Monte Carlo Methods
Monte Carlo methods use random sampling to approximate complex mathematical or physical systems. The principle is to generate a large number of random samples from a probability distribution and use these samples to estimate the properties of the distribution.
This process involves the following steps:
- Define the Problem: Identify the quantity to be estimated (e.g., an integral or a probability).
- Generate Random Samples: Use a random number generator to produce samples from the distribution of interest.
- Compute the Estimate: Calculate the desired quantity using the generated samples, often by averaging the results of the sampled data.
Estimating the value of π by randomly placing points in a square that encloses a quarter circle and calculating the ratio of points inside the quarter circle to the total number of points.
Approximate Inference in Bayesian Networks
Bayesian Networks (BNs) are powerful frameworks for modeling probabilistic relationships among variables. They are widely used in various fields such as artificial intelligence, bioinformatics, and decision analysis. However, exact inference in Bayesian Networks is often computationally impractical for large or complex networks due to the exponential growth of computational requirements. Approximate inference methods provide a feasible alternative, offering probabilistic estimates with significantly reduced computational costs.
This article explores the key concepts, methods, challenges, and applications of approximate inference in Bayesian Networks.
Table of Content
- Need for Approximate Inference
- Approximate Inference Techniques
- Monte Carlo Methods
- Variational Inference
- Loopy Belief Propagation
- Challenges in Approximate Inference
- Application Examples of Approximate Inference in Bayesian Networks
- Conclusion