What is HiddenMarkovModels?

A Hidden Markov Model (HMM) is a mathematical tool that helps us guess a sequence of hidden (unseen) states by looking at a sequence of visible observations. It assumes that the system moves from one hidden state to another in a chain, and each hidden state produces an observable output with a certain probability.

Let's break it down

  • Hidden: The true condition we want to know (like a weather condition) isn’t directly visible.
  • Markov: The next hidden state depends only on the current state, not on how we got there (memory-less property).
  • Model: A set of equations and probabilities that describe how hidden states generate observable data.
  • Sequence of observations: The data we can actually see (e.g., words spoken, sensor readings).
  • Guessing hidden states: Using the observed data and the model to infer the most likely hidden sequence.

Why does it matter?

HMMs let us make sense of noisy or incomplete data by uncovering the underlying patterns that aren’t directly observable. This ability to infer hidden information is crucial in many fields where direct measurement is impossible or expensive.

Where is it used?

  • Speech recognition: Turning audio waves into words by modeling phoneme sequences.
  • Bioinformatics: Predicting gene regions or protein structures from DNA/RNA sequences.
  • Finance: Detecting market regimes (bull vs. bear) from price movements.
  • Activity monitoring: Recognizing human activities (walking, running) from wearable sensor data.

Good things about it

  • Simple and well-understood mathematics make it easy to implement.
  • Works well with relatively small amounts of training data.
  • Provides a clear probabilistic framework for handling uncertainty.
  • Can be extended (e.g., with Gaussian emissions) to model continuous observations.
  • Efficient algorithms (Viterbi, Baum-Welch) exist for inference and learning.

Not-so-good things

  • Assumes the Markov property, which may be too restrictive for complex dependencies.
  • Requires the number of hidden states to be chosen beforehand, which can be hard to set correctly.
  • Can struggle with very long sequences or high-dimensional observations without modifications.
  • Training can get stuck in local optima, leading to sub-optimal models.