Activation Function _ day 11

Activation Functions in Neural Networks Activation Functions in Neural Networks: Why They Matter ? Activation functions are pivotal in neural networks, transforming the input of each neuron to its output signal, thus determining the neuron’s activation level. This process allows neural networks to handle tasks such as image recognition and language processing effectively. The Role of Different Activation Functions Neural networks employ distinct activation functions in their inner and outer layers, customized to the specific requirements of the network: Inner Layers: Functions like ReLU (Rectified Linear Unit) introduce necessary non-linearity, allowing the network to learn complex patterns in the data. Without these functions, neural networks would not be able to model anything beyond simple linear relationships. Outer Layers: Depending on the task, different functions are used. For example, a softmax function is used for multiclass classification to convert the logits to probabilities that sum to one, which are essential for classification tasks. Practical Application Understanding the distinction and application of different activation functions is crucial for designing networks that perform efficiently across various tasks. Neural Network Configuration Example Building a Neural Network for Image Classification This example demonstrates setting up a neural network in Python using TensorFlow/Keras, designed to classify...

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12

Regression vs Classification Multi Layer Perceptrons (MLPs) _ day 10

Regression with Multi-Layer Perceptrons (MLPs) Introduction Neural networks, particularly Multi-Layer Perceptrons (MLPs), are essential tools in machine learning for solving both regression and classification problems. This guide will provide a detailed explanation of MLPs, covering their structure, activation functions, and implementation using Scikit-Learn. Regression vs. Classification: Key Differences Regression Objective: Predict continuous values. Output: Single or multiple continuous values. Example: Predicting house prices, stock prices, or temperature. Classification Objective: Predict discrete class labels. Output: Class probabilities or specific class labels. Example: Classifying emails as spam or not spam, recognizing handwritten digits, or identifying types of animals in images. Regression with MLPs MLPs can be utilized for regression tasks, predicting continuous outcomes. Let’s walk through the implementation using the California housing dataset. Activation Functions in Regression MLPs In regression tasks, MLPs typically use non-linear activation functions like ReLU in the hidden layers to capture complex patterns in the data. The output layer may use a linear activation function to predict continuous values. Fetching and Preparing the Data from sklearn.datasets import fetch_california_housing from sklearn.model_selection import train_test_split # Load the California housing dataset housing = fetch_california_housing() # Split the data into training, validation, and test sets X_train_full, X_test, y_train_full, y_test = train_test_split(housing.data, housing.target,...

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38

3 Types of Gradient Decent Types : Batch, Stochastic & Mini-Batch _ Day 8

Understanding Gradient Descent: Batch, Stochastic, and Mini-Batch Understanding Gradient Descent: Batch, Stochastic, and Mini-Batch Learn the key differences between Batch Gradient Descent, Stochastic Gradient Descent, and Mini-Batch Gradient Descent, and how to apply them in your machine learning models. Batch Gradient Descent Batch Gradient Descent uses the entire dataset to calculate the gradient of the cost function, leading to stable, consistent steps toward an optimal solution. It is computationally expensive, making it suitable for smaller datasets where high precision is crucial. Formula: \[\theta := \theta – \eta \cdot \frac{1}{m} \sum_{i=1}^{m} \nabla_{\theta} J(\theta; x^{(i)}, y^{(i)})\] \(\theta\) = parameters \(\eta\) = learning rate \(m\) = number of training examples \(\nabla_{\theta} J(\theta; x^{(i)}, y^{(i)})\) = gradient of the cost function Stochastic Gradient Descent (SGD) Stochastic Gradient Descent updates parameters using each training example individually. This method can quickly adapt to new patterns, potentially escaping local minima more effectively than Batch Gradient Descent. It is particularly useful for large datasets and online learning environments. Formula: \[\theta := \theta – \eta \cdot \nabla_{\theta} J(\theta; x^{(i)}, y^{(i)})\] \(\theta\) = parameters \(\eta\) = learning rate \(\nabla_{\theta} J(\theta; x^{(i)}, y^{(i)})\) = gradient of the cost function for a single training example Mini-Batch Gradient Descent Mini-Batch Gradient Descent is...

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16

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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23

Regression & Classification with MNIST. _ day 4

  A Comprehensive Guide to Machine Learning: Regression and Classification with the MNIST Dataset Introduction to Supervised Learning: Regression and Classification In the realm of machine learning, supervised learning involves training a model on a labeled dataset, which means the dataset includes both input data and the corresponding output labels. Supervised learning tasks can be broadly categorized into two types: regression and classification.     Regression tasks aim to predict continuous numerical values. For example, predicting house prices based on various features such as location, size, and number of bedrooms. The output is a continuous value that can range over an infinite set of possible values. Common regression algorithms include linear regression, decision trees, and support vector regression.     Classification, on the other hand, deals with predicting discrete categorical values. The goal is to assign input data to one of several predefined classes. For instance, classifying emails as either spam or not spam, or recognizing handwritten digits as one of the digits from 0 to 9. The output is a discrete value representing the class label. Popular classification algorithms include logistic regression, support vector machines, decision trees, and neural networks. The MNIST Dataset: A Benchmark for Classification The MNIST...

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