We introduce a novel capacity measure 2sED for statistical models based on
the effective dimension. The new quantity provably bounds the generalization
error under mild assumptions on the model. Furthermore, simulations on standard
data sets and popular model architectures show that 2sED correlates well with
the training error. For Markovian models, we show how to efficiently
approximate 2sED from below through a layerwise iterative approach, which
allows us to tackle deep learning models with a large number of parameters.
Simulation results suggest that the approximation is good for different
prominent models and data sets.

我们引入了一种基于有效维度的统计模型的新容量度量 2sED。这个新数量在模型的温和假设下能证明地限制了泛化误差。此外，对标准数据集和流行的模型架构的模拟结果表明，2sED 与训练误差具有良好的相关性。对于马尔可夫模型，我们展示了如何通过分层迭代方法从下方高效地逼近 2sED，这使我们能够处理具有大量参数的深度学习模型。模拟结果表明，这种逼近适用于不同的突出模型和数据集。

深度学习模型的双尺度复杂度度量

A Two-Scale Complexity Measure for Deep Learning Models

Planning for autonomous driving in complex, urban scenarios requires accurate
prediction of the trajectories of surrounding traffic participants. Their
future behavior depends on their route intentions, the road-geometry, traffic
rules and mutual interaction, resulting in interdependencies between their
trajectories. We present a probabilistic prediction framework based on a
dynamic Bayesian network, which represents the state of the complete scene
including all agents and respects the aforementioned dependencies. We propose
Markovian, context-dependent motion models to define the interaction-aware
behavior of drivers. At first, the state of the dynamic Bayesian network is
estimated over time by tracking the single agents via sequential Monte Carlo
inference. Secondly, we perform a probabilistic forward simulation of the
network's estimated belief state to generate the different combinatorial scene
developments. This provides the corresponding trajectories for the set of
possible, future scenes. Our framework can handle various road layouts and
number of traffic participants. We evaluate the approach in online simulations
and real-world scenarios. It is shown that our interaction-aware prediction
outperforms interaction-unaware physics- and map-based approaches.

本研究提出了基于动态贝叶斯网络的概率性交通预测模型，结合马尔科夫模型和上下文感知的车辆运动模型，可以更精准地预测未来的交通路径和解决交互问题。相较于基于物理学和地图的方法，该模型表现更加优越。

城市环境中基于交互感知的行为概率预测

Interaction-Aware Probabilistic Behavior Prediction in Urban  Environments

Optimizing shared vehicle systems (bike/scooter/car/ride-sharing) is more
challenging compared to traditional resource allocation settings due to the
presence of \emph{complex network externalities} -- changes in the
demand/supply at any location affect future supply throughout the system within
short timescales. These externalities are well captured by steady-state
Markovian models, which are therefore widely used to analyze such systems.
However, using such models to design pricing and other control policies is
computationally difficult since the resulting optimization problems are
high-dimensional and non-convex.
To this end, we develop a \emph{rigorous approximation framework} for shared
vehicle systems, providing a unified approach for a wide range of controls
(pricing, matching, rebalancing), objective functions (throughput, revenue,
welfare), and system constraints (travel-times, welfare benchmarks,
posted-price constraints). Our approach is based on the analysis of natural
convex relaxations, and obtains as special cases existing approximate-optimal
policies for limited settings, asymptotic-optimality results, and heuristic
policies. The resulting guarantees are non-asymptotic and parametric, and
provide operational insights into the design of real-world systems. In
particular, for any shared vehicle system with $n$ stations and $m$ vehicles,
our framework obtains an approximation ratio of $1+(n-1)/m$, which is
particularly meaningful when $m/n$, the average number of vehicles per station,
is large, as is often the case in practice.

提出了一种基于凸松弛的近似框架，用于对共享车辆系统进行建模和优化，通过分析此近似框架的性质，得出了计算复杂度更低的解决方案并提供实际操作洞见，实现了对共享车辆系统的有效控制与管理。