The ability to forecast a set of likely yet diverse possible future behaviors
of an agent (e.g., future trajectories of a pedestrian) is essential for
safety-critical perception systems (e.g., autonomous vehicles). In particular,
a set of possible future behaviors generated by the system must be diverse to
account for all possible outcomes in order to take necessary safety
precautions. It is not sufficient to maintain a set of the most likely future
outcomes because the set may only contain perturbations of a single outcome.
While generative models such as variational autoencoders (VAEs) have been shown
to be a powerful tool for learning a distribution over future trajectories,
randomly drawn samples from the learned implicit likelihood model may not be
diverse -- the likelihood model is derived from the training data distribution
and the samples will concentrate around the major mode that has most data. In
this work, we propose to learn a diversity sampling function (DSF) that
generates a diverse and likely set of future trajectories. The DSF maps
forecasting context features to a set of latent codes which can be decoded by a
generative model (e.g., VAE) into a set of diverse trajectory samples.
Concretely, the process of identifying the diverse set of samples is posed as a
parameter estimation of the DSF. To learn the parameters of the DSF, the
diversity of the trajectory samples is evaluated by a diversity loss based on a
determinantal point process (DPP). Gradient descent is performed over the DSF
parameters, which in turn move the latent codes of the sample set to find an
optimal diverse and likely set of trajectories. Our method is a novel
application of DPPs to optimize a set of items (trajectories) in continuous
space. We demonstrate the diversity of the trajectories produced by our
approach on both low-dimensional 2D trajectory data and high-dimensional human
motion data.

本文介绍了一种使用 DPP 技术优化轨迹样本集合并实现预测多样性的方法，通过生成多种可能性来确保安全，特别是在自动驾驶等关键领域。

利用行列式点过程实现多样的轨迹预测

Diverse Trajectory Forecasting with Determinantal Point Processes

Outlier detection is the identification of points in a dataset that do not
conform to the norm. Outlier detection is highly sensitive to the choice of the
detection algorithm and the feature subspace used by the algorithm. Extracting
domain-relevant insights from outliers needs systematic exploration of these
choices since diverse outlier sets could lead to complementary insights. This
challenge is especially acute in an interactive setting, where the choices must
be explored in a time-constrained manner. In this work, we present REMIX, the
first system to address the problem of outlier detection in an interactive
setting. REMIX uses a novel mixed integer programming (MIP) formulation for
automatically selecting and executing a diverse set of outlier detectors within
a time limit. This formulation incorporates multiple aspects such as (i) an
upper limit on the total execution time of detectors (ii) diversity in the
space of algorithms and features, and (iii) meta-learning for evaluating the
cost and utility of detectors. REMIX provides two distinct ways for the analyst
to consume its results: (i) a partitioning of the detectors explored by REMIX
into perspectives through low-rank non-negative matrix factorization; each
perspective can be easily visualized as an intuitive heatmap of experiments
versus outliers, and (ii) an ensembled set of outliers which combines outlier
scores from all detectors. We demonstrate the benefits of REMIX through
extensive empirical validation on real-world data.

REMIX 是第一个解决交互式环境下异常检测问题的系统，它使用新颖的混合整数规划 (MIP) 公式，在规定时间内自动选择和执行多样化的异常检测器，包括数据处理算法和特征选择，为分析人员提供两种不同的结果消费方式，即透视图和集成异常检测器。