Understanding the “hidden” story in time-series data
Many real-world datasets are sequential: sensor readings over time, user actions in an app, words in a sentence, or price movements in a market. In these settings, the observations you record are often driven by underlying conditions that you cannot directly see. For instance, a machine’s vibration signal may look noisy, but the machine could be switching between hidden health conditions such as “normal,” “wearing,” and “near failure.” The key question becomes: given a sequence of observations, what is the most likely sequence of hidden states that produced them?
This is where Hidden Markov Models (HMMs) and the Viterbi algorithm become practical tools. If you are exploring sequence modelling concepts as part of an AI course in Delhi, HMM decoding is one of the clearest examples of how probabilistic assumptions translate into a reliable, production-friendly algorithm.
Hidden Markov Models in simple terms
An HMM is a probabilistic model for sequences with two layers:
- Hidden states (latent states): the unobserved conditions that evolve over time (e.g., “calm vs stressed,” “bull vs bear,” “healthy vs degraded”).
- Observations: the data you actually measure (e.g., heart rate, stock returns, vibration features, words).
An HMM is built on two core assumptions:
- Markov property for states: the next hidden state depends only on the current hidden state (not the entire past).
- Conditional independence for observations: each observation depends only on the current hidden state.
To specify an HMM, you typically define:
- Initial state probabilities: how likely each state is at time step 1.
- Transition probabilities: how likely it is to move from one state to another.
- Emission probabilities: how likely each observation is under each state.
With these, the model can be used for three common tasks:
- Evaluation: how likely is an observation sequence under the model?
- Decoding: what hidden state sequence best explains the observations?
- Learning: how do we estimate the probabilities from data?
This article focuses on decoding—specifically, the Viterbi algorithm.
Why Viterbi decoding matters (and why “greedy” fails)
A tempting approach is to label each time step with the most likely state for that observation alone. That is usually wrong because it ignores transitions. A state might explain a single observation well, but switching into it may be unlikely given the prior state. Decoding needs to balance:
- how well states explain observations (emissions), and
- how plausible state changes are (transitions).
The Viterbi algorithm solves this by finding the single most probable hidden-state path across the full sequence. It is a dynamic programming method, meaning it breaks the problem into smaller subproblems and reuses computed results.
The Viterbi algorithm: how it works in practice
At a high level, Viterbi keeps track of the best path to each state at each time step.
For time step t and state j, it computes:
- the best score of any path that ends in j at time t, and
- a pointer to the previous state that achieved that best score.
This requires:
- Initialisation: compute starting scores using initial probabilities and emissions.
- Recursion: for each time step and state, pick the best previous state and update the score.
- Termination: choose the final state with the best score.
- Backtracking: follow the stored pointers backward to recover the full hidden-state sequence.
In real implementations, probabilities can become extremely small when multiplied over long sequences, leading to numerical underflow. A standard fix is to work in log space, converting multiplications into additions. This also makes the method more stable and easier to debug.
Complexity-wise, Viterbi is typically O(T × N²) where:
- T = number of time steps,
- N = number of hidden states.
This is efficient enough for many practical systems, especially when N is moderate (for example, 5–50 states). If you are practising sequence modelling in an AI course in Delhi, Viterbi is a good bridge between theory and deployable engineering because it is deterministic, explainable, and fast.
Applications: finding latent regimes and improving downstream decisions
Viterbi-based decoding appears in many domains because “hidden states” are a natural way to describe changing conditions.
1) NLP tagging and sequence labelling
Classic examples include part-of-speech tagging and shallow parsing, where words are observed and grammatical tags are hidden. Transitions capture linguistic structure (some tags tend to follow others), while emissions capture how likely a word is given a tag.
2) Speech and audio segmentation
Speech signals vary by phoneme, silence, or noise conditions. Decoding can identify the most likely sequence of hidden acoustic states, which can be helpful for segmentation or feature alignment.
3) Predictive maintenance and IoT monitoring
Sensors may reflect different machine states—stable operation, mild anomaly, severe anomaly. Viterbi decoding can provide a clean state timeline that is easier to interpret than raw anomaly scores.
4) Finance and demand regimes
Markets often shift between regimes (low volatility vs high volatility). Retail demand can switch between “baseline,” “promotion-driven,” and “stockout.” Decoding provides a regime sequence that can guide forecasting models, pricing rules, or alerts.
A practical benefit is that decoded state sequences can support smooth data generation and simulation: once you have a plausible state path (or state transition structure), you can sample observations conditioned on those states to create realistic synthetic sequences for testing pipelines, monitoring dashboards, or scenario analysis.
Conclusion
Hidden Markov Models help you represent temporal data where observations are driven by unobserved conditions. The Viterbi algorithm is the standard tool for decoding: it finds the most likely hidden-state sequence for an entire observation timeline, balancing emission fit with transition plausibility. With stable implementation techniques like log probabilities and backpointers, Viterbi becomes a reliable method for building interpretable state timelines across NLP, speech, sensors, and regime detection. For learners taking an AI course in Delhi, HMM decoding is a valuable topic because it shows how probabilistic modelling leads directly to efficient, real-world decision logic.