随机数据集上验证其收敛更优，并揭示松弛解与最优解的关系。

Nonnegative/binary matrix factorization with a D-Wave quantum annealer

D-Wave quantum annealers represent a novel computational architecture and have attracted significant interest, but have been used for few real-world computations. Machine learning has been identified as an area where quantum annealing may be useful. Here, we show that the D-Wave 2X can be effectively used as part of an unsupervised machine learning method. This method can be used to analyze large datasets. The D-Wave only limits the number of features that can be extracted from the dataset. We apply this method to learn the features from a set of facial images.

精确非负矩阵分解的启发式方法

Heuristics for Exact Nonnegative Matrix Factorization

本文提出两种启发式方法用于精确非负矩阵分解，通过模拟退火和贪心随机自适应搜索启发式方法，展示了其在多种非负矩阵类别的应用优势，并探讨了非负秩的行为特性。

Quantum Semantic Learning by Reverse Annealing an Adiabatic Quantum Computer

Boltzmann Machines constitute a class of neural networks with applications to image reconstruction, pattern classification and unsupervised learning in general. Their most common variants, called Restricted Boltzmann Machines (RBMs) exhibit a good trade-off between computability on existing silicon-based hardware and generality of possible applications. Still, the diffusion of RBMs is quite limited, since their training process proves to be hard. The advent of commercial Adiabatic Quantum Computers (AQCs) raised the expectation that the implementations of RBMs on such quantum devices could inc…

Accurate and Conservative Estimates of MRF Log-likelihood using Reverse Annealing

Markov random fields (MRFs) are difficult to evaluate as generative models because computing the test log-probabilities requires the intractable partition function. Annealed importance sampling (AIS) is widely used to estimate MRF partition functions, and often yields quite accurate results. However, AIS is prone to overestimate the log-likelihood with little indication that anything is wrong. We present the Reverse AIS Estimator (RAISE), a stochastic lower bound on the log-likelihood of an approximation to the original MRF model. RAISE requires only the same MCMC transition operators as stand…

Continuous black-box optimization with quantum annealing and random subspace coding

A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such algorithms perform poorly due to the difficulty of acquisition function optimization. Herein, we apply quantum annealing (QA) to overcome the difficulty in the continuous black-box optimization. As QA specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution of QA has to be translated back. Our method has the…