Machine Learning Concepts and Types

Hypothesis Class

• A hypothesis class represents the set of all possible functions that a learning algorithm can output
• It defines the space of potential solutions to the learning problem
• Examples include linear models, decision trees, neural networks

Types of Regression

• A supervised learning technique used for predicting continuous target variables
• Linear Regression: Assumes a linear relationship between the independent and dependent variables
• Logistic Regression: Predicts the probability of a binary outcome (0 or 1)
• Polynomial Regression: Uses a polynomial function to fit the data, allowing for more complex relationships
• Ridge Regression: Utilizes L2 regularization to prevent overfitting
• Lasso Regression: Employs L1 regularization to perform feature selection by shrinking coefficients of irrelevant features to zero

Types of Machine Learning Techniques

• Supervised Learning: Trains on labeled data to make predictions on unseen data
  • Regression: Predicts continuous values (e.g., price, temperature)
  • Classification: Predicts categorical values (e.g., spam or not spam, cat or dog)
• Unsupervised Learning: Discovers patterns in unlabeled data
  • Clustering: Groups data points into clusters based on similarity (e.g., customer segmentation)
  • Dimensionality Reduction: Reduces the complexity of data by extracting essential features
• Reinforcement Learning: Trains an agent to learn optimal actions by interacting with an environment
  • Trial and Error: Agent learns through rewards and punishments for its actions
  • Applications: Robotics, game playing

Roles of Vectors and Matrices in ML

• Vectors: Represent data points as ordered lists of numbers
  • Facilitates mathematical operations on data
  • Enables efficient storage and retrieval of data
• Matrices: Store and manipulate multi-dimensional data
  • Representing data sets: Rows - instances, Columns - features
  • Linear transformations: Matrix multiplication allows for feature scaling and rotation
  • Solving linear equations: Essential in gradient descent and other optimization algorithms

Mean, Mode, and Median

• Mean: The average of a set of numbers
• Mode: The most frequent value in a set of numbers
• Median: The middle value of a sorted dataset
• Examples:
  • List of natural numbers: Mean, mode, and median can be calculated directly
  • List of random numbers: Mean, mode, and median may not be representative of the dataset due to randomness

Statistical Measures for Evaluating ML Performance

• Accuracy: Proportion of correct predictions
• Precision: Proportion of correctly predicted positive instances out of all predicted positive instances
• Recall: Proportion of correctly predicted positive instances out of all actual positive instances
• F1-score: Harmonic mean of precision and recall
• Specificity: Proportion of correctly predicted negative instances out of all actual negative instances
• Example: In a spam detection system, high precision means a low rate of false positive emails being classified as spam, while high recall means a low rate of actual spam emails not being detected.

Representations of Input Data Sets

• Tabular Data: Data organized in rows and columns (e.g., CSV files)
• Text Data: Unstructured data like documents, emails, and social media posts
• Image Data: Pixel values representing images
• Audio Data: Sound waves converted into numerical data
• Time Series Data: Data collected over time, often with a temporal dependency

Null Hypothesis and Alternative Hypothesis

• Null hypothesis (H0): A statement that there is no relationship between variables or no difference between groups
• Alternative hypothesis (H1): A statement that there is a relationship or difference
• Example: In a medical study, H0: The new drug does not improve patient outcomes. H1: The new drug improves patient outcomes.

Supervised and Unsupervised Learning

• Supervised Learning: Trains a model on labeled data, with the goal of making predictions on new data.
  • Regression aims to predict continuous values (e.g., house prices), while classification predicts categorical values (e.g., spam or not spam).
• Unsupervised Learning: Discovers patterns in unlabeled data without any prior knowledge.
  • Clustering groups similar data points together (e.g., customer segmentation) while dimensionality reduction simplifies data by extracting essential features.

Reinforcement Learning

• An agent learns to perform an action in an environment to maximize rewards.
• The agent learns by trial and error, receiving rewards for desirable actions and punishments for undesirable actions.
• Examples include playing games, controlling robots, and optimizing resource allocation.

Working Procedure of a ML System

1. Data Collection and Preparation: Gather, cleanse, and prepare data for training.
2. Model Selection and Training: Choose a suitable model (e.g., linear regression, decision tree) and train it on the data.
3. Model Evaluation: Assess the performance of the trained model using metrics like accuracy, precision, and recall.
4. Model Deployment: Deploy the trained model to make predictions on new data.
5. Model Monitoring and Maintenance: Continuously monitor and update the model to maintain its performance.

Statistical Concepts in ML

• Probability: A measure of the likelihood of an event occurring.
• Distributions: Mathematical functions describing the distribution of data (e.g., normal distribution).
• Hypothesis Testing: Used to determine if there is enough evidence to reject the null hypothesis.
• Statistical Significance: A measure of the likelihood that the observed results are due to chance.
• Confidence Intervals: A range of values that is likely to contain the true population parameter.
• Bayesian Statistics: A framework for updating beliefs in the face of new evidence.

