Advait Ramesh Iyer

I find unbiased and generalisable patterns, and effectively communicate insights to non-technical audiences.

Mathematics for Gradient Descent

less than 1 minute read

Assuming a linear model of the form $\hat{y}=b_{0}+b_{1}x$ and a dataset $[(x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3}),...,(x_{n},y_{n})]$ .

Using the following loss function:

$L(b_{0},b_{1})=\sum_{i=1}^{n}(\hat{y_{i}}-y_{i})^{2}+\lambda.b_{1}^{2}$ , where $\lambda>0$

the objective is to derive the best values by solving the following set of equations:

$dL/db_{0}=0$
$dL/db_{1}=0$

Solution

Twitter Facebook Google+ LinkedIn

You May Also Enjoy

Dynamic newsvendor model for Optimistic and Pessimistic policy-based profit forecasting

Abstract

Primer for Linear Algebra

Character Recognition: Can Machine Learning Identify Human Written Characters?

Despite the rise of personal computers and smartphones, many people and businesses are dependant on hand written notes. For many people, written notes are fa...

Analysis of co-purchased products on Amazon

Large sized graphs are difficult to visualize, as they are computationally very expensive to plot. In such cases, we have to rely on algorithms which help us...