We consider the task of predicting a response Y from a set of covariates X in
settings where the conditional distribution of Y given X changes over time. For
this to be feasible, assumptions on how the conditional distribution changes
over time are required. Existing approaches assume, for example, that changes
occur smoothly over time so that short-term prediction using only the recent
past becomes feasible. In this work, we propose a novel invariance-based
framework for linear conditionals, called Invariant Subspace Decomposition
(ISD), that splits the conditional distribution into a time-invariant and a
residual time-dependent component. As we show, this decomposition can be
utilized both for zero-shot and time-adaptation prediction tasks, that is,
settings where either no or a small amount of training data is available at the
time points we want to predict Y at, respectively. We propose a practical
estimation procedure, which automatically infers the decomposition using tools
from approximate joint matrix diagonalization. Furthermore, we provide finite
sample guarantees for the proposed estimator and demonstrate empirically that
it indeed improves on approaches that do not use the additional invariant
structure.

我们提出了一种基于不变子空间分解（ISD）的线性条件分布的新型不变性框架，将条件分布分解为一个时间不变和一个时间相关的分量，并展示了如何利用该分解进行零样本和时间适应预测任务，通过使用近似联合矩阵对角化的技术自动推断分解，并通过有限样本保证证明了该估计方法的有效性。

不变子空间分解

Invariant Subspace Decomposition

Gastric cancer (GC) is a prevalent malignancy worldwide, ranking as the fifth
most common cancer with over 1 million new cases and 700 thousand deaths in
2020. Locally advanced gastric cancer (LAGC) accounts for approximately
two-thirds of GC diagnoses, and neoadjuvant chemotherapy (NACT) has emerged as
the standard treatment for LAGC. However, the effectiveness of NACT varies
significantly among patients, with a considerable subset displaying treatment
resistance. Ineffective NACT not only leads to adverse effects but also misses
the optimal therapeutic window, resulting in lower survival rate. However,
existing multimodal learning methods assume the availability of all modalities
for each patient, which does not align with the reality of clinical practice.
The limited availability of modalities for each patient would cause information
loss, adversely affecting predictive accuracy. In this study, we propose an
incomplete multimodal data integration framework for GC (iMD4GC) to address the
challenges posed by incomplete multimodal data, enabling precise response
prediction and survival analysis. Specifically, iMD4GC incorporates unimodal
attention layers for each modality to capture intra-modal information.
Subsequently, the cross-modal interaction layers explore potential inter-modal
interactions and capture complementary information across modalities, thereby
enabling information compensation for missing modalities. To evaluate iMD4GC,
we collected three multimodal datasets for GC study: GastricRes (698 cases) for
response prediction, GastricSur (801 cases) for survival analysis, and
TCGA-STAD (400 cases) for survival analysis. The scale of our datasets is
significantly larger than previous studies. The iMD4GC achieved impressive
performance with an 80.2% AUC on GastricRes, 71.4% C-index on GastricSur, and
66.1% C-index on TCGA-STAD, significantly surpassing other compared methods.

提出了一种不完整的多模态数据集成框架用于胃癌研究，以满足临床实践中存在的多模态数据缺失挑战，实现精确的治疗反应预测和生存分析。通过在各模态中使用单模态注意力层以捕捉内部模态信息，并通过交叉模态交互层来探索潜在的模态之间相互作用和捕捉跨模态的互补信息，从而弥补遗漏模态的信息损失。在胃癌研究中收集了三个多模态数据集，并取得了显著的性能，分别在反应预测、生存分析上达到了 80.2% 的 AUC、71.4% 的 C-index 和 66.1% 的 C-index，明显超过其他比较方法。

iMD4GC: 不完全的多模式数据融合以提升胃癌精准治疗反应预测和生存分析

iMD4GC: Incomplete Multimodal Data Integration to Advance Precise  Treatment Response Prediction and Survival Analysis for Gastric Cancer

Objective: Neoadjuvant chemotherapy (NACT) is one kind of treatment for
advanced stage ovarian cancer patients. However, due to the nature of tumor
heterogeneity, the patients' responses to NACT varies significantly among
different subgroups. To address this clinical challenge, the purpose of this
study is to develop a novel image marker to achieve high accuracy response
prediction of the NACT at an early stage. Methods: For this purpose, we first
computed a total of 1373 radiomics features to quantify the tumor
characteristics, which can be grouped into three categories: geometric,
intensity, and texture features. Second, all these features were optimized by
principal component analysis algorithm to generate a compact and informative
feature cluster. Using this cluster as the input, an SVM based classifier was
developed and optimized to create a final marker, indicating the likelihood of
the patient being responsive to the NACT treatment. To validate this scheme, a
total of 42 ovarian cancer patients were retrospectively collected. A nested
leave-one-out cross-validation was adopted for model performance assessment.
Results: The results demonstrate that the new method yielded an AUC (area under
the ROC [receiver characteristic operation] curve) of 0.745. Meanwhile, the
model achieved overall accuracy of 76.2%, positive predictive value of 70%, and
negative predictive value of 78.1%. Conclusion: This study provides meaningful
information for the development of radiomics based image markers in NACT
response prediction.

开发一种新的图像标记来实现早期高准确率的新辅助化疗反应预测，通过计算 1373 个放射组学特征来量化肿瘤特征，利用 SVM 分类器生成标记，并验证其性能表现。