Training generative adversarial networks is unstable in high-dimensions as
the true data distribution tends to be concentrated in a small fraction of the
ambient space. The discriminator is then quickly able to classify nearly all
generated samples as fake, leaving the generator without meaningful gradients
and causing it to deteriorate after a point in training. In this work, we
propose training a single generator simultaneously against an array of
discriminators, each of which looks at a different random low-dimensional
projection of the data. Individual discriminators, now provided with restricted
views of the input, are unable to reject generated samples perfectly and
continue to provide meaningful gradients to the generator throughout training.
Meanwhile, the generator learns to produce samples consistent with the full
data distribution to satisfy all discriminators simultaneously. We demonstrate
the practical utility of this approach experimentally, and show that it is able
to produce image samples with higher quality than traditional training with a
single discriminator.

本文提出了一种针对高维度情况下 GAN 训练不稳定的方法，即使用一个生成器同时生成多个不同低维度投影数据的判别器来提供连续的梯度，实验结果表明该方法能够生成较高质量的图像样本。

使用多个随机投影稳定 GAN 训练

Stabilizing GAN Training with Multiple Random Projections

We propose a novel, efficient approach for distributed sparse learning in
high-dimensions, where observations are randomly partitioned across machines.
Computationally, at each round our method only requires the master machine to
solve a shifted ell_1 regularized M-estimation problem, and other workers to
compute the gradient. In respect of communication, the proposed approach
provably matches the estimation error bound of centralized methods within
constant rounds of communications (ignoring logarithmic factors). We conduct
extensive experiments on both simulated and real world datasets, and
demonstrate encouraging performances on high-dimensional regression and
classification tasks.

提出了一种新颖、高效的分布式稀疏学习方法，可在高维度中随机分割观测数据，并在通信效率方面展现极佳的表现。

稀疏性下的高效分布式学习

Efficient Distributed Learning with Sparsity

Bayesian optimization techniques have been successfully applied to robotics,
planning, sensor placement, recommendation, advertising, intelligent user
interfaces and automatic algorithm configuration. Despite these successes, the
approach is restricted to problems of moderate dimension, and several workshops
on Bayesian optimization have identified its scaling to high-dimensions as one
of the holy grails of the field. In this paper, we introduce a novel random
embedding idea to attack this problem. The resulting Random EMbedding Bayesian
Optimization (REMBO) algorithm is very simple, has important invariance
properties, and applies to domains with both categorical and continuous
variables. We present a thorough theoretical analysis of REMBO. Empirical
results confirm that REMBO can effectively solve problems with billions of
dimensions, provided the intrinsic dimensionality is low. They also show that
REMBO achieves state-of-the-art performance in optimizing the 47 discrete
parameters of a popular mixed integer linear programming solver.

本文介绍了 Random Embedding Bayesian Optimization (REMBO) 算法，运用随机嵌入思想来攻克高维度问题，此算法简单且具有重要的不变性，应用于具有连续和分类变量的领域，经理论和实证分析证明 REMBO 可在高达数十亿个维度的问题中有效地解决问题，其在优化流行的混合整数线性规划求解器的 47 个离散参数方面也达到了状态的最佳表现。

通过随机嵌入在十亿维度上进行贝叶斯优化

Bayesian Optimization in a Billion Dimensions via Random Embeddings

The versatility of exponential families, along with their attendant convexity
properties, make them a popular and effective statistical model. A central
issue is learning these models in high-dimensions, such as when there is some
sparsity pattern of the optimal parameter. This work characterizes a certain
strong convexity property of general exponential families, which allow their
generalization ability to be quantified. In particular, we show how this
property can be used to analyze generic exponential families under L_1
regularization.

本文研究指出指数分布族拥有的一种强凸性质对于分析一般指数分布族在 L_1 正则化下的泛化能力具有重要作用。