In order to understand the complexities of cellular biology, researchers are
interested in two important metrics: the genetic expression information of
cells and their spatial coordinates within a tissue sample. However,
state-of-the art methods, namely single-cell RNA sequencing and image based
spatial transcriptomics can only recover a subset of this information, either
full genetic expression with loss of spatial information, or spatial
information with loss of resolution in sequencing data. In this project, we
investigate a probabilistic machine learning method to obtain the full genetic
expression information for tissues samples while also preserving their spatial
coordinates. This is done through mapping both datasets to a joint latent space
representation with the use of variational machine learning methods. From here,
the full genetic and spatial information can be decoded and to give us greater
insights on the understanding of cellular processes and pathways.

通过使用概率机器学习方法，将细胞的遗传表达信息和细胞在组织样本中的空间坐标映射到一个联合潜变量空间中，可以获得完整的遗传表达和空间信息，从而更好地理解细胞过程和通路。

空间转录组学的潜在空间推理

Latent Space Inference For Spatial Transcriptomics

Modern communication systems rely on accurate channel estimation to achieve
efficient and reliable transmission of information. As the communication
channel response is highly related to the user's location, one can use a neural
network to map the user's spatial coordinates to the channel coefficients.
However, these latter are rapidly varying as a function of the location, on the
order of the wavelength. Classical neural architectures being biased towards
learning low frequency functions (spectral bias), such mapping is therefore
notably difficult to learn. In order to overcome this limitation, this paper
presents a frugal, model-based network that separates the low frequency from
the high frequency components of the target mapping function. This yields an
hypernetwork architecture where the neural network only learns low frequency
sparse coefficients in a dictionary of high frequency components. Simulation
results show that the proposed neural network outperforms standard approaches
on realistic synthetic data.

为了克服通信信道在用户位置发生变化和学习低频函数的偏见带来的困难，本文提出了一种节俭、基于模型的网络，将目标映射函数的低频部分与高频部分分离出来，形成一个超网络架构，其中神经网络只学习高频组件字典中的低频稀疏系数。仿真结果表明，所提出的神经网络在真实合成数据上优于标准方法。