A large-scale dynamic network (LDN) is a source of data in many big
data-related applications due to their large number of entities and large-scale
dynamic interactions. They can be modeled as a high-dimensional incomplete
(HDI) tensor that contains a wealth of knowledge about time patterns. A Latent
factorization of tensors (LFT) model efficiently extracts this time pattern,
which can be established using stochastic gradient descent (SGD) solvers.
However, LFT models based on SGD are often limited by training schemes and have
poor tail convergence. To solve this problem, this paper proposes a novel
nonlinear LFT model (MNNL) based on momentum-incorporated SGD, which extracts
non-negative latent factors from HDI tensors to make training unconstrained and
compatible with general training schemes, while improving convergence accuracy
and speed. Empirical studies on two LDN datasets show that compared to existing
models, the MNNL model has higher prediction accuracy and convergence speed.

本文提出了一种基于动量梯度下降的非线性潜在张量因子分解模型 (MNNL)，可从高维不完整张量 (HDI) 中提取非负潜在因子，改善了传统 LFT 模型的训练问题，提高了预测准确性和收敛速度。

动态网络表示的动量非负张量因式分解模型

A Momentum-Incorporated Non-Negative Latent Factorization of Tensors  Model for Dynamic Network Representation

Modern applications in sensitive domains such as biometrics and medicine
frequently require the use of non-decomposable loss functions such as
precision@k, F-measure etc. Compared to point loss functions such as
hinge-loss, these offer much more fine grained control over prediction, but at
the same time present novel challenges in terms of algorithm design and
analysis. In this work we initiate a study of online learning techniques for
such non-decomposable loss functions with an aim to enable incremental learning
as well as design scalable solvers for batch problems. To this end, we propose
an online learning framework for such loss functions. Our model enjoys several
nice properties, chief amongst them being the existence of efficient online
learning algorithms with sublinear regret and online to batch conversion
bounds. Our model is a provable extension of existing online learning models
for point loss functions. We instantiate two popular losses, prec@k and pAUC,
in our model and prove sublinear regret bounds for both of them. Our proofs
require a novel structural lemma over ranked lists which may be of independent
interest. We then develop scalable stochastic gradient descent solvers for
non-decomposable loss functions. We show that for a large family of loss
functions satisfying a certain uniform convergence property (that includes
prec@k, pAUC, and F-measure), our methods provably converge to the empirical
risk minimizer. Such uniform convergence results were not known for these
losses and we establish these using novel proof techniques. We then use
extensive experimentation on real life and benchmark datasets to establish that
our method can be orders of magnitude faster than a recently proposed cutting
plane method.

本文提出了一种针对非可分离损失函数的在线学习框架，通过引入新型算法设计和分析，该模型具有高效的在线学习算法，具有亚线性遗憾和在线转换界限；进一步开发了可扩展的随机梯度下降求解器，经过实验在真实数据集上证明，该方法比近期提出的切割面算法快得多。