The rapid progress of Artificial Intelligence research came with the
development of increasingly complex deep learning models, leading to growing
challenges in terms of computational complexity, energy efficiency and
interpretability. In this study, we apply advanced network-based information
filtering techniques to design a novel deep neural network unit characterized
by a sparse higher-order graphical architecture built over the homological
structure of underlying data. We demonstrate its effectiveness in two
application domains which are traditionally challenging for deep learning:
tabular data and time series regression problems. Results demonstrate the
advantages of this novel design which can tie or overcome the results of
state-of-the-art machine learning and deep learning models using only a
fraction of parameters.

本研究应用基于网络的信息过滤技术设计了一种新的深度神经网络单元，其具有由基础数据的同调结构构建的稀疏高阶图形架构，同时证明它在传统难以解决的领域，如表格数据和时间序列回归问题中的有效性，仅使用一小部分参数即可超越最先进的机器学习和深度学习模型的结果。

同调神经网络：一个适用于多变量复杂性的稀疏架构

Homological Neural Networks: A Sparse Architecture for Multivariate  Complexity

We propose a framework for general probabilistic multi-step time series
regression. Specifically, we exploit the expressiveness and temporal nature of
Sequence-to-Sequence Neural Networks (e.g. recurrent and convolutional
structures), the nonparametric nature of Quantile Regression and the efficiency
of Direct Multi-Horizon Forecasting. A new training scheme,
*forking-sequences*, is designed for sequential nets to boost stability and
performance. We show that the approach accommodates both temporal and static
covariates, learning across multiple related series, shifting seasonality,
future planned event spikes and cold-starts in real life large-scale
forecasting. The performance of the framework is demonstrated in an application
to predict the future demand of items sold on Amazon.com, and in a public
probabilistic forecasting competition to predict electricity price and load.

提出一种概率多步时间序列回归的框架，使用序列到序列神经网络（如递归和卷积结构）的表达力和时间特性，量化回归的非参数特性以及直接多视角预测的有效性；并通过针对连续网络的分支序列新训练方案来提高稳定性和性能。通过预测亚马逊销售的商品未来需求和公共概率预测竞赛来展示该框架的性能。

多层时间跨度分位数循环预测器

A Multi-Horizon Quantile Recurrent Forecaster

We address the problem of dynamic variable selection in time series
regression with unknown residual variances, where the set of active predictors
is allowed to evolve over time. To capture time-varying variable selection
uncertainty, we introduce new dynamic shrinkage priors for the time series of
regression coefficients. These priors are characterized by two main
ingredients: smooth parameter evolutions and intermittent zeroes for modeling
predictive breaks. More formally, our proposed Dynamic Spike-and-Slab (DSS)
priors are constructed as mixtures of two processes: a spike process for the
irrelevant coefficients and a slab autoregressive process for the active
coefficients. The mixing weights are themselves time-varying and depend on
lagged values of the series. Our DSS priors are probabilistically coherent in
the sense that their stationary distribution is fully known and characterized
by spike-and-slab marginals. For posterior sampling over dynamic regression
coefficients, model selection indicators as well as unknown dynamic residual
variances, we propose a Dynamic SSVS algorithm based on forward-filtering and
backward-sampling. To scale our method to large data sets, we develop a Dynamic
EMVS algorithm for MAP smoothing. We demonstrate, through simulation and a
topical macroeconomic dataset, that DSS priors are very effective at separating
active and noisy coefficients. Our fast implementation significantly extends
the reach of spike-and-slab methods to large time series data.

研究动态变量选择在时间序列回归中的应用，提出了构造时间系数的新型动态收缩先验 (Dynamic Spike-and-Slab)，并提出了动态 SSVS 和 Dynamic EMVS 算法，旨在解决数据集规模大的问题。