Multimodal contrastive representation learning methods have proven successful
across a range of domains, partly due to their ability to generate meaningful
shared representations of complex phenomena. To enhance the depth of analysis
and understanding of these acquired representations, we introduce a unified
causal model specifically designed for multimodal data. By examining this
model, we show that multimodal contrastive representation learning excels at
identifying latent coupled variables within the proposed unified model, up to
linear or permutation transformations resulting from different assumptions. Our
findings illuminate the potential of pre-trained multimodal models, eg, CLIP,
in learning disentangled representations through a surprisingly simple yet
highly effective tool: linear independent component analysis. Experiments
demonstrate the robustness of our findings, even when the assumptions are
violated, and validate the effectiveness of the proposed method in learning
disentangled representations.

用于多模态数据的统一因果模型，通过线性独立成分分析的方法，可以提高对多模态对比表示学习的理解和分析深度，发现预训练的多模态模型可以通过学习解缠表示来提高其性能和鲁棒性。

通过潜在的部分因果模型揭示多模态对比表示学习

Revealing Multimodal Contrastive Representation Learning through Latent  Partial Causal Models

Linear Independent Component Analysis (ICA) is a blind source separation
technique that has been used in various domains to identify independent latent
sources from observed signals. In order to obtain a higher signal-to-noise
ratio, the presence of multiple views of the same sources can be used. In this
work, we present MultiView Independent Component Analysis with Delays (MVICAD).
This algorithm builds on the MultiView ICA model by allowing sources to be
delayed versions of some shared sources: sources are shared across views up to
some unknown latencies that are view- and source-specific. Using simulations,
we demonstrate that MVICAD leads to better unmixing of the sources. Moreover,
as ICA is often used in neuroscience, we show that latencies are age-related
when applied to Cam-CAN, a large-scale magnetoencephalography (MEG) dataset.
These results demonstrate that the MVICAD model can reveal rich effects on
neural signals without human supervision.

多视角延迟独立成分分析（MVICAD）算法通过将源信号视为互相延迟版本的某些共享源信号，扩展了多视角独立成分分析（ICA）模型，以提高信号与噪声比，并展示了在神经信号处理中具有年龄相关的潜在延迟效应。

多视角延迟独立分量分析

MultiView Independent Component Analysis with Delays

Linear principal component analysis (PCA), nonlinear PCA, and linear
independent component analysis (ICA) -- those are three methods with
single-layer autoencoder formulations for learning linear transformations from
data. Linear PCA learns orthogonal transformations (rotations) that orient axes
to maximise variance, but it suffers from a subspace rotational indeterminacy:
it fails to find a unique rotation for axes that share the same variance. Both
nonlinear PCA and linear ICA reduce the subspace indeterminacy from rotational
to permutational by maximising statistical independence under the assumption of
unit variance. The main difference between them is that nonlinear PCA only
learns rotations while linear ICA learns not just rotations but any linear
transformation with unit variance. The relationship between all three can be
understood by the singular value decomposition of the linear ICA transformation
into a sequence of rotation, scale, rotation. Linear PCA learns the first
rotation; nonlinear PCA learns the second. The scale is simply the inverse of
the standard deviations. The problem is that, in contrast to linear PCA,
conventional nonlinear PCA cannot be used directly on the data to learn the
first rotation, the first being special as it reduces dimensionality and orders
by variances. In this paper, we have identified the cause, and as a solution we
propose $\sigma$-PCA: a unified neural model for linear and nonlinear PCA as
single-layer autoencoders. One of its key ingredients: modelling not just the
rotation but also the scale -- the variances. This model bridges the disparity
between linear and nonlinear PCA. And so, like linear PCA, it can learn a
semi-orthogonal transformation that reduces dimensionality and orders by
variances, but, unlike linear PCA, it does not suffer from rotational
indeterminacy.

线性主成分分析、非线性主成分分析、线性独立成分分析、子空间不确定性和神经模型