The paper introduces a method for learning disentangled signals via non‑linear Independent Component Analysis (ICA) by defining self‑sufficient signals, where the conditional distribution of a missing value given the rest remains unchanged when other signals are observed. It formulates this as a conditional KL divergence minimization and proposes a sequential, prior‑free, likelihood‑free algorithm that learns a demixing flow model at each iteration. The authors provide theoretical guarantees of local descent for an idealized Wasserstein‑gradient‑flow variant and demonstrate the method’s effectiveness on toy and real‑world datasets.
Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures. To achieve this, classical ICA algorithms attempt to maximize non-Gaussianity, measured by negentropy, which is linked to independence by information theory.
arXiv:2607. 14081v1 Announce Type: new Abstract: Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures.
arXiv:2411. 00214v2 Announce Type: replace-cross Abstract: Otto's Wasserstein gradient flow of the inclusive (forward) Kullback--Leibler (KL) divergence offers a principled framework for analyzing statistical inference algorithms, yet algorithms targeting the exclusive (reverse) KL divergence are rarely studied with such tools.
To leverage the full potential of multimodal data, we need representations that go beyond the state-of-the-art alignment and fusion approaches and exploit all cross-modal interactions without sacrificing modality-specific information. Learning disentangled representations is a principled way to identify these underlying shared and unique factors that are hidden in observational data.
Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density. However, this choice of latent density can impose unnecessary complexity on the learned flow transformation due to the topological mismatch between the latent and data densities, leading to slower training and suboptimal performance.
arXiv:2606. 05109v1 Announce Type: new Abstract: To leverage the full potential of multimodal data, we need representations that go beyond the state-of-the-art alignment and fusion approaches and exploit all cross-modal interactions without sacrificing modality-specific information.
arXiv:2608. 13229v1 Announce Type: cross Abstract: We present the mathematical foundations of linear independent component analysis (ICA) models based on standard literature in a self-contained note.
arXiv:2606. 29724v1 Announce Type: new Abstract: Normalizing flows are powerful generative models that learn an invertible mapping between complex data distributions and simple latent distributions, typically a standard normal density.
arXiv:2606. 21385v2 Announce Type: replace-cross Abstract: This paper explores unsupervised disentangled representation learning from a functional perspective.
The paper introduces a new approach to learning disentangled representations by directly sculpting the aggregate posterior using the non‑parametric Maximum Mean Discrepancy (MMD) and programmable priors. It demonstrates that traditional Variational Autoencoders and Adversarial Training consistently fail to enforce a factorized latent space, as quantified by the Latent Predictability Score (LPS). The proposed method achieves state‑of‑the‑art unsupervised statistical independence, a 70% reduction in entanglement, optional semi‑supervised semantic alignment, and precise shaping of the posterior without compromising reconstruction quality.
arXiv:2607. 16725v1 Announce Type: cross Abstract: Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant.
The paper introduces MS‑WDRO, a multi‑source Wasserstein distributionally robust optimization framework for reconstructing complex network topologies from scarce target‑domain data and abundant heterogeneous source data. It fuses sources via a weighted Wasserstein barycenter, builds an ambiguity set around it, and solves a regularized Laplacian estimator using a provably convergent ADMM scheme. The authors provide finite‑sample guarantees, demonstrate that naive aggregation is suboptimal, and show through experiments on synthetic data and the ABIDE I neuroimaging dataset that MS‑WDRO outperforms seven baselines in graph recovery, sample efficiency, and diagnostic utility, especially when target samples are limited.