📐 Definitions (for clarity) Let errors be . MAE MSE RMSE 📐 Relationship Between and Let the errors be Then: Mean Absolute Error (MAE) Mean Squared Error (MSE) Key Relationship 1. Jensen’s Inequality gives: Why?… Relationship Between MAE, MSE, RMSE
Polynomial regression is a form of regression analysis where the relationship between the independent variable and the dependent variable is modeled as an degree polynomial. Polynomial regression fits a nonlinear relationship between the value of… Polynomial regression in Python
Choosing a boyfriend as a maximum likelihood problem can be framed as an exercise in probabilistic decision-making, where the goal is to maximize the likelihood of selecting a partner who best fits your desired criteria… Choosing a Boyfriend Explained: Dating as a Maximum Likelihood Problem with the EM Algorithm
Common distance measures in machine learning, their formulas, use cases, and detailed properties: 1. Euclidean Distance 2. Manhattan Distance (L1 Norm) 3. Minkowski Distance 4. Cosine Similarity 5. Hamming Distance 6. Jaccard Distance 7. Mahalanobis… Common distance measures in machine learning and their properties
The Expectation-Maximization (EM) algorithm is an iterative approach to estimate the parameters of probabilistic models, such as a Gaussian (normal) distribution, when the data is incomplete or has missing values. It alternates between two steps:… EM algorithm
Here are some more examples of MCAR (recall that Missing completely at random (MCAR) data occurs when the probability of missing data on a variable is independent of any other measured variables and the underlying… What’s missing completely at random data
The story of Kiko the overconfident student is a simple but accurate analogy for the concept of overfitting in machine learning and how cross-validation is used to prevent it. Here is a more technical breakdown… Overfitting, Cross validation: a story example of Kiko’s super secret
Forward feature selection with cross-validation incorporates cross-validation at each step to get a reliable estimate of how well a model with a particular set of features is likely to perform on unseen data. Without cross-validation,… A comparison between forward feature selection with cross-validation, forward selection guided by AIC/BIC, and Lasso regularization with Python Code
Explainable AI refers to methods and techniques that help humans understand and interpret the predictions and decisions made by machine learning (ML) models. It aims to open up the “black box” nature of complex models… Explainable AI (XAI) methods & Cheat Sheet
Polynomial regression is a form of regression analysis in which the relationship between the independent variable and the dependent variable is modeled as an nth degree polynomial. This approach allows for a more flexible fit… Enhancing Regression Models with Polynomial Features and L1 Lasso Regularization
Analyzing various data types and characteristics enhances model efficiency, aiding in pattern recognition and informed decisions. An example of building a Predictive Model for Customer Churn is provided to illustrate this idea.
Statistical Context: Projection and transformation matrices appear frequently in statistics, especially in regression and PCA, where they play a crucial role in simplifying complex datasets and revealing underlying patterns. These matrices help in miniminimizemizing errors… Key Roles of Transformation Matrices in Regression and PCA
Basic probability & statistics Optimization & Background for Machine Learning and Deep Learning Machine Learning Deep learning: Introductory courses Advanced: Programming courses Other: Google Cloud Machine Learning Crash Course:
Polynomial regression is a form of regression analysis in which the relationship between the independent variable and the dependent variable is modeled as an -degree polynomial. It’s an extension of linear regression that can capture… Understanding Polynomial Regression: A Comprehensive Comic Guide with codes
Random forests enhance predictive performance by allowing quantile predictions, offering insights into outcome variability. This method is vital for risk assessment, aiding informed decision-making in uncertain environments.
Support Vector Classifier (SVC) is a powerful algorithm for classification tasks, capable of handling linear and non-linear data using different kernel functions. It efficiently handles high-dimensional data for applications like image recognition and bioinformatics. Python and R codes demonstrate SVM usage for binary classification with breast cancer and mtcars datasets, respectively.
