Linear feature extraction at the presence of nonlinear dependencies among the
data is a fundamental challenge in unsupervised learning. We propose using a
Probabilistic Gram-Schmidt (PGS) type orthogonalization process in order to
detect and map out redundant dimensions. Specifically, by applying the PGS
process over any family of functions which presumably captures the nonlinear
dependencies in the data, we construct a series of covariance matrices that can
either be used to remove those dependencies from the principal components, or
to identify new large-variance directions. In the former case, we prove that
under certain assumptions the resulting algorithms detect and remove nonlinear
dependencies whenever those dependencies lie in the linear span of the chosen
function family. In the latter, we provide information-theoretic guarantees in
terms of entropy reduction. Both proposed methods extract linear features from
the data while removing nonlinear redundancies. We provide simulation results
on synthetic and real-world datasets which show improved performance over PCA
and state-of-the-art linear feature extraction algorithms, both in terms of
variance maximization of the extracted features, and in terms of improved
performance of classification algorithms.

使用概率格拉姆 - 施密特（PGS）正交化过程来探测和映射冗余维度，并通过该过程结合捕捉数据中非线性依赖的函数族构建一系列协方差矩阵，从而提取线性特征并移除非线性冗余。

超越 PCA：一种概率 Gram-Schmidt 方法进行特征提取

Beyond PCA: A Probabilistic Gram-Schmidt Approach to Feature Extraction

In some causal inference scenarios, the treatment (i.e. cause) variable is
measured inaccurately, for instance in epidemiology or econometrics. Failure to
correct for the effect of this measurement error can lead to biased causal
effect estimates. Previous research has not studied methods that address this
issue from a causal viewpoint while allowing for complex nonlinear dependencies
and without assuming access to side information. For such as scenario, this
paper proposes a model that assumes a continuous treatment variable which is
inaccurately measured. Building on existing results for measurement error
models, we prove that our model's causal effect estimates are identifiable,
even without knowledge of the measurement error variance or other side
information. Our method relies on a deep latent variable model where Gaussian
conditionals are parameterized by neural networks, and we develop an amortized
importance-weighted variational objective for training the model. Empirical
results demonstrate the method's good performance with unknown measurement
error. More broadly, our work extends the range of applications where reliable
causal inference can be conducted.

本文提出了一种基于深层潜在变量模型和重要性加权变分目标的测量误差下因果推断的方法，使得即使没有测量误差方差和侧面信息，也可以得出可靠的因果效应估计。

带噪声治疗和无附带信息可辨识的因果推断

Identifiable causal inference with noisy treatment and no side  information

Multi-output regression models must exploit dependencies between outputs to
maximise predictive performance. The application of Gaussian processes (GPs) to
this setting typically yields models that are computationally demanding and
have limited representational power. We present the Gaussian Process
Autoregressive Regression (GPAR) model, a scalable multi-output GP model that
is able to capture nonlinear, possibly input-varying, dependencies between
outputs in a simple and tractable way: the product rule is used to decompose
the joint distribution over the outputs into a set of conditionals, each of
which is modelled by a standard GP. GPAR's efficacy is demonstrated on a
variety of synthetic and real-world problems, outperforming existing GP models
and achieving state-of-the-art performance on established benchmarks.

提出了 Gaussian Process Autoregressive Regression (GPAR) 模型， 是一种可伸缩的多输出高斯过程模型，能够简单而可行地捕获可能因输入变化而产生的非线性依赖关系，并在各种合成和真实世界问题上展示了 GPAR 的有效性，优于现有的 GP 模型并实现了在已有基准测试中的最先进性能。

高斯过程自回归回归模型（GPAR）

The Gaussian Process Autoregressive Regression Model (GPAR)

Conditional independence testing is a fundamental problem underlying causal
discovery and a particularly challenging task in the presence of nonlinear and
high-dimensional dependencies. Here a fully non-parametric test for continuous
data based on conditional mutual information combined with a local permutation
scheme is presented. Through a nearest neighbor approach, the test efficiently
adapts also to non-smooth distributions due to strongly nonlinear dependencies.
Numerical experiments demonstrate that the test reliably simulates the null
distribution even for small sample sizes and with high-dimensional conditioning
sets. The test is better calibrated than kernel-based tests utilizing an
analytical approximation of the null distribution, especially for non-smooth
densities, and reaches the same or higher power levels. Combining the local
permutation scheme with the kernel tests leads to better calibration, but
suffers in power. For smaller sample sizes and lower dimensions, the test is
faster than random fourier feature-based kernel tests if the permutation scheme
is (embarrassingly) parallelized, but the runtime increases more sharply with
sample size and dimensionality. Thus, more theoretical research to analytically
approximate the null distribution and speed up the estimation for larger sample
sizes is desirable.

提出了一种基于条件互信息和局部置换方案的全非参数连续数据测试方法，能够适应强非线性相关性，表现优于基于核的测试，并在小样本和高维条件下可靠地模拟零分布。