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TODO (Learn)
* Frequency Analysis - PSD, Band power, Frequency domain
* Singular spectrum analysis -> Taken's embedding, applies PCA to time lags
in phase space to separate signal into stationary components
* Correlation Dimension - Implement. Very beautiful concept
* Recurrence plot - Implement. Seems very reasonable approach to projecting
multidimensional data.
* heteroskedasticity models
TODO (Find Home)
* ANOVA
* Parameter jiggling to get smooth estimators (read pub)
Probability Theory
- Moments
- Empirical Distributions, CDF
Resampling
- IID methods: Bootstrapping, Permutation
- NON IID: (AKA Surrogate data)
Monte Carlo Methods
- Expectation Values
- Integrals
Hypothesis Testing
- Parametric Tests
- T, F, Chi2, Binomial, etc
- Non-Parametric Tests
- Ranksum/Signrank
- Permutation-testing
- Composing p-values
Inference: Non-parametric:
- Static Relation metrics: Corr, Spr, MI
- Dynamic Relation metrics:
- Complexity (PI)
- Stationary (CrossCorr, GC)
- Semi-Stationary (TE)
- Information Theory
- Bulk Metrics: H, TC
- Higher order relations: MMI, PID, AIS
- Graph-Theoretic metrics: Degree, CC, etc.
- Time series analysis:
- Stationarity testing
- Frequency analysis
- Phase-space methods
- Dim. Red. in space and time simultaneously
- Taken's embedding
Inference: Parametric
- Classification: Logit, Cross-Entropy
- Regression: Linear, Logistic, GLM
- Time series analysis
- AR/VAR/MAR, MA, ARMA
- Forecasting
- Model selection
- ROC/AUC
- Cross-validation
- Model Selection Criteria: AIC, BIC, BMS(Bayes factors)
- Regularization
- L1, L2
- Generative Models
Dimensionality Reduction:
- PCA, FA, NMF, tSNE
- Autoencoders