Advanced Statistics Quiz 10 – Pattern Recognition

Today’s lesson would be based on pattern recognition. How well can you explain the concepts of in Pattern Recognition. Lets see.


Question 1: What do you understand by Sufficient Statistic?
If a sample is taken and we obtain the sample mean m and the standard deviation s, then this two parameters are sufficient statistics if all the information contained in the data can be summarized  by just these statistics.

This is based on the assumption that the data follows a multivariate normal distribution.


Question 2: Why are Maximum Likelihood Estimates Preferable
MLE are preferable due to a set of asymptotic properties which includes:

  • Consistency
  • Asymptotic Nomality
  • Efficiency


Question 3: What is Consistency, Asymptotic Normality and Efficiency?
Consistency: This means that the estimator converges in probability the the value that is being estimated
Asymptotic Normality: This means that the estimator has a normal distribution with functionally known variance and standard deviation
Efficiency: This means that the estimator has a low mean squared error.


Question 4: What is Linear Discriminant Analysis
LDA is a statistical procedure that seeks to reduce the dimensionality of the data while preserving as much of the class discriminatory information as possible.


Question 5: What are Limitations of LDA?
LDA is a parametric method, which means that it assumes unimodal Gaussian likelihoods. For Gaussian distributions, LDA projections may not preserve complex structure in the data.
LDA produces at mos C-1 feature projections
LDA will also fail if the discriminatory information is in the variance of the data instead of the mean


Question 6: Wilk’s Lambda Test
The Wilk’s Lamdba Test is a statistical test to find out which variables contribute significantly in the discriminant function. The closer the Wilk’s lambda is to 0, the more the variable contributes to the discriminant function.

Try to digest these ones for now and thanks for reading. Wishing you success in your quiz!