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MLE vs. MAP — worked example
- The article discusses the concepts of Maximum Likelihood Estimation (MLE) and Maximum A Posteriori (MAP) through a worked example.
- It explains likelihood as the probability of observing the data given a hypothesis, and how hypotheses are chosen based on data in MLE.
- In the coin toss example, MLE is applied to find the probability of observing specific outcomes in a series of tosses under different parameters.
- The article delves into the Bayesian perspective, introducing the posterior probability derived from Bayes Theorem, incorporating prior beliefs along with empirical data for hypothesis estimation.
- Under MAP, the most probable hypothesis is determined by considering the prior beliefs and the likelihood of the data, leading to the MAP estimate.
- The relationship between the strength of prior beliefs, data size, and the influence on the posterior probability is highlighted, emphasizing the impact on the final estimates.
- MAP is further discussed in relation to neural networks, where the concept is applied to finding optimal weights for maximum likelihood estimation.
- The article also touches on regularization techniques like L1 and L2 regularization as a way of incorporating prior distributions in MLE/MAP frameworks in neural networks.
- Overall, the article provides insights into the practical application of MLE and MAP in different scenarios, emphasizing the balance between data-driven estimates and prior beliefs.
- The importance of understanding these concepts for data science and neural network optimization is underscored, making it essential knowledge for aspiring data scientists.
- The discussion includes examples of applying these concepts to coin tossing scenarios and neural network weight optimization, illustrating the versatility and relevance of MLE and MAP.
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