Activation Function, Hidden Layer and non linearity. _ day 12

Understanding Non-Linearity in Neural Networks Understanding Non-Linearity in Neural Networks Non-linearity in neural networks is essential for solving complex tasks where the data is not linearly separable. This blog post explains why hidden layers and non-linear activation functions are necessary, using the XOR problem as an example. What is Non-Linearity? Non-linearity in neural networks allows the model to learn and represent more complex patterns. In the context of decision boundaries, a non-linear decision boundary can bend and curve, enabling the separation of classes that are not linearly separable. Role of Activation Functions The primary role of an activation function is to introduce non-linearity into the neural network. Without non-linear activation functions, even networks with multiple layers would behave like a single-layer network, unable to learn complex patterns. Common non-linear activation functions include sigmoid, tanh, and ReLU. Role of Hidden Layers Hidden layers provide the network with additional capacity to learn complex patterns by applying a series of transformations to the input data. However, if these transformations are linear, the network will still be limited to linear decision boundaries. The combination of hidden layers and non-linear activation functions enables the network to learn non-linear relationships and form non-linear decision boundaries. Mathematical...

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59

What is Gradient Decent in Machine Learning? _ Day 7

Mastering Gradient Descent in Machine Learning Mastering Gradient Descent: A Comprehensive Guide to Optimizing Machine Learning Models Gradient Descent is a foundational optimization algorithm used in machine learning to minimize a model’s cost function, typically Mean Squared Error (MSE) in linear regression. By iteratively adjusting the model’s parameters (weights), Gradient Descent seeks to find the optimal values that reduce the prediction error. What is Gradient Descent? Gradient Descent works by calculating the gradient (slope) of the cost function with respect to each parameter and moving in the direction opposite to the gradient. This process is repeated until the algorithm converges to a minimum point, ideally the global minimum, where the cost function is minimized. Types of Learning Rates in Gradient Descent: Too Small Learning Rate Slow Convergence: A very small learning rate makes the algorithm take tiny steps toward the minimum, resulting in a long training process. High Precision: Useful when fine adjustments are needed to avoid overshooting the minimum, but impractical for large-scale problems due to time inefficiency. Too Large Learning Rate Risk of Divergence: A large learning rate can cause the algorithm to overshoot the minimum, leading to oscillations or divergence where the cost function increases instead of...

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26

Can we make prediction without need of going through iteration ? yes with the Normal Equation _ Day 6

Understanding Linear Regression: The Normal Equation and Matrix Multiplications Explained Understanding Linear Regression: The Normal Equation and Matrix Multiplications Explained Linear regression is a fundamental concept in machine learning and statistics, used to predict a target variable based on one or more input features. While gradient descent is a popular method for finding the best-fitting line, the normal equation offers a direct, analytical approach that doesn’t require iterations. This blog post will walk you through the normal equation step-by-step, explaining why and how it works, and why using matrices simplifies the process. Table of Contents Introduction to Linear Regression Gradient Descent vs. Normal Equation Step-by-Step Explanation of the Normal Equation Step 1: Add Column of Ones Step 2: Transpose of X (XT) Step 3: Matrix Multiplication (XTX) Step 4: Matrix Multiplication (XTy) Step 5: Inverse of XTX ((XTX)-1) Step 6: Final Multiplication to Get θ Why the Normal Equation Works Without Gradient Descent Advantages of Using Matrices Conclusion Introduction to Linear Regression Linear regression aims to fit a line to a dataset, predicting a target variable $y$ based on input features $x$. The model is defined as: $$ y = \theta_0 + \theta_1 x $$ For multiple features, it generalizes...

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