Deep Deterministic Nonlinear ICA via Total Correlation Minimization with Matrix-Based Entropy Functional

Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully data-driven nature that minimizes reliance on prior assumptions. However, conventional ICA methods rely on an assumption of linear mixing, limiting their ability to capture complex nonlinear relationships and to maintain robustness in noisy environments. In this work, we present deep deterministic nonlinear independent component analysis (DDICA), a novel deep neural network-based framework designed to address these limitations. DDICA leverages a matrix-based entropy function to directly optimize the independence criterion via stochastic gradient descent, bypassing the need for variational approximations or adversarial schemes. This results in a streamlined training process and improved resilience to noise. We validated the effectiveness and generalizability of DDICA across a range of applications, including simulated signal mixtures, hyperspectral image unmixing, modeling of primary visual receptive fields, and resting-state functional magnetic resonance imaging (fMRI) data analysis. Experimental results demonstrate that DDICA effectively separates independent components with high accuracy across a range of applications. These findings suggest that DDICA offers a robust and versatile solution for blind source separation in diverse signal processing tasks.

Multimodal Functional Maximum Correlation for Emotion Recognition

Emotional states manifest as coordinated yet heterogeneous physiological responses across central and autonomic systems, posing a fundamental challenge for multimodal representation learning in affective computing. Learning such joint dynamics is further complicated by the scarcity and subjectivity of affective annotations, which motivates the use of self-supervised learning (SSL). However, most existing SSL approaches rely on pairwise alignment objectives, which are insufficient to characterize dependencies among more than two modalities and fail to capture higher-order interactions arising from coordinated brain and autonomic responses. To address this limitation, we propose Multimodal Functional Maximum Correlation (MFMC), a principled SSL framework that maximizes higher-order multimodal dependence through a Dual Total Correlation (DTC) objective. By deriving a tight sandwich bound and optimizing it using a functional maximum correlation analysis (FMCA) based trace surrogate, MFMC captures joint multimodal interactions directly, without relying on pairwise contrastive losses. Experiments on three public affective computing benchmarks demonstrate that MFMC consistently achieves state-of-the-art or competitive performance under both subject-dependent and subject-independent evaluation protocols, highlighting its robustness to inter-subject variability. In particular, MFMC improves subject-dependent accuracy on CEAP-360VR from 78.9% to 86.8%, and subject-independent accuracy from 27.5% to 33.1% using the EDA signal alone. Moreover, MFMC remains within 0.8 percentage points of the best-performing method on the most challenging EEG subject-independent split of MAHNOB-HCI. Our code is available at https://github.com/DY9910/MFMC.

Explainable Multimodal Regression via Information Decomposition

Multimodal regression aims to predict a continuous target from heterogeneous input sources and typically relies on fusion strategies such as early or late fusion. However, existing methods lack principled tools to disentangle and quantify the individual contributions of each modality and their interactions, limiting the interpretability of multimodal fusion. We propose a novel multimodal regression framework grounded in Partial Information Decomposition (PID), which decomposes modality-specific representations into unique, redundant, and synergistic components. The basic PID framework is inherently underdetermined. To resolve this, we introduce inductive bias by enforcing Gaussianity in the joint distribution of latent representations and the transformed response variable (after inverse normal transformation), thereby enabling analytical computation of the PID terms. Additionally, we derive a closed-form conditional independence regularizer to promote the isolation of unique information within each modality. Experiments on six real-world datasets, including a case study on large-scale brain age prediction from multimodal neuroimaging data, demonstrate that our framework outperforms state-of-the-art methods in both predictive accuracy and interpretability, while also enabling informed modality selection for efficient inference. Implementation is available at https://github.com/zhaozhaoma/PIDReg.

When Brain Foundation Model Meets Cauchy-Schwarz Divergence: A New Framework for Cross-Subject Motor Imagery Decoding

Decoding motor imagery (MI) electroencephalogram (EEG) signals, a key non-invasive brain-computer interface (BCI) paradigm for controlling external systems, has been significantly advanced by deep learning. However, MI-EEG decoding remains challenging due to substantial inter-subject variability and limited labeled target data, which necessitate costly calibration for new users. Many existing multi-source domain adaptation (MSDA) methods indiscriminately incorporate all available source domains, disregarding the large inter-subject differences in EEG signals, which leads to negative transfer and excessive computational costs. Moreover, while many approaches focus on feature distribution alignment, they often neglect the explicit dependence between features and decision-level outputs, limiting their ability to preserve discriminative structures. To address these gaps, we propose a novel MSDA framework that leverages a pretrained large Brain Foundation Model (BFM) for dynamic and informed source subject selection, ensuring only relevant sources contribute to adaptation. Furthermore, we employ Cauchy-Schwarz (CS) and Conditional CS (CCS) divergences to jointly perform feature-level and decision-level alignment, enhancing domain invariance while maintaining class discriminability. Extensive evaluations on two benchmark MI-EEG datasets demonstrate that our framework outperforms a broad range of state-of-the-art baselines. Additional experiments with a large source pool validate the scalability and efficiency of BFM-guided selection, which significantly reduces training time without sacrificing performance.

