Artificial Intelligence Theory and Application

 In Gradient Descent - Is the Gradient (Slope) a vector and related question Question 1: Is the Gradient a Vector? Yes, absolutely.  In multi-dimensional space, the gradient is a vector with both  magnitude  and  direction . The Gradient Vector For a function f(w₁, w₂, ..., wₙ), the gradient is: ┌ ∂f/∂w₁ ┐ │ ∂f/∂w₂ │ ∇f = │ ⋮ │ └ ∂f/∂wₙ ┘ Each component tells you: "How much does the loss change if I nudge this particular weight?" Direction and Magnitude Property Meaning Direction Points toward steepest  ascent  (we move opposite for descent) Magnitude How steep the slope is (larger = steeper terrain) Question 2: One Shot or One-at-a-Time? One shot — all dimensions simultaneously. This is crucial: standard gradient descent updates ALL parameters together in a single step, not sequentially. Concrete Example: 2D Landscape Consider a simple loss function with two weights: L(w₁, w₂) = w₁² + 4w₂² This creates an elliptical bow...

  1. RMS Prop Math 2. Momentum Math

ML — Machine Learning How do we handle data? 1. Don't jump straight to Neural Networks or Deep Learning! 2. How to split data into Training, Validation and Test data (parts) 3. What is Data Leak 4. What is Forward Propagation and Backward Propagation? 5. Dropout in Neural Networks This applies to both the Methods: Non-Neural Network Methods — Traditional ML algorithms (e.g., SVM, Random Forest, Logistic Regression, KNN, Naive Bayes) Neural Network Methods (Deep Learning) — Multi-layered networks that learn complex patterns Important Note: Don't jump straight to Neural Networks or Deep Learning! Always check first if the problem can be solved using traditional machine learning models. Neural networks are powerful but come with added complexity, longer training times, and require more data. Use Neural Networks when: You have large amounts of data The problem involves images, audio, video, or text Traditional methods aren't giving good results The patterns are hig...

KNN (K-Nearest Neighbors) is primarily a classification algorithm, though it can also be used for regression. How KNN Classification works: Choose a value for K (number of neighbors to consider) For a new data point, find the K closest points in the training data (using distance measures like Euclidean distance) Assign the class based on majority voting among those K neighbors Example: If K=5 and 3 of the 5 nearest neighbors are "Cat" and 2 are "Dog," the new point is classified as "Cat." Key characteristics: Lazy learner — it doesn't build a model during training; it just stores the data and does all the work at prediction time Non-parametric — makes no assumptions about the underlying data distribution Instance-based — uses actual training instances to make predictions KNN for Regression: When used for regression, instead of voting, it takes the average (or weighted average) of the K neighbors' values to predict a continuous...

  Quiz: Underfitting, Overfitting, Bias & Variance Questions Q1. A model performs poorly on both training data and test data. What is this called? A) Overfitting B) Underfitting C) High variance D) Good generalization Q2. A model achieves 99% accuracy on training data but only 60% on test data. What problem does this indicate? A) Underfitting B) Overfitting C) High bias D) Low variance Q3. Which of the following best describes bias in machine learning? A) Random fluctuations in model predictions B) Systematic error from oversimplified model assumptions C) Error caused by noisy data D) Difference between training and test accuracy Q4. High variance in a model means: A) The model is too simple B) The model's predictions are stable across different training sets C) The model is overly sensitive to the training data D) The model has high bias Q5. A linear regression model is used to fit a highly nonlinear dataset. This will likely result in: ...

 https://www.geeksforgeeks.org/machine-learning/underfitting-and-overfitting-in-machine-learning/ Machine learning models aim to perform well on both training data and new, unseen data and is considered "good" if: It learns patterns effectively from the training data. It generalizes well to new, unseen data. It avoids memorizing the training data (overfitting) or failing to capture relevant patterns (underfitting). To evaluate how well a model learns and generalizes, we monitor its performance on both the training data and a separate validation or test dataset which is often measured by its  accuracy  or  prediction errors . However, achieving this balance  can be challenging . Two common issues that affect a model's performance and generalization ability are  overfitting  and  underfitting . These problems are major contributors to poor performance in machine learning models. Let's us understand what they are and how they contribute to ML mo...