The long short-term memory (LSTM) neural network is capable of processing
complex sequential information since it utilizes special gating schemes for
learning representations from long input sequences. It has the potential to
model any sequential time-series data, where the current hidden state has to be
considered in the context of the past hidden states. This property makes LSTM
an ideal choice to learn the complex dynamics of various actions.
Unfortunately, the conventional LSTMs do not consider the impact of
spatio-temporal dynamics corresponding to the given salient motion patterns,
when they gate the information that ought to be memorized through time. To
address this problem, we propose a differential gating scheme for the LSTM
neural network, which emphasizes on the change in information gain caused by
the salient motions between the successive frames. This change in information
gain is quantified by Derivative of States (DoS), and thus the proposed LSTM
model is termed as differential Recurrent Neural Network (dRNN). We demonstrate
the effectiveness of the proposed model by automatically recognizing actions
from the real-world 2D and 3D human action datasets. Our study is one of the
first works towards demonstrating the potential of learning complex time-series
representations via high-order derivatives of states.

本文提出了一种差分门控 LSTM 神经网络，它采用导数来量化关键运动模式对时间序列数据的信息增益，从而提高动作识别的准确率。

差分循环神经网络用于动作识别

Differential Recurrent Neural Networks for Action Recognition

Cointegration is an important topic for time-series, and describes a
relationship between two series in which a linear combination is stationary.
Classically, the test for cointegration is based on a two stage process in
which first the linear relation between the series is estimated by Ordinary
Least Squares. Subsequently a unit root test is performed on the residuals. A
well-known deficiency of this classical approach is that it can lead to
erroneous conclusions about the presence of cointegration. As an alternative,
we present a framework for estimating whether cointegration exists using
Bayesian inference which is empirically superior to the classical approach.
Finally, we apply our technique to model segmented cointegration in which
cointegration may exist only for limited time. In contrast to previous
approaches our model makes no restriction on the number of possible
cointegration segments.

本文提出了一个贝叶斯推断的框架，用于确定是否存在协整关系，并成功地应用于建模分段协整关系，该模型不限制可能的协整片段数。

贝叶斯条件协整

Bayesian Conditional Cointegration

Many methods for causal inference generate directed acyclic graphs (DAGs)
that formalize causal relations between $n$ variables. Given the joint
distribution on all these variables, the DAG contains all information about how
intervening on one variable changes the distribution of the other $n-1$
variables. However, quantifying the causal influence of one variable on another
one remains a nontrivial question. Here we propose a set of natural, intuitive
postulates that a measure of causal strength should satisfy. We then introduce
a communication scenario, where edges in a DAG play the role of channels that
can be locally corrupted by interventions. Causal strength is then the relative
entropy distance between the old and the new distribution. Many other measures
of causal strength have been proposed, including average causal effect,
transfer entropy, directed information, and information flow. We explain how
they fail to satisfy the postulates on simple DAGs of $\leq3$ nodes. Finally,
we investigate the behavior of our measure on time-series, supporting our
claims with experiments on simulated data.

本文提出了一组自然、直观的因果强度度量法，并通过时间序列的模拟实验证实了我们提出的度量法的有效性。

量化因果影响

Quantifying causal influences

We derive the exact form of the eigenvalue spectra of correlation matrices
derived from a set of time-shifted, finite Brownian random walks (time-series).
These matrices can be seen as random, real, asymmetric matrices with a special
structure superimposed due to the time-shift. We demonstrate that the
associated eigenvalue spectrum is circular symmetric in the complex plane for
large matrices. This fact allows us to exactly compute the eigenvalue density
via an inverse Abel-transform of the density of the symmetrized problem. We
demonstrate the validity of this approach by numerically computing eigenvalue
spectra of lagged correlation matrices based on uncorrelated, Gaussian
distributed time-series. We then compare our theoretical findings with
eigenvalue densities obtained from actual high frequency (5 min) data of the
S&P500 and discuss the observed deviations. We identify various non-trivial,
non-random patterns and find asymmetric dependencies associated with
eigenvalues departing strongly from the Gaussian prediction in the imaginary
part. For the same time-series, with the market contribution removed, we
observe strong clustering of stocks, i.e. causal sectors. We finally comment on
the time-stability of the observed patterns.

通过时间序列获得的自相关矩阵的特殊结构，以及基于逆 Abel 变换等方法获得其精确的特征值密度。研究发现，标准的高斯误差预测无法解释通过实际高频数据计算出的特征值密度的非随机模式，如 Imaginary 部分的不对称依赖性和市场影响下的股票聚类现象。