K-Means Clustering is a popular unsupervised machine learning algorithm used for clustering data into groups. It is widely used in various fields such as image processing, market segmentation, and document clustering. The algorithm works by… K-Means Clustering Method & Python Codes
Logistic regression with L1 or L2 penalty adds regularization to prevent overfitting and improve model generalization. L1 penalty (Lasso) encourages sparsity in the model, making it suitable for datasets with many irrelevant features. L2 penalty (Ridge) retains all features with reduced importance. Python and R codes demonstrate implementation and evaluation of these regression techniques.
Classification organizes items based on criteria. In data, it involves sorting into categories. It’s manual or automated with algorithms. Used in science, business, and technology to analyze and predict based on data. Crucial in document categorization, image recognition, sentiment analysis, and spam filtering for efficient data organization and analysis.
The coefficient of determination, or R-squared, measures how well an independent variable explains the variability of a dependent variable in a regression model. Its limitation lies in the fact that it does not decrease when a new feature is added, whether useful or not. Adjusted R-squared is an improvement, considering the number of predictors in a model, making it more reliable for assessing explanatory power.
Feature selection involves identifying and including essential variables in the model, possibly leading to improved performance and interpretability. Adjusted R-squared is a common metric for regression analysis, addressing overfitting by penalizing unnecessary variables and offering an accurate model representation.
The coefficient of determination (R-squared) measures how well a model explains the variance of the response variable. In this example, Python and R are used to calculate R-squared for linear regression. Higher R-squared value and the plot indicate a good fit, demonstrating the effectiveness of the model.
This content provides an example of simulating and detecting heteroscedasticity in data using Python. We simulate the data, fit the model, and analyze how to detect heteroscedasticity, and how to address this using a log transformation.
Multiple linear regression is a powerful tool for modeling relationships between multiple independent variables and a single dependent variable. Let’s take a look at some examples with codes in Python and R to demonstrate its practical application
Maximum Likelihood Estimation (MLE) is a statistical method that estimates parameters by maximizing the likelihood function. For example, in a Poisson distribution, the MLE for the rate parameter ? is the sample mean. And here is the detailed derivation
Forward selection adds features one by one, optimizing model performance but potentially missing the best subset. Backward selection starts with all features and removes the least significant, refining the model but being more computationally intensive. Stepwise selection combines both methods, adding or removing features for a balanced approach but can be complex.
implementing Lasso regression with train-validation-test split and finding the optimal regularization parameter. In Python, it involves splitting the data, training Lasso model with different alpha values, finding the best alpha, retraining the model, and evaluating on the test set. In R, it includes data splitting, training Lasso models, finding the best lambda, retraining, and testing.
The training-validation-test split involves using the training set to fit the model, the validation set to tune hyperparameters, and the test set to evaluate performance. Python’s scikit-learn library can be used for this process, ensuring the model generalizes well to new data by evaluating it on unseen data and avoiding overfitting.
Underfitting in machine learning occurs when a model fails to capture underlying data patterns due to simplicity or insufficient training data. To address underfitting, select complex models, add features, and obtain more training data. Also, fine-tune hyperparameters and optimize the model’s architecture. Few features in a model can also cause underfitting, requiring the identification of relevant additional features or more advanced modeling techniques.
This comic explains MSE and MAE, the commonly used evaluation metrics for regression. MSE emphasizes large deviations, while MAE provides a more robust measure when outliers are less significant. MSE is preferred as a loss function due to its ability to penalize larger errors more heavily and its suitability for mathematical optimization, stability, and statistical interpretation. RMSE is the square root of MSE and also penalizes large errors.
Machine learning parameters are values learned from training data to minimize prediction errors. For example, in a uniform distribution for bus arrival times, parameters $latex a$ and $latex b$ define the range. They are the model’s knobs for accurate predictions.
Unsupervised learning is a type of machine learning algorithm used to draw inferences from datasets consisting of input data without labeled responses. In unsupervised learning, the goal is to infer the natural structure present within… Unsupervised learning helps detect shady people