**What is sequential data?**

- Data with poor or no i.i.d assumption
- Often found in time series data. For instance,
- Rainfall measurements on successive days at a particular location
- Daily values of a currency exchange rate
- Acoustic features at successive time frames used for speech recognition)

**Stationary vs. nonstationary sequential distributions**

- Stationary: data evolves in time but the distribution from which it is generated remains the same
- Nonstationary: the generative distribution itself evolves with time

**Applications of Markov Models**

- Financial forecasting: predict the next value in a time series given observations of the previous values
- Speech recognition: predict the next speech spectrum given observations of the previous speech spectrum values
- Note: Markov models are useful in applications where more recent observations are more informative than less recent observations

Latent variable

- Hidden Markov model: where the latent variables are discrete
- Linear dynamical systems: where latent variables are Gaussian

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