In this paper, we aim to answer three key open questions: (i) whether and how brain networks are cross-correlated at different time scales with long-range dependencies ("long-memory" process,

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.

In this work, the authors describe the use of detrended partial cross correlation (DPCCA) as a quantity to capture short and long memory connections among brain recordings, for connectivity analysis. DPPCA is complemented with CCA to study the efficacy of detecting connectivity on simulated data (generated with NatSim), and compared to partial correlation and regularized inverse covriance (ICOV). On real fMRI data, DPCCA is first used together with PCA to show representative correlation profiles and perform dimensionality reduction (with Isomap (Iso) and autoencorder (AutoE)). Second, various combinations of DPCCA values and dimensionality reduction methods are used as feature for predicting cocaine dependent class from control. The paper is sufficiently well written and most parts is described in enough detail to reproduce the technical steps of the proposed methodology. I appreciate the use of DPCCA which is definitely new to the neuroimaging data analysis domain.

Neural Information Processing Systems http://nips.cc/

Brain connectivity analysis is a critical component of ongoing human connectome projects to decipher the healthy and diseased brain. Recent work has highlighted the power-law (multi-time scale) properties of brain signals; however, there remains a lack of methods to specifically quantify short- vs. long- time range brain connections. In this paper, using detrended partial cross-correlation analysis (DPCCA), we propose a novel functional connectivity measure to delineate brain interactions at multiple time scales, while controlling for covariates. We use a rich simulated fMRI dataset to validate the proposed method, and apply it to a real fMRI dataset in a cocaine dependence prediction task. We show that, compared to extant methods, the DPCCA-based approach not only distinguishes short and long memory functional connectivity but also improves feature extraction and enhances classification accuracy. Together, this paper contributes broadly to new computational methodologies in understanding neural information processing.