Principal Component Analysis (PCA) is a statistical technique used for dimensionality reduction, which simplifies the complexity in high-dimensional data while retaining important infomation. The basic idea of this method is to transform a large set… Introduction to Principal Component Analysis (PCA) and implementation in R and Python
Here, we denote by the event NOT . Example 1: Magical Investment Returns In the magical forest, gnomes invest in enchanted acorns, which sometimes turn into golden trees. A gnome named Glim invests in an… Bayes theorem in finance of a magical forest
Here, we denote by the event NOT . Example 1: Squirrel Flu Testing In a forest, a group of squirrels is concerned about a new illness called “Squirrel Flu.” It’s more dangerous than the ordinary… Conditional probability for medical testing in a forest
First, it’s easier to understand & remember the keys properties of multivariate normal distribution by understanding the Mahalanobis distance. So, to start, recall that the Mahalanobis distance is a measure of the distance between a… Tricks for remembering formulas & properties of multivariate normal distribution
Understanding the relationship between derivatives and antiderivatives can significantly help in remembering and applying the rules for finding antiderivatives (also known as integrals). Here’s how this relationship aids in comprehension and recall: 1. Fundamental Theorem… Tricks for remembering integral rules
Mutually exclusive events are events that cannot occur at the same time. In other words, the occurrence of one event excludes the occurrence of the other. Here are some examples:
A permutation refers to the arrangement of objects in a specific order. The order of arrangement is important in permutation. A permutation let us know how many different ways a set or number of things… Permutation
The exponential distribution is commonly used to model the time between events in a Poisson process. It is defined by a single parameter, , which is the rate parameter. The probability density function (PDF) of… Examples of Exponential distribution
The chain rule is a fundamental technique in calculus for finding the derivative of a composite function. Here are some examples that illustrate its use: Example 1: Simple Composite Function Let’s find the derivative of… Finding the derivative of a composite function with chain rule
Here are a few more examples of limit computations involving various techniques: Example 1: Basic Limit Find the limit: Solution: This is a basic limit where we can directly substitute : Example 2: Limit Involving… examples of limit computations
A function in mathematics and computer science is a relation between a set of inputs and a set of permissible outputs. It assigns each input exactly one output. Functions can be simple or complex, depending… Mathematical functions
Dimension reduction methods like Principal Component Analysis (PCA) or Singular Value Decomposition (SVD) can be used for denoising data because they work by retaining the most important features (or dimensions) that capture the majority of… denoising via dimension reduction in python
Missing At Random (MAR) imputation methods are based on the assumption that the chance of missing data is not related to the missing data itself, but might be related to some of the observed data.… why we can & probably should use missing at random imputation methods for data that’s not missing at random?
Why missing data occurs can be attributed to various reasons, including human error, malfunctioning equipment, or even intentional omission. It is important to handle missing data because it can significantly impact the reliability and accuracy… Missing data analysis: where’s your missing piece?
SoftImpute is a matrix completion algorithm in Python that allows you to fill in missing data in your dataset. This method is based on Singular Value Decomposition (SVD) and Iterative Soft Thresholding. Here’s a basic… Imputation using SoftImpute in python
MICE (Multiple Imputation by Chained Equations) is a statistical method used for handling missing data by creating multiple imputations or “guesses” for the missing values. It works by using a set of regression models to… Multiple Imputation with Chained Equations method & Python codes
K-Nearest Neighbors (KNN) imputation is another method to handle missing data. It uses the ‘k’ closest instances (rows) to each instance that contains any missing values to fill in those values. In sklearn, you can… K-Nearest Neighbors (KNN) imputation in sklearn
Handling missing data is a common preprocessing task in machine learning. In scikit-learn, you can handle missing data by using imputation techniques provided by the SimpleImputer class or by employing other strategies like dropping rows/columns with missing… A comic guide to mean/median/mode imputation & Python codes
Singular Value Decomposition (SVD) is a powerful matrix decomposition technique that generalizes the concept of eigenvalue decomposition to non-square matrices. Eigenvalue decomposition specifically decomposes a square matrix into its constituent eigenvalues and eigenvectors. This decomposition… SVD for dimension reduction
To test for outliers in multivariate data in Python, you can use several libraries like numpy, scipy, pandas, sklearn, etc. Here’s how you can do it: Mahalanobis distance using Scipy library The Mahalanobis distance is a statistical measure used… test for outliers in multivariate data in Python
Example 1: Spam Detection Let’s say historically, 20% of emails are spam, so and the probability that the email is not spam is . Suppose the probability of observing the word “free” in a spam… Application of Bayesian theorem in spam detection & medical diagnosis