This work is concerned with the problem of recovering high-dimensional
signals $\mathbf{x} \in \mathbb{R}^n$ which belong to a convex set of
low-complexity from a small number of quantized measurements. We propose to
estimate the signals via a convex program based on rectified linear units
(ReLUs) for two different quantization schemes, namely one-bit and uniform
multi-bit quantization. Assuming that the linear measurement process can be
modelled by a sensing matrix with i.i.d. subgaussian rows, we obtain for both
schemes near-optimal uniform reconstruction guarantees by adding well-designed
noise to the linear measurements prior to the quantization step. In the one-bit
case, we show that the program is robust against adversarial bit corruptions as
well as additive noise on the linear measurements. Further, our analysis
quantifies precisely how the rate-distortion relationship of the program
changes depending on whether we seek reconstruction accuracies above or below
the noise floor. The proofs rely on recent results by Dirksen and Mendelson on
non-Gaussian hyperplane tessellations. Finally, we complement our theoretical
analysis with numerical experiments which compare our method to other
state-of-the-art methodologies.

本研究旨在针对高维信号恢复问题，提出了基于修正线性单元的一比特和均匀多比特量化的凸规划算法，在线性测量过程中添加设计良好的噪声，从而获得最优近似重构保证，并证明了该算法对位坏的鲁棒性。其中，Dirksen 和 Mendelson 对非高斯超平面镶嵌的最新结果作为证明依据。

通过修正线性单元的量化压缩感知

Quantized Compressed Sensing by Rectified Linear Units

We consider the problem of inferring the values of an arbitrary set of
variables (e.g., risk of diseases) given other observed variables (e.g.,
symptoms and diagnosed diseases) and high-dimensional signals (e.g., MRI images
or EEG). This is a common problem in healthcare since variables of interest
often differ for different patients. Existing methods including Bayesian
networks and structured prediction either do not incorporate high-dimensional
signals or fail to model conditional dependencies among variables. To address
these issues, we propose bidirectional inference networks (BIN), which stich
together multiple probabilistic neural networks, each modeling a conditional
dependency. Predictions are then made via iteratively updating variables using
backpropagation (BP) to maximize corresponding posterior probability.
Furthermore, we extend BIN to composite BIN (CBIN), which involves the
iterative prediction process in the training stage and improves both accuracy
and computational efficiency by adaptively smoothing the optimization
landscape. Experiments on synthetic and real-world datasets (a sleep study and
a dermatology dataset) show that CBIN is a single model that can achieve
state-of-the-art performance and obtain better accuracy in most inference tasks
than multiple models each specifically trained for a different task.

提出了一种称为双向推理网络（BIN）的方法，它可以将多个概率神经网络缝合在一起，以建模变量之间的条件依赖关系，并通过迭代更新变量来进行预测。同时，将 BIN 扩展到了复合 BIN（CBIN），通过自适应平滑优化器的方法，在训练阶段的迭代预测过程中提高了精度和计算效率，并在人工合成数据集和真实数据集上展示了 CBIN 单个模型可以实现最先进的性能，而且在大多数推理任务中比为不同任务专门训练的多个模型获得更高的准确性。

双向推理网络：一类用于健康画像的深度贝叶斯网络

Bidirectional Inference Networks: A Class of Deep Bayesian Networks for  Health Profiling

This paper offers a characterization of fundamental limits on the
classification and reconstruction of high-dimensional signals from
low-dimensional features, in the presence of side information. We consider a
scenario where a decoder has access both to linear features of the signal of
interest and to linear features of the side information signal; while the side
information may be in a compressed form, the objective is recovery or
classification of the primary signal, not the side information. The signal of
interest and the side information are each assumed to have (distinct) latent
discrete labels; conditioned on these two labels, the signal of interest and
side information are drawn from a multivariate Gaussian distribution. With
joint probabilities on the latent labels, the overall signal-(side information)
representation is defined by a Gaussian mixture model. We then provide sharp
sufficient and/or necessary conditions for these quantities to approach zero
when the covariance matrices of the Gaussians are nearly low-rank. These
conditions, which are reminiscent of the well-known Slepian-Wolf and Wyner-Ziv
conditions, are a function of the number of linear features extracted from the
signal of interest, the number of linear features extracted from the side
information signal, and the geometry of these signals and their interplay.
Moreover, on assuming that the signal of interest and the side information obey
such an approximately low-rank model, we derive expansions of the
reconstruction error as a function of the deviation from an exactly low-rank
model; such expansions also allow identification of operational regimes where
the impact of side information on signal reconstruction is most relevant. Our
framework, which offers a principled mechanism to integrate side information in
high-dimensional data problems, is also tested in the context of imaging
applications.

本研究考虑通过低维特征提取高维信号的分类与恢复问题，研究了侧信息对于高维信号恢复的影响及其本质极限，其中使用高斯混合模型描述信号与侧信息之间的关联关系并分析了该模型的近似低秩结构。

在存在辅助信息的情况下，根据低维特征对高维信号进行分类和重建

Classification and Reconstruction of High-Dimensional Signals from  Low-Dimensional Features in the Presence of Side Information

Compressed sensing is a novel research area, which was introduced in 2006,
and since then has already become a key concept in various areas of applied
mathematics, computer science, and electrical engineering. It surprisingly
predicts that high-dimensional signals, which allow a sparse representation by
a suitable basis or, more generally, a frame, can be recovered from what was
previously considered highly incomplete linear measurements by using efficient
algorithms. This article shall serve as an introduction to and a survey about
compressed sensing.

介绍压缩感知的基本概念和应用，并总结了目前的研究现状。