Clustering of time series is a well-studied problem, with applications
ranging from quantitative, personalized models of metabolism obtained from
metabolite concentrations to state discrimination in quantum information
theory. We consider a variant, where given a set of trajectories and a number
of parts, we jointly partition the set of trajectories and learn linear
dynamical system (LDS) models for each part, so as to minimize the maximum
error across all the models. We present globally convergent methods and EM
heuristics, accompanied by promising computational results.

时间序列聚类是一个研究深入的问题，本文提出了一种变体方法，在给定一组轨迹和一定数量的部分的情况下，共同划分轨迹集并学习每个部分的线性动态系统（LDS）模型，以最小化所有模型的最大误差，给出了全局收敛方法和 EM 启发式算法，并伴随着有希望的计算结果。

学习多个动态系统中的联合问题

Joint Problems in Learning Multiple Dynamical Systems

We investigate explainability via short Boolean formulas in the data model
based on unary relations. As an explanation of length k, we take a Boolean
formula of length k that minimizes the error with respect to the target
attribute to be explained. We first provide novel quantitative bounds for the
expected error in this scenario. We then also demonstrate how the setting works
in practice by studying three concrete data sets. In each case, we calculate
explanation formulas of different lengths using an encoding in Answer Set
Programming. The most accurate formulas we obtain achieve errors similar to
other methods on the same data sets. However, due to overfitting, these
formulas are not necessarily ideal explanations, so we use cross validation to
identify a suitable length for explanations. By limiting to shorter formulas,
we obtain explanations that avoid overfitting but are still reasonably accurate
and also, importantly, human interpretable.

考虑使用简短的布尔公式对数据模型进行可解释性分析，得出适当长度的解释公式，避免过度拟合但仍然准确且人类可解释。

实践中的短布尔公式解释

Short Boolean Formulas as Explanations in Practice

We consider the computational complexity of training depth-2 neural networks
composed of rectified linear units (ReLUs). We show that, even for the case of
a single ReLU, finding a set of weights that minimizes the squared error (even
approximately) for a given training set is NP-hard. We also show that for a
simple network consisting of two ReLUs, the error minimization problem is
NP-hard, even in the realizable case. We complement these hardness results by
showing that, when the weights and samples belong to the unit ball, one can
(agnostically) properly and reliably learn depth-2 ReLUs with $k$ units and
error at most $\epsilon$ in time $2^{(k/\epsilon)^{O(1)}}n^{O(1)}$; this
extends upon a previous work of Goel, Kanade, Klivans and Thaler (2017) which
provided efficient improper learning algorithms for ReLUs.

针对由修正线性单元（ReLU）组成的两层神经网络的训练的计算复杂度进行了探讨，发现该问题是 NP-hard 的，但在权重和样本都属于单位球时，可以通过特定算法在有限时间内得到令人满意的学习效果。

训练 ReLU 的计算复杂性

The Computational Complexity of Training ReLU(s)

We consider a generalized version of the correlation clustering problem,
defined as follows. Given a complete graph $G$ whose edges are labeled with $+$
or $-$, we wish to partition the graph into clusters while trying to avoid
errors: $+$ edges between clusters or $-$ edges within clusters. Classically,
one seeks to minimize the total number of such errors. We introduce a new
framework that allows the objective to be a more general function of the number
of errors at each vertex (for example, we may wish to minimize the number of
errors at the worst vertex) and provide a rounding algorithm which converts
"fractional clusterings" into discrete clusterings while causing only a
constant-factor blowup in the number of errors at each vertex. This rounding
algorithm yields constant-factor approximation algorithms for the discrete
problem under a wide variety of objective functions.

提出了一个新的框架，使得在完全图上具有带权边标识的相关性聚类问题得以处理，该算法可近似求解多种目标函数下的离散聚类问题。