Skip to main content

 Bayesian Learning: Inference & 

EM Algorithm Explained

Bayesian learning updates beliefs using Bayes' theorem, refining models with new data. Inference estimates hidden variables, while the Expectation-Maximization (EM) algorithm iteratively finds maximum likelihood estimates for models with latent variables. EM alternates between expectation (E-step) and maximization (M-step) to improve parameter estimates until convergence, making it powerful for probabilistic learning.

Bayesian Learning & Inference

Bayesian learning is a statistical approach that updates probabilities as more evidence (data) becomes available. It relies on Bayes' Theorem:

P(θ∣D)=P(D∣θ)P(θ)P(D)P(\theta | D) = \frac{P(D | \theta) P(\theta)}{P(D)}

where:

  • P(θ∣D)P(\theta | D) is the posterior probability of parameters θ\theta given data DD.
  • P(D∣θ)P(D | \theta) is the likelihood (probability of data given parameters).
  • P(θ)P(\theta) is the prior belief about parameters.
  • P(D)P(D) is the evidence (normalizing constant).

Bayesian inference refines parameter estimates using this principle, making it effective for probabilistic modeling.

Expectation-Maximization (EM) Algorithm

The EM algorithm is used when data has latent (hidden) variables, making direct estimation difficult. It iterates between two steps:

  1. Expectation (E-step): Computes expected values of hidden variables based on current parameter estimates.
  2. Maximization (M-step): Updates parameters to maximize the expected likelihood.

This process continues until convergence, refining model parameters iteratively. EM is widely used in clustering (e.g., Gaussian Mixture Models), missing data problems, and probabilistic learning.

International Research Awards on Network Science and Graph Analytics

🔗 Nominate now! 👉 https://networkscience-conferences.researchw.com/award-nomination/?ecategory=Awards&rcategory=Awardee

🌐 Visit: networkscience-conferences.researchw.com/awards/
📩 Contact: networkquery@researchw.com

Get Connected Here:
*****************

Instagram: https://www.instagram.com/network_science_awards
Whatsapp : https://whatsapp.com/channel/0029Vb4g03T9WtC76K5xcm3r
Tumblr: https://www.tumblr.com/emileyvaruni
Pinterest: https://in.pinterest.com/network_science_awards/
Blogger: https://networkscienceawards.blogspot.com/
Twitter: https://x.com/netgraph_awards
YouTube: https://www.youtube.com/@network_science_awards

#sciencefather #researchw #researchawards #NetworkScience #GraphAnalytics #ResearchAwards #InnovationInScience #TechResearch #DataScience #GraphTheory #ScientificExcellence #AIandNetworkScience   #BayesianLearning #MachineLearning #Probability #StatisticalInference #BayesTheorem #ExpectationMaximization #EMAlgorithm #DataScience #AI #HiddenVariables #ProbabilisticModeling #LikelihoodEstimation #MLAlgorithms #UnsupervisedLearning

Comments

Post a Comment

Popular posts from this blog

Global Lighthouse Network

Smart, sustainable manufacturing: 3 lessons from the Global Lighthouse Network Launched in 2018, when more than 70% of factories struggled to scale digital transformation beyond isolated pilots, the Global Lighthouse Network set out to identify the world’s most advanced production sites and create a shared learning journey to up-level the global manufacturing community. In the past seven years, the network has grown from 16 to 201 industrial sites in more than 30 countries and 35 sectors, including the latest cohort of 13 new sites. This growing community of organizations is setting new standards for operational excellence, leveraging advanced technologies to drive growth, productivity, resilience and environmental sustainability. But what exactly is a Global Lighthouse and what has the network achieved? What is the Global Lighthouse Network? The Global Lighthouse Network is a community of operational facilities and value chains that harness digital technologies at scale to ac...
Post a Comment
Read more

Multi-Modal Data

Multi-Task Federated Split Learning Across Multi-Modal Data with Privacy Preservation With the advancement of federated learning (FL), there is a growing demand for schemes that support multi-task learning on multi-modal data while ensuring robust privacy protection, especially in applications like intelligent connected vehicles. Traditional FL schemes often struggle with the complexities introduced by multi-modal data and diverse task requirements, such as increased communication overhead and computational burdens. In this paper, we propose a novel privacy-preserving scheme for multi-task federated split learning across multi-modal data (MTFSLaMM). Our approach leverages the principles of split learning to partition models between clients and servers, employing a modular design that reduces computational demands on resource-constrained clients. To ensure data privacy, we integrate differential privacy to protect intermediate data and employ homomorphic encryption to safeguard client m...
Post a Comment
Read more
 How Network Polarization Shapes Our Politics! Network polarization amplifies political divisions by clustering like-minded individuals into echo chambers, where opposing views are rarely encountered. This reinforces biases, reduces dialogue, and deepens ideological rifts. Social media algorithms further intensify this divide, shaping public opinion and influencing political behavior in increasingly polarized and fragmented societies. Network polarization refers to the phenomenon where social networks—both offline and online—become ideologically homogenous, clustering individuals with similar political beliefs together. This segregation leads to the formation of echo chambers , where people are primarily exposed to information that reinforces their existing views and are shielded from opposing perspectives. In political contexts, such polarization has profound consequences: Reinforcement of Biases : When individuals only interact with like-minded peers, their existing beliefs bec...
Post a Comment
Read more