ECE662Selecture zhenpengMLE - Rhea

1. Motivation

• Most likely converge as number of number of training sample increase.
• Simpler than alternate methods such as Bayesian technique.

2. Motivation

• Statistical Density Theory Context
  • Given c classes + some knowledge about features $ x \in \mathbb{R}^n $ (or some other space)
  • Given training data, $ x_j\sim\rho(x)=\sum\limits_{i=1}^n\rho(x|w_i) Prob(w_i) $, unknown class $ w_{ij} $ for $ x_j $ is know, $ \forall{j}=1,...,N $ (N hopefully large enough)
  • In order to make decision, we need to estimate $ \rho(x|w_i) $, $ Prob(w_i) $ $ \rightarrow $ use Bayes rule, or $ \rho(x|w_i) $ $ \rightarrow $ use Neyman-Pearson Criterion
  • To estimate the above two, use training data.

• The parametric pdf|Prob estimation problem
  • Let $ D={x_1,x_2,...,x_N} $, $ x_j $ is drown independently from some probability law.
  • Choose parametric from $ \rho(x|\theta) $ for the pdf of x or $ Prob(x|\theta) $ for the probability of x $ \rightarrow $ an unknown parametric vector
  • Use $ D $ to estimate $ \theta $

• The maximum likelihood estimate of $ \theta $ is the value $ \hat{\theta} $ that maximize

$ \rho_D(D|\theta) $, if x is continuous R.V., or $ Prob(D|\theta) $, if x is discrete R.V.

(create a question page and put a link below)

Questions and comments

If you have any questions, comments, etc. please post them on https://kiwi.ecn.purdue.edu/rhea/index.php/ECE662Selecture_ZHenpengMLE_Ques.

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