Difference between revisions of "BCI"
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===PPCA=== | ===PPCA=== | ||
* [https://www.tensorflow.org/probability/examples/Probabilistic_PCA#:~:text=Probabilistic%20principal%20components%20analysis%20(PCA,data%20or%20for%20multidimensional%20scaling. PPCA] | * [https://www.tensorflow.org/probability/examples/Probabilistic_PCA#:~:text=Probabilistic%20principal%20components%20analysis%20(PCA,data%20or%20for%20multidimensional%20scaling. PPCA] | ||
| + | * How to tell stochastic from deterministic variable? Are expectation and variance deterministic? | ||
| + | * Recap: joint and conditional distribution, marginalization. | ||
* Sampling principle | * Sampling principle | ||
* VAE as PPCA encoder-decoder | * VAE as PPCA encoder-decoder | ||
Revision as of 00:13, 28 March 2023
Contents
Brain-Computer Interfaces and Functional Data Analysis
This course is under construction. It enlightens fundamental mathematical concepts of brain signal analysis.
Each class combines five parts:
- Comprehensive introduction
- Practical example with code and homework
- Algebraic part of modeling
- Statistical part of modeling
- Join them in Hilbert (or any convenient) space
- Quiz for the next part (could be in the beginning) to show the theory to catch up
Linear models
SSA, SVD, PCA
- non-parametric phase space Hankel matrix
- convoluion ?
- forecasting with SSA
Acceleroneter data
- Energy
Tensor product and spectral decomposition
- vector, covector, dot product
- linear operator
- in Euclidean and (Hilbert space with useful example) dot product=bilinear form
- bilinear form
- factorization
- spectral decomposition
- SVD
- ??? SVD in Hilbert space
Why do we go from Eucledian to Hilbert space? Was: a vector as a number of measurements. Now it is a finite number of samples. Then it is a distribution of samples. The distribution is a point in the Hilbert space. We can make an inner product and tensor product of two and more distributions. Machine learning: given samples, multivariate distribution can be represented as a (direct?) sum of elements' tensor products.
PPCA
- PPCA
- How to tell stochastic from deterministic variable? Are expectation and variance deterministic?
- Recap: joint and conditional distribution, marginalization.
- Sampling principle
- VAE as PPCA encoder-decoder