Projects/BCI-FDA: Brain-computer interface with Functional data analysis

Brain-computer interface with Functional data analysis, Human behavioral analysis, and forecasting requires models that have to predict target variables of complex structures. We develop PLS and CCA (Projection to latent space and Canonic correlation analysis) methods towards the Multiview with continuous-time data representation.

Generative time series decoding models

1. The goal is to create a generative state-space model for BCI
2. The impact is to boost the behavioral classification quality by decision-rejecting
3. The principle if a generated pattern does not belong to one of the expected patterns (one-class classification) we reject the decision
4. The plan
   1. Create the simplest generative model for selected data
   2. apply SSM (state-space model) principles to make CCA (canonic-correlation analysis)
   3. Introduce classification model and decision-rejecting criterion
   4. compare quality

References

1. Direct Discriminative Decoder Models for Analysis of High-Dimensional Dynamical Neural Data by M.R. Rezaei et al. 2022 [DOI https://doi.org/10.1162/neco_a_01491]
2. Deep Direct Discriminative Decoders for High-dimensional Time-series Data Analysis by M.R. Rezaei 2023 (NTDB)
3. Decoding Hidden Cognitive States From Behavior and Physiology Using a Bayesian Approach by Ali Yousefi et al. DOI
4. Bayesian Decoder Models with a Discriminative Observation Process by M.R. Rezaei et al. 2020 DOI
5. Deep Discriminative Direct Decoders for High-dimensional Time-series Analysis by M.R. Rezaei 2020 ArXiv
6. Real-Time Point Process Filter for Multidimensional Decoding Problems Using Mixture Models by M.R. Rezaei 2020 DOI
7. Basic code D4
8. Variational auto-encoded deep gaussian processes by Z. Dai et al. 2021 ArXiv
9. Parametric Gaussian process regressors by M. Jankowiak et al. 2020 ArXiv
10. A Tutorial on Gaussian Processes by Z. Ghahramani 2010 PDF
11. An Intuitive Tutorial to Gaussian Processes Regression by J. Wang 2021 ArXiv

Riemannian Geometry and Graph Laplacian metric models

1. The goal is to create a metric behavioral forecasting model for BCI
2. The impact is to construct time-embedding metric space so that it is compatible with the generative models
3. The principle a dynamic system changes its state consequently, so we construct a metric state space that could be decomposed with one of diffusion models
4. The plan
   1. select a metric model with continuous time
   2. use Riemannian geometry and Graph-Laplacian approaches
   3. make diffusion decomposition
   4. boost decoding models with metric space

References

1. Classification of covariance matrices using a Riemannian-based kernel for BCI applications by A. Barachant et al. 2013 (Neurocomputing)
2. Multi-class Brain-Computer Interface Classification by Riemannian Geometry by A. Barachant et al.
3. Riemannian Geometry for EEG-based Brain-Computer Interfaces by M. Congedo et al.
4. Online SSVEP-based BCI using Riemannian geometry by E. K. Kalunga 2016 DOI
5. A Plug&Play P300 BCI Using Information Geometry by A. Barachant 2014 ArXiv
6. Longitudinal predictive modeling of tau progression along the structural connectome by J.Dutta et al. 2021 DOI
7. Grand: Graph neural diffusion by M.M. Bronstein et al. ICML, 2021.
8. (inspiring) The inverse problem in electroencephalography using the bidomain model of electrical activity by A.L. Rincon and S. Shimoda, 2016 DOI
9. (inverse) High-Resolution EEG Source Reconstruction with Boundary Element Fast Multipole Method, N. Makaroff et al. 2022 DOI

Data

Any data that has

1. timeline with a behavioral pattern, synchronous both for source and target data
2. source time series with
   • probabilistic assumptions for diffusion probabilistic models
3. target time series with
   • behavioral pattern to make a decision

To select from

• List of datasets and tools
• Scientific lessons from a catalog of 6674 brain recordings by A.D.J. Makin

