This course delivers methods of model selection in machine learning and forecasting. The modelling data are videos, audios, encephalograms, fMRIs and another measurements in natural science. The models are linear, tensor, deep neural networks, and neural ODEs. The practical examples are brain-computer interfaces, weather forecasting and various spatial-time series forecasting. The lab works are organised as paper-with-code reports.
- Energy forecasting exampl
- Regression
- Singular spectrum analysis
- SSA forecasting
- Forecasting protocols and verification (before AR)
- Autoregression
- Singular values decomposition (PCA, AE, Kar-Lo)
- QPFS model selection
- Auto, corss-correlation (?cointegration)
- Diagrams for ML and PLS (Before PLS)
- Projection to latent space (and relation to PCA), canonical-correlation analysis
- PLS-QPFS model selection
- Higer-order SSA
- Tensor decomposition
- Tensor model selection
- HOPLS
- Granger causality test
- Convergent cross mapping
- HOCCM (materials?)
- Takens theorem
- Neural ODE
- Ajoint and backpropagation
- Flows and forecasting
- Space state models
- S4, Hippo, SaShiMi models
To include
- RNN, LSTM, attention, transformer models
- Directional regression
- Harmonic functions
- Phase extraction
- Non-parametric regression (+ customer demands forecasting)
- Graph (earth prediction)
- Find your data
- Questionnaires during lectures (4)
- Two application projects (2+2)
- The final exam: problems with discussion (1)
- Bonus for active participation (2)
- October 14th, (October 7th one-week before preliminary show is strongly advised)
- December 2nd, (November 25th one-week before preliminary show is strongly advised)
- Title and motivated abstract
- Problem statement
- Problem solution
- Link to the code
- Analysis and illustrative plots
- References