Unsupervised discovery of the shared and private geometry in multi-view data

Abstract: Studying complex real-world phenomena often involves data from multiple views (e.g. sensor modalities or brain regions), each capturing different aspects of the underlying system. Within neuroscience, there is growing interest in large-scale simultaneous recordings across multiple brain regions. Understanding the relationship between views (e.g., the neural activity in each region recorded) can reveal fundamental insights into each view and the system as a whole. However, existing methods to characterize such relationships lack the expressivity required to capture nonlinear relationships, describe only shared sources of variance, or discard geometric information that is crucial to drawing insights from data. Here, we present SPLICE: a neural network-based method that infers disentangled, interpretable representations of private and shared latent variables from paired samples of high-dimensional views. Compared to competing methods, we demonstrate that SPLICE 1) disentangles shared and private representations more effectively, 2) yields more interpretable representations by preserving geometry, and 3) is more robust to incorrect a priori estimates of latent dimensionality. We propose our approach as a general-purpose method for finding succinct and interpretable descriptions of paired data sets in terms of disentangled shared and private latent variables.

• The paper introduces SPLICE, a novel neural architecture that disentangles shared and private latent variables using predictability minimization and manifold learning.
• It demonstrates robust performance on rotated MNIST and neuroscience data by preserving intrinsic geometric structures and reducing overestimated dimensionality.
• The method enhances the interpretability of multi-view datasets by accurately reconstructing neural dynamics and capturing nonlinear relationships.

Unsupervised Discovery of Shared and Private Geometry in Multi-View Data

The paper "Unsupervised Discovery of the Shared and Private Geometry in Multi-View Data" (2408.12091) introduces a novel technique, SPLICE, designed to extract disentangled, interpretable representations from paired high-dimensional datasets. This approach is grounded in the need for precise modeling of data with multiple views, which is commonplace across domains such as neuroscience and multi-modal machine learning. The primary aim of SPLICE is to segregate the shared and private aspects of these datasets while maintaining the intrinsic geometric features for enhanced interpretability.

Problem Formulation and Methodology

Multi-view data, which captures different perspectives of the same underlying phenomenon, demands robust analysis techniques that can distinguish between shared and private information. The authors address the shortcomings of existing models that typically ignore nonlinear relationships and geometric structures, limiting their utility in domains requiring nuanced understanding, such as neuroscience.

SPLICE employs a neural network-based architecture to solve this problem. It models the data as being generated from a set of statistically independent latent variables: shared variables that are constant across views, and private variables unique to each view. The insight comes from understanding that these variables can be nonlinearly mixed, necessitating advanced disentangling methods.

SPLICE Architecture

The architecture of SPLICE incorporates two main phases: disentangling and geometry preservation. The first step involves a predictability minimization approach within a crossed autoencoder framework, ensuring effective separation of shared and private latents. Predictability minimization uses adversarial networks to reduce mutual information between latents and unconditioned data, promoting independence.

In the second phase, SPLICE fine-tunes the separated latents to preserve submanifold structures, which is crucial for ensuring that the learned representations are not only disentangled but also geometrically faithful to the original data relationships. This is achieved by adjusting the encoders and decoders using manifold learning techniques to align with geodesic distances computed from the latent spaces.

Experimental Results

Rotated MNIST Dataset

SPLICE's efficacy is validated on a rotated MNIST dataset, showcasing its ability to maintain circular geometric structure in the latent space. Compared to competitors like DMVAE and methods by Lyu et al., SPLICE excels in restricting private variance to fewer dimensions, emphasizing its robustness to mis-specified dimensionality.

Synthetic Neuroscience Data

SPLICE is also tested on datasets mimicking neural activity in response to shared and private stimuli. It accurately reconstructs the neural responses and captures true underlying geometries, clearly delineating shared variables as a 2D sheet correlated with visual stimulus positions, outperforming standard approaches like Reduced Rank Regression which overestimate dimensionality.

Neurophysiological Data

On real neurophysiological data, SPLICE successfully infers shared information regarding task-relevant variables, substantiating its utility in neuroscientific applications. It reconstructs complex population dynamics with a minimal set of shared dimensions, highlighting nonlinear relationships inadequately addressed by traditional linear models.

Theoretical Implications and Future Directions

SPLICE fundamentally advances the state-of-the-art in multi-view learning by prioritizing geometric preservation within disentangled representations, a gap largely unfulfilled by prior methods. Future investigations may integrate SPLICE with temporally-aware models to capture dynamic data aspects, potentially expanding its scope to temporal multi-view datasets.

Additionally, while SPLICE currently supports dual-view datasets, exploring extensions for datasets with more than two views represents a promising avenue for further research. This extension could significantly enhance its applicability to more complex real-world problems.

Conclusion

The model put forth in the paper stands as a significant contribution to the domain of unsupervised multi-view learning. Through a novel architecture that leverages predictability minimization and manifold learning, SPLICE presents itself as an effective tool for extracting interpretable insights from high-dimensional data across various fields, with particular success demonstrated in synthetic and real neuroscience applications. This capability for unsupervised discovery of shared and private latent geometries is both timely and essential, promising to enrich our understanding of complex multi-modal datasets.