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Lecture notes. Written from the material of MIT 6047, licensed CC BY-NC-SA 4.0. These are notes, not a transcript: the material has been reorganised and rewritten. This adaptation carries the same licence, and the original is linked above.

4. Recap: Markov Chains and HMMs

What this covers

This "chapter" is a recap slide, not a lecture: MIT 6.047's lecture 4 opens by listing, in four bullet groups, what the course had established by the end of the sequential-data / hidden Markov model unit that preceded it. It assumes the reader has already met Markov chains, hidden Markov models (HMMs), and the Viterbi algorithm elsewhere in the course — none of them is defined or re-derived here, only named. Nothing beyond this outline was supplied for this lecture: no transcript, no notes, no exercises, and the slide deck itself is a single recap slide plus one uncaptioned figure.

The recap, as given

The slide groups what had been covered into four points.

Modeling sequential data. The first task was recognizing that data comes as a sequence, and that sequences come in different types — the slide lists genomic, oral, verbal, and visual as examples of the kinds of sequence a model might need to distinguish.

Definitions. Two formal objects had been introduced: Markov chains and hidden Markov models (HMMs). The slide does not restate either definition here — they belong to the lecture(s) this one is recapping.

Examples of HMMs. The class of problems HMMs had been applied to, per the slide: recognizing GC-rich regions, preferentially-conserved elements, coding exons, protein-coding gene structures, and chromatin states. No detail on any one of these examples is given on this slide.

Our first computations. Three questions about an HMM had been posed, each stated as an input-to-output relation:

  • Running the model: given the model, generate a sequence of a given type.
  • Evaluation: given the model, its emissions, and its states, compute a probability.
  • Viterbi: named only — the slide does not say here what it computes or how.

Sources

  • Slide: computational-biology/mit-ocw/6047/lectures/04-slides.md ("What have we learned?"), the single content slide of lecture 4 (page 1 of the deck; the four bullet groups reproduced above are the entire text of the slide).
  • The deck also contains one figure, an uncaptioned portrait photograph extracted from page 8 of the source PDF, listed in the converted markdown without a caption or surrounding text tying it to a specific claim; it is not used above because nothing in the supplied material says what it illustrates.
  • No transcript, written notes, or exercises were supplied for this lecture.
  • The Markov chain and HMM definitions, and the HMM examples and computations this slide is recapping, were covered in an earlier lecture of this course that was not among the inputs to this chapter — this chapter does not reconstruct them, since they are not in the material given.

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