Procedural activities are sequences of key-steps aimed at achieving specific
goals. They are crucial to build intelligent agents able to assist users
effectively. In this context, task graphs have emerged as a
human-understandable representation of procedural activities, encoding a
partial ordering over the key-steps. While previous works generally relied on
hand-crafted procedures to extract task graphs from videos, in this paper, we
propose an approach based on direct maximum likelihood optimization of edges'
weights, which allows gradient-based learning of task graphs and can be
naturally plugged into neural network architectures. Experiments on the
CaptainCook4D dataset demonstrate the ability of our approach to predict
accurate task graphs from the observation of action sequences, with an
improvement of +16.7% over previous approaches. Owing to the differentiability
of the proposed framework, we also introduce a feature-based approach, aiming
to predict task graphs from key-step textual or video embeddings, for which we
observe emerging video understanding abilities. Task graphs learned with our
approach are also shown to significantly enhance online mistake detection in
procedural egocentric videos, achieving notable gains of +19.8% and +7.5% on
the Assembly101 and EPIC-Tent datasets. Code for replicating experiments is
available at this https URL

通过最大似然优化边权重的方法，从动作序列中预测任务图，与之前的方法相比提高了 16.7% 的准确性；同时可通过文本或视频嵌入来预测任务图，并在程序性自我中心视频中显著提高在线错误检测的准确性，分别在 Assembly101 和 EPIC-Tent 数据集上获得了 19.8% 和 7.5% 的显著增益。

可微分任务图学习：程序化活动表示和基于自我感知视频的在线错误检测

Differentiable Task Graph Learning: Procedural Activity Representation  and Online Mistake Detection from Egocentric Videos

We consider covariance estimation in the multivariate generalized Gaussian
distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum
likelihood optimization associated with this problem is non-convex, yet it has
been proved that its global solution can be often computed via simple fixed
point iterations. Our first contribution is a new analysis of this likelihood
based on geodesic convexity that requires weaker assumptions. Our second
contribution is a generalized framework for structured covariance estimation
under sparsity constraints. We show that the optimizations can be formulated as
convex minimization as long the MGGD shape parameter is larger than half and
the sparsity pattern is chordal. These include, for example, maximum likelihood
estimation of banded inverse covariances in multivariate Laplace distributions,
which are associated with time varying autoregressive processes.

本文探讨了多元广义高斯分布（MGGD）和椭圆对称分布下的协方差估计的最大似然优化问题，提供了一种新的基于测地线凸性分析该似然函数的方法以及通过结构化稀疏性限制的广义协方差估计框架。