In meteorology, finding similar weather patterns or analogs in historical
datasets can be useful for data assimilation, forecasting, and postprocessing.
In climate science, analogs in historical and climate projection data are used
for attribution and impact studies. However, most of the time, those large
weather and climate datasets are nearline. They must be downloaded, which takes
a lot of bandwidth and disk space, before the computationally expensive search
can be executed. We propose a dimension reduction technique based on
autoencoder (AE) neural networks to compress those datasets and perform the
search in an interpretable, compressed latent space. A distance-regularized
Siamese twin autoencoder (DIRESA) architecture is designed to preserve distance
in latent space while capturing the nonlinearities in the datasets. Using
conceptual climate models of different complexities, we show that the latent
components thus obtained provide physical insight into the dominant modes of
variability in the system. Compressing datasets with DIRESA reduces the online
storage and keeps the latent components uncorrelated, while the distance
(ordering) preservation and reconstruction fidelity robustly outperform
Principal Component Analysis (PCA) and other dimension reduction techniques
such as UMAP or variational autoencoders.

使用基于自编码器神经网络的维度缩减技术，通过 DIRESA 架构来压缩大气候和天气数据集，并在压缩的潜在空间中进行可解释的搜索，从而提供物理洞察力和降低在线存储需求。

基于正则化自编码器的 DIRESA，一种保持距离的非线性降维技术

DIRESA, a distance-preserving nonlinear dimension reduction technique  based on regularized autoencoders

The interactions of users and items in recommender system could be naturally
modeled as a user-item bipartite graph. In recent years, we have witnessed an
emerging research effort in exploring user-item graph for collaborative
filtering methods. Nevertheless, the formation of user-item interactions
typically arises from highly complex latent purchasing motivations, such as
high cost performance or eye-catching appearance, which are indistinguishably
represented by the edges. The existing approaches still remain the differences
between various purchasing motivations unexplored, rendering the inability to
capture fine-grained user preference. Therefore, in this paper we propose a
novel Multi-Component graph convolutional Collaborative Filtering (MCCF)
approach to distinguish the latent purchasing motivations underneath the
observed explicit user-item interactions. Specifically, there are two
elaborately designed modules, decomposer and combiner, inside MCCF. The former
first decomposes the edges in user-item graph to identify the latent components
that may cause the purchasing relationship; the latter then recombines these
latent components automatically to obtain unified embeddings for prediction.
Furthermore, the sparse regularizer and weighted random sample strategy are
utilized to alleviate the overfitting problem and accelerate the optimization.
Empirical results on three real datasets and a synthetic dataset not only show
the significant performance gains of MCCF, but also well demonstrate the
necessity of considering multiple components.

研究了协同过滤方法中用户和商品之间的图模型，提出了一种新的多组件图卷积协同过滤算法 (MCCF)，旨在区分观察到的显式用户 - 商品交互背后的购买动机。该算法通过分解和组合两个模块，设计了一种新的方式以获得对用户消费行为的高精度预测，实验结果表明，该算法不仅在三个真实数据集上表现优异，而且还证明了考虑多个组件的必要性。

多组分图卷积协同过滤

Multi-Component Graph Convolutional Collaborative Filtering

In many settings, we have multiple data sets (also called views) that capture
different and overlapping aspects of the same phenomenon. We are often
interested in finding patterns that are unique to one or to a subset of the
views. For example, we might have one set of molecular observations and one set
of physiological observations on the same group of individuals, and we want to
quantify molecular patterns that are uncorrelated with physiology. Despite
being a common problem, this is highly challenging when the correlations come
from complex distributions. In this paper, we develop the general framework of
Rich Component Analysis (RCA) to model settings where the observations from
different views are driven by different sets of latent components, and each
component can be a complex, high-dimensional distribution. We introduce
algorithms based on cumulant extraction that provably learn each of the
components without having to model the other components. We show how to
integrate RCA with stochastic gradient descent into a meta-algorithm for
learning general models, and demonstrate substantial improvement in accuracy on
several synthetic and real datasets in both supervised and unsupervised tasks.
Our method makes it possible to learn latent variable models when we don't have
samples from the true model but only samples after complex perturbations.

本文介绍了一个名为 RCA 的模型框架，它可以用于分析多个数据集中的不同潜在组件，通过累积量提取算法，该模型可以明确地学习每个组件而无需构建其他组件，进而与随机梯度下降方法组合实现通用模型的无监督学习，从而在多个真实数据集上证明了其准确性的优势。

富组分分析

Rich Component Analysis

The recent proliferation of richly structured probabilistic models raises the
question of how to automatically determine an appropriate model for a dataset.
We investigate this question for a space of matrix decomposition models which
can express a variety of widely used models from unsupervised learning. To
enable model selection, we organize these models into a context-free grammar
which generates a wide variety of structures through the compositional
application of a few simple rules. We use our grammar to generically and
efficiently infer latent components and estimate predictive likelihood for
nearly 2500 structures using a small toolbox of reusable algorithms. Using a
greedy search over our grammar, we automatically choose the decomposition
structure from raw data by evaluating only a small fraction of all models. The
proposed method typically finds the correct structure for synthetic data and
backs off gracefully to simpler models under heavy noise. It learns sensible
structures for datasets as diverse as image patches, motion capture, 20
Questions, and U.S. Senate votes, all using exactly the same code.

通过生成上下文无关文法来组织矩阵分解模型以进行模型选择，使用小型可重用算法估计预测似然和推断潜在组件，通过贪心搜索自动选择分解结构。