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Linear Regression - 5

Logistic Regression

Linear Regression Logistic Regression Different from previous linear regression, logistic regression output discreate value like 0 or 1. So logistic regression is a claasification algorithm. ...

Posted by William on December 1, 2018

Linear Regression - 4

regularization

Linear Regression ##

Posted by William on December 1, 2018

Linear Regression - 3

Hypothesis Testing on Regression

Basic Linear Regression

Posted by William on November 30, 2018

Linear Regression - 2

Evaluate the fittness of regression

Linear Regression $R^2$ - Evaluation from econometrics perspective SST - total sum of squares. It measures the total variation in the dependent variable. \[SST = \sum_{i=1}^n(y_i-\bar y)^2\] ...

Posted by William on November 30, 2018

PCA VaR (Value at Risk)

Principle Components Analysis in Market Risk

PCA VaR PCA - Principle Components Analysis Suppose we have a point $a = (x,y)$, it represents the linear combination under Orthonormal basis $e_1$, $e_2$. \[a = \left[\begin{matrix} x\\y \end...

Posted by William on November 26, 2018

Gradient Descent

Convex Optimization Basic

Gradient Descent Introduction Suppose $C(w)$ is the cost function and it’s convex which means it’s free of local minimum. Gradient Descent is a way to minimize $C(w)$. Fisrt, let’s define t...

Posted by William on November 25, 2018

Linear Regression - 1

Explain OLS from probability and econometrics

Linear Regression Definition Suppose $y$ is terget value vector, $X$ is input matrix. X has n samples and each sample has m features with 1 intercept. \[y = \left[\begin{matrix} y_1\\ y_2\\ .....

Posted by William on November 25, 2018