Hidden Markov Model (HMM)

How Hidden Markov Models Work

An HMM consists of several key components that work together to model sequential data:

• Hidden States: These are the unobservable states of the system that the model tries to infer. For example, in weather forecasting, the hidden states might be "Sunny," "Cloudy," or "Rainy."
• Observable Outputs (Emissions): These are the visible data points that each hidden state can produce. Following the weather example, observations could be "High Temperature," "Low Temperature," or "High Humidity."
• Transition Probabilities: These probabilities govern the likelihood of moving from one hidden state to another. For example, there is a certain probability that a "Sunny" day will be followed by a "Cloudy" day.
• Emission Probabilities: These probabilities represent the likelihood of observing a particular output given that the system is in a specific hidden state. For instance, the probability of observing "High Humidity" is likely higher if the hidden state is "Rainy."

To make predictions, HMMs use established algorithms. The Viterbi algorithm is commonly used to find the most likely sequence of hidden states given a sequence of observations. To train the model and learn its probability distributions from training data, the Baum-Welch algorithm is often employed.

Real-World Applications

HMMs have been successfully applied in various domains for decades. Here are a couple of prominent examples:

1. Speech Recognition: In classic speech recognition systems, HMMs were instrumental. The hidden states correspond to phonemes (the basic units of sound in a language), and the observable outputs are acoustic features extracted from recorded speech. The HMM's task is to determine the most likely sequence of phonemes from the audio signal, which is then used to identify the spoken words.
2. Bioinformatics: HMMs are a cornerstone of computational biology, particularly for gene finding. In this context, hidden states might represent parts of a gene, like "exon" (coding region) or "intron" (non-coding region), while the observations are the sequence of DNA bases (A, C, G, T). By analyzing a long DNA sequence, an HMM can identify the most probable locations of genes. The National Center for Biotechnology Information (NCBI) details these methods.

Comparison with Related Concepts

It's important to distinguish HMMs from other sequence models:

• Markov Decision Processes (MDPs): While both involve states and transitions, MDPs assume states are fully observable and focus on decision-making (finding optimal actions) within the framework of Reinforcement Learning (RL). HMMs focus on inferring hidden states from observations. Resources like DeepMind's introductory materials cover RL and MDPs.
• Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTMs): These are Deep Learning (DL) models also designed for sequential data. Unlike HMMs' explicit probabilistic states, RNNs/LSTMs maintain an internal hidden state vector that evolves implicitly as they process sequences. They can capture more complex and longer-range dependencies, often achieving higher accuracy on tasks like machine translation and advanced speech recognition. Understanding LSTMs provides a good overview. Modern vision models like Ultralytics YOLO use DL architectures, often built with frameworks like PyTorch or TensorFlow, for tasks like object detection and instance segmentation.

While newer deep learning methods often achieve state-of-the-art results, HMMs remain valuable for their interpretability (explicit states and probabilities) and effectiveness, especially when training data is limited or domain knowledge can be incorporated into the model structure. Understanding foundational concepts like HMMs provides valuable context in the broader ML landscape, even when using platforms like Ultralytics HUB which primarily facilitate the development and deployment of DL models like YOLOv8 or YOLO11.