Auto-encoding is an important task which is typically realized by deep neural
networks (DNNs) such as convolutional neural networks (CNN). In this paper, we
propose EncoderForest (abbrv. eForest), the first tree ensemble based
auto-encoder. We present a procedure for enabling forests to do backward
reconstruction by utilizing the equivalent classes defined by decision paths of
the trees, and demonstrate its usage in both supervised and unsupervised
setting. Experiments show that, compared with DNN autoencoders, eForest is able
to obtain lower reconstruction error with fast training speed, while the model
itself is reusable and damage-tolerable.

本文提出了基于树集成的自编码器模型 EncoderForest，可以利用决策树的等价类进行反向重建， 相较于深度神经网络的自编码器，具有更低的重建误差和快速训练速度，并且易于复用和耐损伤。

森林中的自编码器

AutoEncoder by Forest

Many approaches for estimation of Remaining Useful Life (RUL) of a machine,
using its operational sensor data, make assumptions about how a system degrades
or a fault evolves, e.g., exponential degradation. However, in many domains
degradation may not follow a pattern. We propose a Long Short Term Memory based
Encoder-Decoder (LSTM-ED) scheme to obtain an unsupervised health index (HI)
for a system using multi-sensor time-series data. LSTM-ED is trained to
reconstruct the time-series corresponding to healthy state of a system. The
reconstruction error is used to compute HI which is then used for RUL
estimation. We evaluate our approach on publicly available Turbofan Engine and
Milling Machine datasets. We also present results on a real-world industry
dataset from a pulverizer mill where we find significant correlation between
LSTM-ED based HI and maintenance costs.

使用 Long Short Term Memory 编码器 - 解码器方案获取多传感器时间序列数据的无监督健康指数来进行设备剩余寿命估计。

基于 LSTM 编码器 - 解码器的无监督健康指数的多传感器预测

Multi-Sensor Prognostics using an Unsupervised Health Index based on  LSTM Encoder-Decoder

The completion of low rank matrices from few entries is a task with many
practical applications. We consider here two aspects of this problem:
detectability, i.e. the ability to estimate the rank $r$ reliably from the
fewest possible random entries, and performance in achieving small
reconstruction error. We propose a spectral algorithm for these two tasks
called MaCBetH (for Matrix Completion with the Bethe Hessian). The rank is
estimated as the number of negative eigenvalues of the Bethe Hessian matrix,
and the corresponding eigenvectors are used as initial condition for the
minimization of the discrepancy between the estimated matrix and the revealed
entries. We analyze the performance in a random matrix setting using results
from the statistical mechanics of the Hopfield neural network, and show in
particular that MaCBetH efficiently detects the rank $r$ of a large $n\times m$
matrix from $C(r)r\sqrt{nm}$ entries, where $C(r)$ is a constant close to $1$.
We also evaluate the corresponding root-mean-square error empirically and show
that MaCBetH compares favorably to other existing approaches.

本文提出了一种名为 MaCBetH 的矩阵完成问题的谱算法，该算法可以用于在很少的随机输入下可靠地估计矩阵的秩，并在实现小重构误差方面表现良好。

矩阵填充：谱可检测性与秩估计

Matrix Completion from Fewer Entries: Spectral Detectability and Rank  Estimation

What do auto-encoders learn about the underlying data generating
distribution? Recent work suggests that some auto-encoder variants do a good
job of capturing the local manifold structure of data. This paper clarifies
some of these previous observations by showing that minimizing a particular
form of regularized reconstruction error yields a reconstruction function that
locally characterizes the shape of the data generating density. We show that
the auto-encoder captures the score (derivative of the log-density with respect
to the input). It contradicts previous interpretations of reconstruction error
as an energy function. Unlike previous results, the theorems provided here are
completely generic and do not depend on the parametrization of the
auto-encoder: they show what the auto-encoder would tend to if given enough
capacity and examples. These results are for a contractive training criterion
we show to be similar to the denoising auto-encoder training criterion with
small corruption noise, but with contraction applied on the whole
reconstruction function rather than just encoder. Similarly to score matching,
one can consider the proposed training criterion as a convenient alternative to
maximum likelihood because it does not involve a partition function. Finally,
we show how an approximate Metropolis-Hastings MCMC can be setup to recover
samples from the estimated distribution, and this is confirmed in sampling
experiments.

本文探讨了利用正则化重建误差最小化的方法来捕捉数据密度和得分匹配的思想，从而实现对自编码器对于数据生成分布的学习和采样。