Databricks-Certified-Professional-Data-Scientist Exam Dumps : Databricks Certified Professional Data Scientist Exam

Given two random variables X and Y whose joint distribution is known, the marginal distribution of X is simply the probability distribution of X averaging over information about Y. It is the probability distribution of X when the value of Y is not known. This is typically calculated by summing or integrating the joint probability distribution over Y. '

For discrete random variables, the marginal probability mass function can be written as Pr(X = x). This is

Text Description automatically generated with low confidence

where Pr(X = x,Y = y) is the joint distribution of X and Y, while Pr(X = x|Y = y) is the conditional distribution of X given Y In this case, the variable Y has been marginalized out.

Bivariate marginal and joint probabilities for discrete random variables are often displayed as two-way tables.

Similarly for continuous random variables, the marginal probability density function

can be written as pX(x). This is

Diagram Description automatically generated with medium confidence

where pX.Y(x.y) gives the joint distribution of X and Y while pX|Y(x|y) gives the

conditional distribution for X given Y Again: the variable Y has been marginalized

out.

Note that a marginal probability can always be written as an expected value:

Text, letter Description automatically generated

Intuitively, the marginal probability of X is computed by examining the conditional probability of X given a particular value of Y, and then averaging this conditional probability over the distribution of all values of Y This follows from the definition of expected value, i.e. in general

A picture containing diagram Description automatically generated

Regularization is a very important technique in machine learning to prevent overfitting. Mathematically speaking, it adds a regularization term in order to prevent the coefficients to fit so perfectly to overfit. The difference between the L1 and L2 is just that L2 is the sum of the square of the weights, while L1 is just the sum of the weights. As follows: L1 regularization on least squares:

A picture containing text Description automatically generated