Over the last two decades, the robotics community witnessed the emergence of
various motion representations that have been used extensively, particularly in
behavorial cloning, to compactly encode and generalize skills. Among these,
probabilistic approaches have earned a relevant place, owing to their encoding
of variations, correlations and adaptability to new task conditions. Modulating
such primitives, however, is often cumbersome due to the need for parameter
re-optimization which frequently entails computationally costly operations. In
this paper we derive a non-parametric movement primitive formulation that
contains a null space projector. We show that such formulation allows for fast
and efficient motion generation with computational complexity O(n2) without
involving matrix inversions, whose complexity is O(n3). This is achieved by
using the null space to track secondary targets, with a precision determined by
the training dataset. Using a 2D example associated with time input we show
that our non-parametric solution compares favourably with a state-of-the-art
parametric approach. For demonstrated skills with high-dimensional inputs we
show that it permits on-the-fly adaptation as well.

本文提出了一种具有空间零投影器的非参数化运动基元公式，以避免频繁的参数重新优化，从而实现快速高效的运动生成，并通过采用空间零以追踪二级目标来实现 On-the-fly 的自适应技能。

非参数技能表示：软零空间投影器用于快速推广

A Non-parametric Skill Representation with Soft Null Space Projectors for Fast Generalization

Recent work has discussed the limitations of counterfactual explanations to
recommend actions for algorithmic recourse, and argued for the need of taking
causal relationships between features into consideration. Unfortunately, in
practice, the true underlying structural causal model is generally unknown. In
this work, we first show that it is impossible to guarantee recourse without
access to the true structural equations. To address this limitation, we propose
two probabilistic approaches to select optimal actions that achieve recourse
with high probability given limited causal knowledge (e.g., only the causal
graph). The first captures uncertainty over structural equations under additive
Gaussian noise, and uses Bayesian model averaging to estimate the
counterfactual distribution. The second removes any assumptions on the
structural equations by instead computing the average effect of recourse
actions on individuals similar to the person who seeks recourse, leading to a
novel subpopulation-based interventional notion of recourse. We then derive a
gradient-based procedure for selecting optimal recourse actions, and
empirically show that the proposed approaches lead to more reliable
recommendations under imperfect causal knowledge than non-probabilistic
baselines.

通过两种概率方法选取最优行动以在有限的因果知识下实现补救，以解决缺乏真实结构因果模型的限制，并在不完美的因果知识下提供比非概率基线更可靠的建议。

不完善因果知识下的算法补救：一种概率方法

Algorithmic recourse under imperfect causal knowledge: a probabilistic  approach

In probabilistic approaches to classification and information extraction, one
typically builds a statistical model of words under the assumption that future
data will exhibit the same regularities as the training data. In many data
sets, however, there are scope-limited features whose predictive power is only
applicable to a certain subset of the data. For example, in information
extraction from web pages, word formatting may be indicative of extraction
category in different ways on different web pages. The difficulty with using
such features is capturing and exploiting the new regularities encountered in
previously unseen data. In this paper, we propose a hierarchical probabilistic
model that uses both local/scope-limited features, such as word formatting, and
global features, such as word content. The local regularities are modeled as an
unobserved random parameter which is drawn once for each local data set. This
random parameter is estimated during the inference process and then used to
perform classification with both the local and global features--- a procedure
which is akin to automatically retuning the classifier to the local
regularities on each newly encountered web page. Exact inference is intractable
and we present approximations via point estimates and variational methods.
Empirical results on large collections of web data demonstrate that this method
significantly improves performance from traditional models of global features
alone.

本文提出了一种可以同时利用局部和全局特征的分层概率模型，从而提高分类和信息抽取的准确性。通过估计局部数据集中的随机参数，并在推断过程中使用其进行分类，该模型能够自适应地捕捉到新发现的数据中的规律性。实验结果表明，相对于仅使用全局特征的传统模型，本模型能显著提升性能。