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  "body": "\n## Summary\n\nThe Baum–Welch algorithm estimates the parameters of a [[hidden Markov model|HJVM390354]] from a sequence of observations alone.\nIt is the [[expectation–maximization algorithm|11N1AXSXYK]] for this model.\nIt alternates between computing the expected hidden path under the current parameters and re-estimating the parameters from those expectations.\nThe expectations are computed efficiently by the forward–backward recursions.\nIt is a standard tool in speech recognition and in biological sequence analysis.\n\n## Explanations\n\n### L1 human\n\nImagine a machine that switches between hidden moods and emits visible symbols, with each mood favouring different symbols.\nYou see only the symbols and want to learn how often the moods switch and what each mood emits.\nBaum–Welch starts from a guess, works out for each time how likely each mood was, and then updates the guess using these soft counts.\nRepeating this never lowers the likelihood of the observed data.\nWith only one mood, a single step gives the observed frequencies of the symbols.\n",
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