MvHo-IB: Multi-View Higher-Order Information Bottleneck for Brain Disorder Diagnosis

Recent evidence suggests that modeling higher-order interactions (HOIs) in functional magnetic resonance imaging (fMRI) data can enhance the diagnostic accuracy of machine learning systems. However, effectively extracting and utilizing HOIs remains a significant challenge. In this work, we propose MvHo-IB, a novel multi-view learning framework that integrates both pairwise interactions and HOIs for diagnostic decision-making, while automatically compressing task-irrelevant redundant information. MvHo-IB introduces several key innovations: (1) a principled method that combines O-information from information theory with a matrix-based Renyi alpha-order entropy estimator to quantify and extract HOIs, (2) a purpose-built Brain3DCNN encoder to effectively utilize these interactions, and (3) a new multi-view learning information bottleneck objective to enhance representation learning. Experiments on three benchmark fMRI datasets demonstrate that MvHo-IB achieves state-of-the-art performance, significantly outperforming previous methods, including recent hypergraph-based techniques. The implementation of MvHo-IB is available at https://github.com/zky04/MvHo-IB.

InfoDPCCA: Information-Theoretic Dynamic Probabilistic Canonical Correlation Analysis

Extracting meaningful latent representations from high-dimensional sequential data is a crucial challenge in machine learning, with applications spanning natural science and engineering. We introduce InfoDPCCA, a dynamic probabilistic Canonical Correlation Analysis (CCA) framework designed to model two interdependent sequences of observations. InfoDPCCA leverages a novel information-theoretic objective to extract a shared latent representation that captures the mutual structure between the data streams and balances representation compression and predictive sufficiency while also learning separate latent components that encode information specific to each sequence. Unlike prior dynamic CCA models, such as DPCCA, our approach explicitly enforces the shared latent space to encode only the mutual information between the sequences, improving interpretability and robustness. We further introduce a two-step training scheme to bridge the gap between information-theoretic representation learning and generative modeling, along with a residual connection mechanism to enhance training stability. Through experiments on synthetic and medical fMRI data, we demonstrate that InfoDPCCA excels as a tool for representation learning. Code of InfoDPCCA is available at https://github.com/marcusstang/InfoDPCCA.

Aggregation of Dependent Expert Distributions in Multimodal Variational Autoencoders

Multimodal learning with variational autoencoders (VAEs) requires estimating joint distributions to evaluate the evidence lower bound (ELBO). Current methods, the product and mixture of experts, aggregate single-modality distributions assuming independence for simplicity, which is an overoptimistic assumption. This research introduces a novel methodology for aggregating single-modality distributions by exploiting the principle of consensus of dependent experts (CoDE), which circumvents the aforementioned assumption. Utilizing the CoDE method, we propose a novel ELBO that approximates the joint likelihood of the multimodal data by learning the contribution of each subset of modalities. The resulting CoDE-VAE model demonstrates better performance in terms of balancing the trade-off between generative coherence and generative quality, as well as generating more precise log-likelihood estimations. CoDE-VAE further minimizes the generative quality gap as the number of modalities increases. In certain cases, it reaches a generative quality similar to that of unimodal VAEs, which is a desirable property that is lacking in most current methods. Finally, the classification accuracy achieved by CoDE-VAE is comparable to that of state-of-the-art multimodal VAE models.

Distributional Vision-Language Alignment by Cauchy-Schwarz Divergence

Multimodal alignment is crucial for various downstream tasks such as cross-modal generation and retrieval. Previous multimodal approaches like CLIP maximize the mutual information mainly by aligning pairwise samples across modalities while overlooking the distributional differences, leading to suboptimal alignment with modality gaps. In this paper, to overcome the limitation, we propose CS-Aligner, a novel and straightforward framework that performs distributional vision-language alignment by integrating Cauchy-Schwarz (CS) divergence with mutual information. In the proposed framework, we find that the CS divergence and mutual information serve complementary roles in multimodal alignment, capturing both the global distribution information of each modality and the pairwise semantic relationships, yielding tighter and more precise alignment. Moreover, CS-Aligher enables incorporating additional information from unpaired data and token-level representations, enhancing flexible and fine-grained alignment in practice. Experiments on text-to-image generation and cross-modality retrieval tasks demonstrate the effectiveness of our method on vision-language alignment.

Deep Dynamic Probabilistic Canonical Correlation Analysis

This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of Canonical Correlation Analysis (CCA), D2PCCA captures nonlinear latent dynamics and supports enhancements such as KL annealing for improved convergence and normalizing flows for a more flexible posterior approximation. D2PCCA naturally extends to multiple observed variables, making it a versatile tool for encoding prior knowledge about sequential datasets and providing a probabilistic understanding of the system's dynamics. Experimental validation on real financial datasets demonstrates the effectiveness of D2PCCA and its extensions in capturing latent dynamics.

Towards the Generalization of Multi-view Learning: An Information-theoretical Analysis

Multiview learning has drawn widespread attention for its efficacy in leveraging cross-view consensus and complementarity information to achieve a comprehensive representation of data. While multi-view learning has undergone vigorous development and achieved remarkable success, the theoretical understanding of its generalization behavior remains elusive. This paper aims to bridge this gap by developing information-theoretic generalization bounds for multi-view learning, with a particular focus on multi-view reconstruction and classification tasks. Our bounds underscore the importance of capturing both consensus and complementary information from multiple different views to achieve maximally disentangled representations. These results also indicate that applying the multi-view information bottleneck regularizer is beneficial for satisfactory generalization performance. Additionally, we derive novel data-dependent bounds under both leave-one-out and supersample settings, yielding computational tractable and tighter bounds. In the interpolating regime, we further establish the fast-rate bound for multi-view learning, exhibiting a faster convergence rate compared to conventional square-root bounds. Numerical results indicate a strong correlation between the true generalization gap and the derived bounds across various learning scenarios.