Many real-world machine learning applications are characterized by a huge
number of features, leading to computational and memory issues, as well as the
risk of overfitting. Ideally, only relevant and non-redundant features should
be considered to preserve the complete information of the original data and
limit the dimensionality. Dimensionality reduction and feature selection are
common preprocessing techniques addressing the challenge of efficiently dealing
with high-dimensional data. Dimensionality reduction methods control the number
of features in the dataset while preserving its structure and minimizing
information loss. Feature selection aims to identify the most relevant features
for a task, discarding the less informative ones. Previous works have proposed
approaches that aggregate features depending on their correlation without
discarding any of them and preserving their interpretability through
aggregation with the mean. A limitation of methods based on correlation is the
assumption of linearity in the relationship between features and target. In
this paper, we relax such an assumption in two ways. First, we propose a
bias-variance analysis for general models with additive Gaussian noise, leading
to a dimensionality reduction algorithm (NonLinCFA) which aggregates non-linear
transformations of features with a generic aggregation function. Then, we
extend the approach assuming that a generalized linear model regulates the
relationship between features and target. A deviance analysis leads to a second
dimensionality reduction algorithm (GenLinCFA), applicable to a larger class of
regression problems and classification settings. Finally, we test the
algorithms on synthetic and real-world datasets, performing regression and
classification tasks, showing competitive performances.

本文提出了两种基于非线性变换和广义线性模型的降维算法，分别适用于回归和分类问题，测试表明算法效果竞争力强。

非线性特征聚合：基于理论的两个算法

Nonlinear Feature Aggregation: Two Algorithms driven by Theory

This paper studies the deflation algorithm when applied to estimate a
low-rank symmetric spike contained in a large tensor corrupted by additive
Gaussian noise. Specifically, we provide a precise characterization of the
large-dimensional performance of deflation in terms of the alignments of the
vectors obtained by successive rank-1 approximation and of their estimated
weights, assuming non-trivial (fixed) correlations among spike components. Our
analysis allows an understanding of the deflation mechanism in the presence of
noise and can be exploited for designing more efficient signal estimation
methods.

研究在大矩阵中包含低秩对称尖峰的加性高斯噪声时，使用通缩算法估算的精确特性，即多个秩 - 1 逼近所得向量的对齐和其权重的估计，可用于设计更有效的信号估计方法。

大型对称尖峰张量上的 Hotelling 缩放

Hotelling Deflation on Large Symmetric Spiked Tensors

We describe a novel method for training high-quality image denoising models
based on unorganized collections of corrupted images. The training does not
need access to clean reference images, or explicit pairs of corrupted images,
and can thus be applied in situations where such data is unacceptably expensive
or impossible to acquire. We build on a recent technique that removes the need
for reference data by employing networks with a "blind spot" in the receptive
field, and significantly improve two key aspects: image quality and training
efficiency. Our result quality is on par with state-of-the-art neural network
denoisers in the case of i.i.d. additive Gaussian noise, and not far behind
with Poisson and impulse noise. We also successfully handle cases where
parameters of the noise model are variable and/or unknown in both training and
evaluation data.

利用一种新颖的训练方法，基于有噪声图像的非组织集合来培训高质量的图像去噪模型，通过采用具有感受野盲区的网络来消除对参考数据的需要，提高了图像质量和训练效率，最终结果质量与最先进的神经网络去噪器相当。

高质量自监督深度图像去噪

High-Quality Self-Supervised Deep Image Denoising

We consider the problem of outlier robust PCA (OR-PCA) where the goal is to
recover principal directions despite the presence of outlier data points. That
is, given a data matrix $M^*$, where $(1-\alpha)$ fraction of the points are
noisy samples from a low-dimensional subspace while $\alpha$ fraction of the
points can be arbitrary outliers, the goal is to recover the subspace
accurately. Existing results for \OR-PCA have serious drawbacks: while some
results are quite weak in the presence of noise, other results have runtime
quadratic in dimension, rendering them impractical for large scale
applications.
In this work, we provide a novel thresholding based iterative algorithm with
per-iteration complexity at most linear in the data size. Moreover, the
fraction of outliers, $\alpha$, that our method can handle is tight up to
constants while providing nearly optimal computational complexity for a general
noise setting. For the special case where the inliers are obtained from a
low-dimensional subspace with additive Gaussian noise, we show that a
modification of our thresholding based method leads to significant improvement
in recovery error (of the subspace) even in the presence of a large fraction of
outliers.

本文提出了基于阈值的迭代算法，用于处理含有离群点的数据集中的偏差鲁棒主成分分析问题，该方法的迭代复杂度最多线性，可以处理至多 α 分数的离群点，并且对于一般噪声设置具有近乎最佳的计算复杂度。对于特殊情况，即噪声是加性高斯噪声，本文改进了该方法，并成功地减小了恢复误差。