A major outstanding problem when interfacing with spinal motor neurons is how
to accurately compensate for non-stationary effects in the signal during source
separation routines, particularly when they cannot be estimated in advance.
This forces current systems to instead use undifferentiated bulk signal, which
limits the potential degrees of freedom for control. In this study we propose a
potential solution, using an unsupervised learning algorithm to blindly correct
for the effects of latent processes which drive the signal non-stationarities.
We implement this methodology within the theoretical framework of a quasilinear
version of independent component analysis (ICA). The proposed design,
HarmonICA, sidesteps the identifiability problems of nonlinear ICA, allowing
for equivalent predictability to linear ICA whilst retaining the ability to
learn complex nonlinear relationships between non-stationary latents and their
effects on the signal. We test HarmonICA on both invasive and non-invasive
recordings both simulated and real, demonstrating an ability to blindly
compensate for the non-stationary effects specific to each, and thus to
significantly enhance the quality of a source separation routine.

使用无监督学习算法解决非平稳效应对信号源分离过程的影响，提出了一种名为 HarmonICA 的设计，能够在实验和真实记录中，盲目补偿与每种记录特定的非平稳效应，从而显著提高源分离过程的质量。

HarmonICA：神经非稳态校正与运动神经元界面的源分离

HarmonICA: Neural non-stationarity correction and source separation for  motor neuron interfaces

The Linear Model of Co-regionalization (LMC) is a very general model of
multitask gaussian process for regression or classification. While its
expressivity and conceptual simplicity are appealing, naive implementations
have cubic complexity in the number of datapoints and number of tasks, making
approximations mandatory for most applications. However, recent work has shown
that under some conditions the latent processes of the model can be decoupled,
leading to a complexity that is only linear in the number of said processes. We
here extend these results, showing from the most general assumptions that the
only condition necessary to an efficient exact computation of the LMC is a mild
hypothesis on the noise model. We introduce a full parametrization of the
resulting \emph{projected LMC} model, and an expression of the marginal
likelihood enabling efficient optimization. We perform a parametric study on
synthetic data to show the excellent performance of our approach, compared to
an unrestricted exact LMC and approximations of the latter. Overall, the
projected LMC appears as a credible and simpler alternative to state-of-the art
models, which greatly facilitates some computations such as leave-one-out
cross-validation and fantasization.

在本研究中，通过对线性协同关联模型（LMC）进行扩展和参数化，我们证明了只需要对噪声模型做一个温和的假设，即可实现高效的 LMC 的精确计算，从而使其成为目前最先进模型的可靠且简化的替代品，极大地方便了一些计算，如留一法交叉验证和虚构。

LMC 多任务高斯过程模型的准确高效解决方案

Exact and efficient solutions of the LMC Multitask Gaussian Process  model

Diffusion processes are a class of stochastic differential equations (SDEs)
providing a rich family of expressive models that arise naturally in dynamic
modelling tasks. Probabilistic inference and learning under generative models
with latent processes endowed with a non-linear diffusion process prior are
intractable problems. We build upon work within variational inference
approximating the posterior process as a linear diffusion process, point out
pathologies in the approach, and propose an alternative parameterization of the
Gaussian variational process using a continuous exponential family description.
This allows us to trade a slow inference algorithm with fixed-point iterations
for a fast algorithm for convex optimization akin to natural gradient descent,
which also provides a better objective for the learning of model parameters.

本文提出了一种基于连续指数族描述的高斯变分过程的参数化方法，利用凸优化算法来解决具有非线性扩散过程先验的潜在过程的生成模型下的概率推断和学习问题。