Many real-world systems produce sequences: daily stock movements, sensor readings from machines, user clicks on a website, or the sounds in spoken language. The challenge is that what we observe is often only a surface signal. The real “state” of the system, such as user intent, machine health, or a phoneme being spoken, is not directly visible. Hidden Markov Models (HMMs) are designed for exactly this situation. They model a process where the underlying state follows a Markov chain, but the states are hidden and can only be inferred from observations. If you are exploring sequential modelling in data science classes in Bangalore, HMMs remain a foundational method worth understanding because they introduce key ideas used in many modern sequence models.
What an HMM Is, in Plain Terms
An HMM assumes there is a sequence of hidden states (for example: “healthy” → “degrading” → “failed”), but you cannot see these states directly. Instead, you see observations generated by those states (for example: vibration levels, temperature spikes, or error counts). The model answers questions like:
- What hidden state sequence is most likely given the data?
- How likely is it that this sequence was generated by the model?
- What states and parameters best explain the observed patterns?
The “Markov” part means the next hidden state depends only on the current hidden state, not the entire past. This is the Markov property. That simple assumption makes complex sequence inference computationally tractable.
Core Components: States, Transitions, and Emissions
An HMM has three key building blocks.
1) Hidden states
These represent the unobserved conditions of the system. You define how many states you expect, often based on domain knowledge. For example:
- Customer journey states: browsing, comparing, purchasing
- Machine health states: normal, warning, critical
- Text tagging states: noun, verb, adjective (in basic NLP use cases)
2) Transition probabilities
Transitions capture how states evolve over time. This is a matrix where each cell represents the probability of moving from one state to another. For instance, a machine might have a high probability of staying “normal” day to day, and a small probability of shifting to “warning.” In many data science classes in Bangalore, learners practise interpreting these matrices because they encode the “dynamics” of the system.
3) Emission probabilities
Emissions connect hidden states to the observed data. Each hidden state has a probability distribution over observations:
- For discrete observations, this could be a probability table.
- For continuous observations, it is often a Gaussian distribution or a mixture of Gaussians.
Together, transitions explain how states change, and emissions explain how states produce data.
The Three Classic Problems HMMs Solve
HMMs are often taught through three canonical tasks, which also help you understand where HMMs fit in a data science pipeline.
1) Evaluation: How likely is the observed sequence?
Given a model (states, transitions, emissions) and an observation sequence, we compute the probability that the model produced that sequence. This is useful for scoring and anomaly detection.
2) Decoding: What is the most likely hidden state sequence?
This is the “labelling” problem: infer the most probable hidden states behind the observations. The Viterbi algorithm is commonly used here to find the best state path efficiently.
3) Learning: What model parameters best fit the data?
If you do not know transitions and emissions upfront, you estimate them from data. A standard method is the Baum–Welch algorithm (a special case of Expectation-Maximisation). Learning is especially valuable when you suspect hidden regimes exist, but you are unsure how they behave.
Where HMMs Are Used in Practice
Even though deep learning dominates many sequence tasks today, HMMs still show up in practical systems because they are interpretable, work with smaller datasets, and provide clear probabilistic outputs.
Common applications include:
- Speech recognition (traditional pipelines): mapping audio features to phoneme/state sequences
- Part-of-speech tagging: assigning grammatical labels to words in a sentence
- Finance and economics: identifying market regimes such as low-volatility vs high-volatility phases
- Predictive maintenance: estimating hidden machine health states from sensor signals
- Behaviour modelling: inferring user intent from clickstream sequences
In data science classes in Bangalore, HMMs are often used as a stepping stone to more advanced models like Conditional Random Fields (CRFs) or recurrent neural networks, because they teach structured thinking about sequences.
Strengths and Limitations You Should Know
HMMs are powerful, but they rely on assumptions. Understanding those assumptions helps you choose the right model.
Strengths
- Interpretable: transition and emission probabilities are easy to explain to stakeholders.
- Efficient: algorithms scale well for many practical sequence lengths.
- Works with limited data: can perform reasonably when deep models would overfit.
- Probabilistic foundation: provides confidence scores and likelihood-based comparisons.
Limitations
- Markov assumption: “next state depends only on current state” can be too simplistic for long-range patterns.
- Emission independence: observations are often assumed independent, given the hidden state, which may not hold in complex data.
- State design sensitivity: Choosing the number of hidden states can significantly affect performance.
A good rule: use HMMs when you need a transparent baseline, have limited data, or want an interpretable state-based explanation of sequential behaviour.
Conclusion
Hidden Markov Models are a principled way to model sequential systems where the true state is not directly observable. By combining a Markov chain of hidden states with emission distributions for observed data, HMMs help you evaluate sequences, decode likely state paths, and learn underlying dynamics from data. They remain a valuable concept because they teach the fundamentals of probabilistic sequence modelling in a clear, structured way. If you are building your foundation in sequential data analysis through data science classes in Bangalore, understanding HMMs will improve how you think about time-ordered patterns, uncertainty, and model interpretability.
