Predictive linear and nonlinear models based on kernel machines or deep
neural networks have been used to discover dependencies among time series. This
paper proposes an efficient nonlinear modeling approach for multiple time
series, with a complexity comparable to linear vector autoregressive (VAR)
models while still incorporating nonlinear interactions among different
time-series variables. The modeling assumption is that the set of time series
is generated in two steps: first, a linear VAR process in a latent space, and
second, a set of invertible and Lipschitz continuous nonlinear mappings that
are applied per sensor, that is, a component-wise mapping from each latent
variable to a variable in the measurement space. The VAR coefficient
identification provides a topology representation of the dependencies among the
aforementioned variables. The proposed approach models each component-wise
nonlinearity using an invertible neural network and imposes sparsity on the VAR
coefficients to reflect the parsimonious dependencies usually found in real
applications. To efficiently solve the formulated optimization problems, a
custom algorithm is devised combining proximal gradient descent, stochastic
primal-dual updates, and projection to enforce the corresponding constraints.
Experimental results on both synthetic and real data sets show that the
proposed algorithm improves the identification of the support of the VAR
coefficients in a parsimonious manner while also improving the time-series
prediction, as compared to the current state-of-the-art methods.

提出了一种高效的非线性建模方法，通过线性 VAR 过程和分量间非线性映射来生成时间序列，并使用定制算法解决优化问题，提高了 VAR 系数的支持识别和时间序列预测能力。

高效易解释的多时间序列非线性建模

Efficient Interpretable Nonlinear Modeling for Multiple Time Series

Most of the successful and predominant methods for bilingual lexicon
induction (BLI) are mapping-based, where a linear mapping function is learned
with the assumption that the word embedding spaces of different languages
exhibit similar geometric structures (i.e., approximately isomorphic). However,
several recent studies have criticized this simplified assumption showing that
it does not hold in general even for closely related languages. In this work,
we propose a novel semi-supervised method to learn cross-lingual word
embeddings for BLI. Our model is independent of the isomorphic assumption and
uses nonlinear mapping in the latent space of two independently trained
auto-encoders. Through extensive experiments on fifteen (15) different language
pairs (in both directions) comprising resource-rich and low-resource languages
from two different datasets, we demonstrate that our method outperforms
existing models by a good margin. Ablation studies show the importance of
different model components and the necessity of non-linear mapping.

提出了一种新的半监督方法，通过两个独立训练的自编码器的潜在空间使用非线性映射，学习用于双语词汇识别的跨语言词嵌入表示，并在 15 种不同方向的语言对（包括资源丰富和低资源语言）的两个数据集上进行了广泛的实验，结果表明该方法优于现有模型。