Why Viterbi is efficient for tasks like speech recognition, POS tagging, genomic analysis?

Why Viterbi algorithm is efficient for NLP tasks?

Decoding problem:

Decoding is the task of inferring the hidden (unobserved) state sequence that best explains a sequence of observable events.

Given an HMM λ = (A, B, π) and an observation sequence O = o₁, o₂, …, o_T, how do we choose the corresponding optimal hidden state sequence (most likely sequence) Q = q₁, q₂, …, q_T that can best explain the observations.

Viterbi algorithm:

You need the Viterbi algorithm whenever you have a decoding problem in a Hidden Markov Model—that is, when you need to infer the most likely sequence of hidden states from a sequence of observations. More specifically, the algorithm is essential when you face problems where hidden states influence observable data, but you only have access to the observations and need to determine what the hidden states were.

The Viterbi algorithm is a dynamic‑programming method that finds the most probable sequence of hidden states (a path) that could have produced a given observation sequence in a Hidden Markov Model (HMM).

Why Viterbi algorithm?

The Viterbi algorithm is the go-to solution for decoding because it combines efficiency with exactness. Without dynamic programming, you'd need to evaluate all possible state sequences—with N states and T observations, that's N^T paths to explore, which becomes exponentially expensive. The Viterbi algorithm reduces this to O(N²T) complexity by storing only the best path to each state at each time step, making it practical even for long sequences.

Example:

For:

• N = 100 hidden states

• T = 1000 observations

Time complexity (without dynamic programming):

O(1001000) operations 

Time complexity (with dynamic programming):

O(100² × 1000) = 10,000,000 operations

This is why Viterbi is efficient enough for speech recognition, POS tagging, genomic analysis, and NLP tasks.