Symmetric positive definite~(SPD) matrices have shown important value and
applications in statistics and machine learning, such as FMRI analysis and
traffic prediction. Previous works on SPD matrices mostly focus on
discriminative models, where predictions are made directly on $E(X|y)$, where
$y$ is a vector and $X$ is an SPD matrix. However, these methods are
challenging to handle for large-scale data, as they need to access and process
the whole data. In this paper, inspired by denoising diffusion probabilistic
model~(DDPM), we propose a novel generative model, termed SPD-DDPM, by
introducing Gaussian distribution in the SPD space to estimate $E(X|y)$.
Moreover, our model is able to estimate $p(X)$ unconditionally and flexibly
without giving $y$. On the one hand, the model conditionally learns $p(X|y)$
and utilizes the mean of samples to obtain $E(X|y)$ as a prediction. On the
other hand, the model unconditionally learns the probability distribution of
the data $p(X)$ and generates samples that conform to this distribution.
Furthermore, we propose a new SPD net which is much deeper than the previous
networks and allows for the inclusion of conditional factors. Experiment
results on toy data and real taxi data demonstrate that our models effectively
fit the data distribution both unconditionally and unconditionally and provide
accurate predictions.

本研究提出了一种新的生成模型 SPD-DDPM，通过在 SPD 空间中引入高斯分布来估计 E (X|y)，从而无条件和有条件地学习数据分布，并提供准确的预测。

SPD-DDPM：在对称正定空间中去噪的扩散概率模型

SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric  Positive Definite Space

While large-scale sequence modeling from offline data has led to impressive
performance gains in natural language and image generation, directly
translating such ideas to robotics has been challenging. One critical reason
for this is that uncurated robot demonstration data, i.e. play data, collected
from non-expert human demonstrators are often noisy, diverse, and
distributionally multi-modal. This makes extracting useful, task-centric
behaviors from such data a difficult generative modeling problem. In this work,
we present Conditional Behavior Transformers (C-BeT), a method that combines
the multi-modal generation ability of Behavior Transformer with
future-conditioned goal specification. On a suite of simulated benchmark tasks,
we find that C-BeT improves upon prior state-of-the-art work in learning from
play data by an average of 45.7%. Further, we demonstrate for the first time
that useful task-centric behaviors can be learned on a real-world robot purely
from play data without any task labels or reward information. Robot videos are
best viewed on our project website: this https URL

本文提出了一种名为 C-BeT 的新方法，结合了 Behavior Transformer 多模态生成能力和条件生成模型技术，实现从多模态、嘈杂数据中提取有用、任务中心的行为，取得了有益的效果，而该方法也是第一个实现从无标签、零奖励信息的玩耍数据里纯学习真实世界机器人有用任务行为的方法。

从游戏到政策：基于未筛选机器人数据的条件行为生成

From Play to Policy: Conditional Behavior Generation from Uncurated Robot Data

The teacher-student (T/S) learning has been shown to be effective for a
variety of problems such as domain adaptation and model compression. One
shortcoming of the T/S learning is that a teacher model, not always perfect,
sporadically produces wrong guidance in form of posterior probabilities that
misleads the student model towards a suboptimal performance. To overcome this
problem, we propose a conditional T/S learning scheme, in which a "smart"
student model selectively chooses to learn from either the teacher model or the
ground truth labels conditioned on whether the teacher can correctly predict
the ground truth. Unlike a naive linear combination of the two knowledge
sources, the conditional learning is exclusively engaged with the teacher model
when the teacher model's prediction is correct, and otherwise backs off to the
ground truth. Thus, the student model is able to learn effectively from the
teacher and even potentially surpass the teacher. We examine the proposed
learning scheme on two tasks: domain adaptation on CHiME-3 dataset and speaker
adaptation on Microsoft short message dictation dataset. The proposed method
achieves 9.8% and 12.8% relative word error rate reductions, respectively, over
T/S learning for environment adaptation and speaker-independent model for
speaker adaptation.

通过提出一种条件性的教师 - 学生 (T/S) 学习方案，在一定程度上解决了 T/S 学习中教师模型不完美时可能会向学生模型提供错误指导的问题，而且在环境适应和说话人适应方面获得了比 T/S 学习更好的结果。

有条件的师生学习

Conditional Teacher-Student Learning

Deep networks trained on demonstrations of human driving have learned to
follow roads and avoid obstacles. However, driving policies trained via
imitation learning cannot be controlled at test time. A vehicle trained
end-to-end to imitate an expert cannot be guided to take a specific turn at an
upcoming intersection. This limits the utility of such systems. We propose to
condition imitation learning on high-level command input. At test time, the
learned driving policy functions as a chauffeur that handles sensorimotor
coordination but continues to respond to navigational commands. We evaluate
different architectures for conditional imitation learning in vision-based
driving. We conduct experiments in realistic three-dimensional simulations of
urban driving and on a 1/5 scale robotic truck that is trained to drive in a
residential area. Both systems drive based on visual input yet remain
responsive to high-level navigational commands. The supplementary video can be
viewed at this https URL

本文提出了一种基于高层指令输入的条件性模仿学习方法，使得经过训练的车辆在测试时间内仍然能够遵循导航指令，本文在仿真实验和机器人卡车实验中对各种条件性模仿学习架构进行了评估和实践。