Exploratory Data Analysis

• Analyzing and visualizing data to gain insights and understand its characteristics.
• Examples:
  • Histograms: Show the distribution of a single variable.
  • Scatter plots: Investigate the relationship between two variables.
  • Box plots: Show the distribution of data in terms of quartiles.
  • Correlation matrix: Visualize the relationships between multiple variables.
  • Pair plots: Display scatter plots for all pairs of variables in a dataset.

Mathematical Operations in Vectors and Matrices

• Vector addition: Add corresponding elements of two vectors.
• Vector subtraction: Subtract corresponding elements of two vectors.
• Scalar multiplication: Multiply each element of a vector by a scalar.
• Matrix addition: Add corresponding elements of two matrices.
• Matrix subtraction: Subtract corresponding elements of two matrices.
• Scalar multiplication: Multiply each element of a matrix by a scalar.
• Matrix multiplication: Requires specific dimensions, multiplying rows of the first matrix by columns of the second matrix.
• Transpose: Switch rows and columns of a matrix.
• Inverse: Multiplied by the original matrix results in the identity matrix (only for square matrices).
• Determinant: A scalar value representing the "scaling factor" of a linear transformation.

### Imbalanced Data

• Datasets where one class has significantly more samples than other classes.
• It can bias model training and lead to poor performance on the minority class.
• Strategies to balance datasets:
  • Oversampling: Duplicating instances of the minority class.
  • Undersampling: Removing instances of the majority class.
  • Synthetic Minority Oversampling Technique (SMOTE): Creating synthetic instances of the minority class.
  • Cost-sensitive learning: Weighing the cost of misclassifying minority class instances higher.

Multi-class Classification

• Classifying instances into more than two classes.
• Methods:
  • One-vs-rest: Training separate binary classifiers for each class, comparing the probability scores.
  • One-vs-one: Training a binary classifier for each pair of classes.
  • Softmax Regression: A generalization of logistic regression for multi-class classification, where the predictions are probabilities for each class.
  • Example: Identifying different flower species (Iris setosa, Iris versicolor, Iris virginica).

Confusion Matrix and Performance Metrics

• Confusion Matrix: A table summarizing the classification performance by showing the number of correct and incorrect predictions for each class.
• True Positives (TP): Correctly predicted positive instances.
• True Negatives (TN): Correctly predicted negative instances.
• False Positives (FP): Incorrectly predicted positive instances (Type I error).
• False Negatives (FN): Incorrectly predicted negative instances (Type II error).
• Example: A spam detection system correctly identifies 100 spam emails and also correctly identifies 200 non-spam emails. But it also misidentifies 10 non-spam emails as spam (FP) and wrongly identifies 5 spam emails as non-spam (FN).

Probably Approximately Correct (PAC) Learning

• A formal framework for analyzing the learnability of concepts.
• A concept is considered PAC learnable if there exists an algorithm that can learn a hypothesis that is close to the true concept with high probability.
• Key factors:
  • Sample complexity: The number of training examples required.
  • Computational complexity: Time and resources required to learn the concept.
  • Error tolerance: The maximum allowed error between the learned hypothesis and the true concept.

### Comparison

• L1 regularization vs L2 regularization:
  • L1 (Lasso): Promotes sparsity by shrinking coefficients of irrelevant features to exactly zero.
  • L2 (Ridge): Penalizes large coefficients, shrinking them towards zero but rarely reaching zero.
• Binary classifier vs Multi-class classifier:
  • Binary classifier: Distinguishes between two classes (e.g., spam or not spam).
  • Multi-class classifier: Differentiates between more than two classes (e.g., cat, dog, bird).
• Overfitting vs Underfitting:
  • Overfitting: A model learns the training data too well, resulting in poor generalization to unseen data.
  • Underfitting: A model fails to capture the underlying patterns in the data and performs poorly on both training and testing data.
• Feature selection vs Feature extraction:
  • Feature selection: Choosing a subset of the original features.
  • Feature Extraction: Transforming the original features into a new set of features.
• Dependence vs Independence event:
  • Dependent events: The outcome of one event influences the outcome of another event.
  • Independent events: The outcome of one event does not influence the outcome of another event.

Definitions

• Conditional probability: The probability of an event occurring given that another event has already occurred.
• Bias: Refers to the difference between the average prediction of a model and the true value.
• Variance: Measures the variability of the model's predictions for different training sets.
• Teacher noise: Errors or inconsistencies in the labels of the training data.
• L1 norm: The sum of the absolute values of a vector's elements.
• L2 norm: The square root of the sum of squares of a vector's elements.