arXiv subjects

Zhiwei Han

Publications and source records attributed to Zhiwei Han.

6 recordsLinked to original sources

arXiv2026

Provable Subspace Identification of Nonlinear Multi-view CCA

We investigate the identifiability of nonlinear canonical correlation analysis (CCA) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise. Rather than pursuing exact unmixing, which is known to be ill-posed under general nonlinear mixing, we instead reframe multi-view CCA as a basis-invariant subspace identification problem. Under suitable latent priors and spectral separation conditions, we prove that the pairwise population CCA objective recovers correlated signal subspaces up to view-wise orthogonal ambiguity. For $N \geq 3$ views, their multi-view aggregation provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variation. We further establish finite-sample statistical consistency guarantees by translating the concentration of empirical cross-covariances into explicit subspace error bounds via spectral perturbation theory. Experiments on synthetic and rendered image datasets support our theoretical findings and illustrate the necessity of the assumed conditions.

cs.LG↗

arXiv2025

Provable Affine Identifiability of Nonlinear CCA under Latent Distributional Priors

In this work, we establish the sufficient conditions under which nonlinear Canonical Correlation Analysis (CCA) recovers ground-truth latent factors up to an affine transformation. By transporting the analysis from the observation space to the source space, we extend classical statistical results on orthogonal polynomial expansions of bivariate distributions to representation learning, proving affine identifiability under specific distributional priors. We formally demonstrate that whitening is strictly necessary to ensure the boundedness and well-conditioning of the learned mappings. Furthermore, we bridge the gap between theory and practice by proving that ridge-regularized empirical CCA converges to its population counterpart in the finite-sample regime. Finally, our findings provide a rigorous theoretical foundation explaining the empirical success of recent correlation-based non-contrastive learning methods. Experiments on synthetic and rendered image datasets, alongside systematic ablations, validate the predicted recovery behavior and illustrate the failure modes that arise when the assumptions are violated.

cs.LG↗

arXiv2025

Mechanistic Independence: A Principle for Identifiable Disentangled Representations

Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through mechanistic independence, which characterizes latent factors by how they act on observed variables rather than by their latent distribution. This perspective is invariant to changes of the latent density, even when such changes induce statistical dependencies among factors. Within this framework, we propose several related independence criteria -- ranging from support-based and sparsity-based to higher-order conditions -- and show that each yields identifiability of latent subspaces, even under nonlinear, non-invertible mixing. We further establish a hierarchy among these criteria and provide a graph-theoretic characterization of latent subspaces as connected components. Together, these results clarify the conditions under which disentangled representations can be identified without relying on statistical assumptions.

cs.LG↗

arXiv2023

Towards a Unified Framework of Contrastive Learning for Disentangled Representations

Contrastive learning has recently emerged as a promising approach for learning data representations that discover and disentangle the explanatory factors of the data. Previous analyses of such approaches have largely focused on individual contrastive losses, such as noise-contrastive estimation (NCE) and InfoNCE, and rely on specific assumptions about the data generating process. This paper extends the theoretical guarantees for disentanglement to a broader family of contrastive methods, while also relaxing the assumptions about the data distribution. Specifically, we prove identifiability of the true latents for four contrastive losses studied in this paper, without imposing common independence assumptions. The theoretical findings are validated on several benchmark datasets. Finally, practical limitations of these methods are also investigated.

cs.LG↗

arXiv2021

Metapath- and Entity-aware Graph Neural Network for Recommendation

In graph neural networks (GNNs), message passing iteratively aggregates nodes' information from their direct neighbors while neglecting the sequential nature of multi-hop node connections. Such sequential node connections e.g., metapaths, capture critical insights for downstream tasks. Concretely, in recommender systems (RSs), disregarding these insights leads to inadequate distillation of collaborative signals. In this paper, we employ collaborative subgraphs (CSGs) and metapaths to form metapath-aware subgraphs, which explicitly capture sequential semantics in graph structures. We propose meta\textbf{P}ath and \textbf{E}ntity-\textbf{A}ware \textbf{G}raph \textbf{N}eural \textbf{N}etwork (PEAGNN), which trains multilayer GNNs to perform metapath-aware information aggregation on such subgraphs. This aggregated information from different metapaths is then fused using attention mechanism. Finally, PEAGNN gives us the representations for node and subgraph, which can be used to train MLP for predicting score for target user-item pairs. To leverage the local structure of CSGs, we present entity-awareness that acts as a contrastive regularizer on node embedding. Moreover, PEAGNN can be combined with prominent layers such as GAT, GCN and GraphSage. Our empirical evaluation shows that our proposed technique outperforms competitive baselines on several datasets for recommendation tasks. Further analysis demonstrates that PEAGNN also learns meaningful metapath combinations from a given set of metapaths.

cs.LG↗

arXiv2019

Interactive Image Restoration

Machine learning and many of its applications are considered hard to approach due to their complexity and lack of transparency. One mission of human-centric machine learning is to improve algorithm transparency and user satisfaction while ensuring an acceptable task accuracy. In this work, we present an interactive image restoration framework, which exploits both image prior and human painting knowledge in an iterative manner such that they can boost on each other. Additionally, in this system users can repeatedly get feedback of their interactions from the restoration progress. This informs the users about their impact on the restoration results, which leads to better sense of control, which can lead to greater trust and approachability. The positive results of both objective and subjective evaluation indicate that, our interactive approach positively contributes to the approachability of restoration algorithms in terms of algorithm performance and user experience.

cs.HC↗