Probabilistic Approach
A probabilistic approach provides a framework for reasoning under uncertainty. It begins with prior knowledge or assumptions about a problem and then updates those beliefs as new evidence becomes available. This idea is central to Bayesian inference, where probabilities are interpreted as degrees of belief that are revised through observed data.
Bayesian Inference and Networks
Inference:
The process of calculating the likelihood of outcomes or hidden variables given observed evidence. Bayesian inference combines prior probabilities with new data using Bayes’ theorem to reach updated conclusions.
These are graphical models that represent random variables as nodes and dependencies as directed edges. Such networks capture complex relationships between variables, allowing efficient reasoning in domains like medical diagnosis, fraud detection, and decision support systems.
Probabilistic Classifiers
Probabilistic methods are also widely used for classification tasks:
1. Prediction of Class Probabilities:
→Instead of giving only a single label, probabilistic classifiers estimate the likelihood of each possible class.
→This makes them useful in applications where confidence scores or risk assessment is required.
2. Efficiency with Large Data:
Many probabilistic classifiers, such as Naïve Bayes, are computationally efficient and scale well to massive datasets, offering both speed and reasonable accuracy.
3. Class Conditional Independence Assumption:
→The Naïve Bayes classifier relies on the assumption that features are conditionally independent given the class label.
→While this assumption is often simplified and not strictly true in practice, it still allows the method to perform surprisingly well in areas like text classification and spam filtering.
Assumptions of Bayesian Modelling
1. Prior Specification: Assumes that meaningful prior information about parameters can be expressed mathematically (informative or non-informative priors).
2. Model Structure is Correct: The likelihood function chosen must appropriately describe the data-generating process.
3. Independence Assumptions: In many Bayesian models (e.g., Naïve Bayes), features are assumed conditionally independent given the class.
4. Data Quality and Representativeness: Assumes observed data are accurate, relevant, and sampled from the population of interest.
5. Computational Feasibility: Assumes posterior distributions can be approximated or sampled effectively (via methods like MCMC or variational inference).
Advantages of Bayesian Modelling
1. Incorporates Prior Knowledge: Enables the use of expert knowledge, previous studies, or domain insights, especially valuable when data are limited.
2. Uncertainty Quantification: Provides full probability distributions for parameters and predictions, not just point estimates.
3. Flexible Framework: Can model complex structures (hierarchical models, latent variables, time-varying effects).
4. Handles Small Data Well: Priors help stabilize estimates when datasets are sparse.
5. Natural Model Updating: New data can be incorporated easily by updating priors to posteriors (sequential learning).
6. Robust Decision-Making: Posterior probabilities make risk assessment and decision-making under uncertainty more transparent.
Disadvantages of Bayesian Modelling
1. Choice of Prior: Results can be sensitive to the prior, especially with limited data. Selecting an appropriate prior can be subjective.
2. Computational Complexity: Exact inference is often infeasible for complex models; approximation methods like MCMC can be slow and resource-intensive.
3. Interpretation Challenges: For non-experts, understanding priors, posteriors, and credible intervals may be less intuitive than frequentist outputs.
4. Scalability Issues: Bayesian methods may struggle with very large datasets or high-dimensional models unless approximate techniques are used.
5. Model Misspecification Risk: If the likelihood function or prior is poorly chosen, results can be misleading.