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+---
+title: "Optimization in Machine Learning"
+description: "Essentials of gradient descent as an optimization technique for regression and classification tasks."
+keywords: "optimization, cost function, Machine learning,learning rate, gradient descent, Batch Gradient Descent, Stochastic Gradient Descent, Mini Batch Gradient Descen, Coordinate Descent"
+date:
+weight: 6
+author: "Kheiry Sohooli"
+authorlink: "https://tilburgsciencehub.com/contributors/kheirysohooli"
+---
+
+## Overview
+
+When training a machine learning model, we use an optimization approach to minimize a cost function. Gradient descent serves as a crucial optimization method for optimizing weights in cost functions during regression and classification tasks. This article aims to provide insights into selecting the best optimization algorithm and pairing it with the appropriate loss function when training a machine learning model.
+
+It is highly recommended to review the [Cost and Loss Functions article](https://tilburgsciencehub.com/topics/analyze/machine-learning/supervised/ml_objective_functions/) before reading this article.
+
+## Optimization
+In the context of machine learning and mathematics, optimization involves finding the best possible solution or configuration for a given problem. This often includes minimizing or maximizing an objective function by adjusting the parameters or variables of a model or system. Feel free to explore more by reading [this paper](https://coral.ise.lehigh.edu/frankecurtis/files/papers/BottCurtNoce18.pdf). In mathematics, various optimization algorithms exist. One of the most common methods, particularly in machine learning, is known as `Gradient Descent`(GD).
+
+## Gradient descent algorithm in simple language
+
+Imagine you're trying to predict house prices based on their sizes. You have a dataset with the sizes of houses $x(i)$ and their corresponding prices $y(i)$. You want to build a model that can accurately predict house prices based on their sizes.
+
+Equation 1 represents the hypothesis function $h_\theta(x)$, which predicts the house price ($y$) based on its size ($x$). In this case, $\theta_0$ is the intercept term (representing the base price of a house) and $\theta_1$ is the coefficient that represents how much the price of a house increases per unit increase in size.
+
+
+{{}}
+h_\theta(x) = \theta_1x + \theta_0
+{{}}
+ :Equation1
+
+
+Now, let's consider Equation 2, which represents the cost function $J(\theta_0, \theta_1)$. This function calculates the difference between the predicted house prices ($h_\theta(x)$) and the actual prices ($y$), squared and averaged over all the data points. The goal of gradient descent is to minimize this cost function by adjusting the parameters $\theta_0$ and $\theta_1$.
+
+
+{{}}
+J(\theta_1, \theta_0) = \left[ \frac{1}{2m} \sum_{i=1}^{m} (y(i) - h_\theta(x(i)))^2 \right]
+{{}}
+ :Equation 2
+
+
+
+
+
+{{}}
+
+\theta_j := \theta_j - \alpha \frac{\sigma J(\theta_0, \theta_1)}{\sigma \theta_j}
+\\{for}\ j=0\ \text{and}\ j=1
+{{}}
+
+
+When optimizing your machine learning algorithm, it's crucial to consider the learning rate, denoted here as $\alpha$. It controls the size of the steps taken during optimization. Let's say we start with $\alpha = 0.01$.
+
+In each iteration, the algorithm computes the partial derivatives of the cost function with respect to $\theta_0$ and $\theta_1$, scales them by $\alpha$, and updates the parameters accordingly. This process continues until the cost function converges to a minimum.
+
+However, choosing the right learning rate is crucial. If the learning rate is too large, the algorithm may overshoot the minimum and fail to converge. Conversely, if it's too small, the algorithm may take too long to converge.
+
+Let's say we experiment with different learning rates: $\alpha = 0.1$, $\alpha = 0.01$, and $\alpha = 0.001$. We visualize their effects on the convergence of the cost function in the graph.
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