The problem

1. To make a classification decision or to reject it
2. To forecast a system behavior (system state) and generate variants
3. The rejection criterion is a mismatch observation from generated scenarios

Assumptions

1. Short time series (relatively, hundreds or thousands of samples)
2. Time series have big variances and systematic errors
3. Time series could be significantly correlated
4. Time series have origins
   1. exogenous, no one can control
   2. control signals
   3. and decisions
   4. behavioral
5. Timeline has structure
   1. periods (seasonal or quasi)
   2. events (forced or selected)
   3. including decision timestamps

Examples

1. Any sports game (exogenous, behavior to model, decisions)
2. Brain computer interfaces
3. Risk management, stock market

The challenge is to put

• generative models
• of time series graph Laplacian
• into seq2seq framework
• to make quality decisions.

Schedule 2023

Date		N	Progress	To discuss	Result
September	16	1	Introduction and planning	Topics for the next week	Subscribed to the schedule
	23	2	Possible models	Introductions to models	Slides, references, questions to reason
	30	3	Model reasoning and selection	Discussion of the questions, refined presentations of models	Role of models in the system
October	7	4	System description	Variants of the system, code sources	List of code references, toolbox(es) selection
	14	5	Architecture planning	Variants of the pipelines	Collection of pipelines, executable
	21	6	Data collection	Discussion of the applications	Links to the data and downloaders
	28	7	Minimum value system	Discussion of the tutorials	Tutorial plan
November	4	8	Examples and documents	Tutorial presentation	List of new models and challenges
	11	9	New directions	Model presentation (week 2)	List of challenges
	18	10	Analysis, testing, and applications	Decomposition of the system	List of possible projects
	25	11	Project proposals	Project presentations	Project descriptions
December	2	12	Project description review	Discussion of the messages	Published descriptions

Week 2. Propedevtics

• The goals and themes to select from

Week 2. Topics to discuss

1. CCA generative models
2. Continous models for graph Laplacian
3. D4 and variants
4. Riemmanian model with time
5. SSM generative models
6. Generative models with time graph convolutions
7. (risky) RL for time series scenario generation
8. (math) CCA Error functions and (tech) Autograd for seq2seq generative pipelines

References by theme

CCA probabilistic

1. DCCA: Deep Canonical Correlation Analysis by Galen Andrew et al., ICML, 2013, GitHub over-engineered
2. Deep Generalized Canonical Correlation Analysis by Adrian Benton et al., 2019, GitHub, pwc
3. Deep Canonical Correlation Analysis by Galen Andrew, 2013, JMLR
4. On Deep Multi-View Representation Learning by Weiran Wang et al., 2015, JMLR

Generative

1. Denoising Diffusion Probabilistic Models by Jonathan Ho, 2020, ArXiv
2. Score-Based Generative Modeling through Stochastic Differential Equations by Yang Song et al., 2020, ArXiv, GitHub
3. Denoising Diffusion Probabilistic Model in Pytorch by Yannic Kilcher et al., 2023, GitHub
4. Collection of Generative Models with PyTorch, 2022, GitHub
5. DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting by Salva Rühling Cachay et al., 2023, ArXiv

CCA generative

1. Deep Variational Canonical Correlation Analysis by Weiran Wang, 2016, ArXiv
2. Deep Probabilistic Canonical Correlation Analysis by Mahdi Karami, 2021 [ AAAI]

Riemannian

1. Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis by Ce Ju and Cuntai Guan, 2022, ArXiv, GitHub, 'explanative figs'
2. From canonical correlation analysis to self-supervised graph neural networks by Hengrui Zhang et al., 2021, NIPS, GitHub, Github

Generative Riemannian

1. Riemannian Diffusion Models by Chin-Wei Huang et al., 2022, ArXiv, nocode

State space models

1. Deep learning for universal linear embeddings of nonlinear dynamics by Bethany Lusch et al., 2018, Nature
2. Data-driven discovery of coordinates and governing equations by Kathleen Championa et al. 2019, PNAS