A Hidden Markov Model (HMM) is a statistical model used to understand systems where underlying processes are not directly visible. It helps infer these unobservable, or “hidden,” internal states from a sequence of observable events. HMMs are designed to handle data that unfolds sequentially, allowing for insights into patterns and structures within such data. These models are a powerful tool for predicting event outcomes based on observable patterns, even when direct causes remain concealed.
The Markov Foundation
The “Markov” component of an HMM refers to a Markov Chain, a mathematical system where the probability of the next event depends solely on the current state, not on the entire history of preceding events. This characteristic is known as the “memoryless” property. In a Markov Chain, “states” represent different situations or conditions, and “transition probabilities” define the likelihood of moving from one state to another.
Imagine modeling daily weather changes with states like “sunny,” “cloudy,” or “rainy.” If today is sunny, there might be a 70% chance it stays sunny tomorrow and a 20% chance it becomes cloudy, with a 10% chance of rain. If it’s rainy, there might be an 80% chance it remains rainy and a 15% chance it becomes cloudy, with a 5% chance of sun. These percentages are the transition probabilities, determining the flow between states. This framework allows for predicting future states based only on the present weather condition.
The Hidden Element
The “hidden” aspect distinguishes an HMM from a simple Markov Chain, meaning the underlying states of the system cannot be directly observed. Instead, we observe outputs or emissions that are probabilistically linked to these hidden states. For instance, if you hear someone coughing, you might infer if they have a cold, the flu, or allergies, which are the hidden states. The cough itself is the observable event, providing clues about the unobservable condition.
HMMs work by determining the most probable sequence of these hidden states based on the sequence of observed events. This involves “emission probabilities,” which quantify the likelihood of observing a particular output given that the system is in a specific hidden state. For example, a hidden “cold” state might have a high emission probability for a “cough” observation, while a “flu” state might have a high emission probability for both “cough” and “fever” observations. These probabilities help the model connect the visible symptoms to their invisible causes.
How HMMs Connect the Dots
HMMs function by integrating state transitions with the likelihood of producing specific observations. The model utilizes both the transition probabilities, which govern movement between hidden states, and the emission probabilities, which link hidden states to observable outputs. This combination allows the HMM to calculate the probability of different hidden state sequences given a particular sequence of observed data. The core task for HMMs is to probabilistically infer the most likely underlying hidden sequence that generated the observed events.
To achieve this, HMMs employ algorithms like the Forward Algorithm to determine the probability of observing a given sequence of events. The Viterbi algorithm is used to find the single most likely sequence of hidden states that would produce a given observation sequence. These algorithms effectively “decode” the hidden processes by considering all possible paths through the hidden states and their corresponding emissions, ultimately identifying the sequence that best explains the observed data.
Where HMMs Shine
Hidden Markov Models are widely applied across various fields.
Speech Recognition
In speech recognition, HMMs have been instrumental in converting spoken words into text. Here, the hidden states represent phonemes, the basic units of sound, while the observable outputs are the acoustic features extracted from recorded speech. The model infers the sequence of phonemes to identify the spoken words.
Bioinformatics
In bioinformatics, HMMs are used for tasks like gene finding and protein sequence analysis. Hidden states might correspond to different regions within a gene, such as “exons” (coding regions) or “introns” (non-coding regions), with the observations being the sequence of DNA bases (A, C, G, T). This allows HMMs to identify the likely locations of genes within a long DNA sequence.
Natural Language Processing (NLP)
Natural Language Processing (NLP) also benefits from HMMs, particularly in part-of-speech tagging, where hidden states represent grammatical categories like nouns or verbs, and observations are the words themselves.