Sequential data

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┬árecent observations

Latent variable

  • Hidden Markov┬ámodel: where the latent variables are discrete
  • Linear dynamical systems: where latent variables are Gaussian