probability density
A probability density function describes the distribution of a continuous random variable. If is continuous, its PDF is a function such that: The key idea For continuous variables: The PDF is not a probability. Probability…
probability mass function
A probability mass function is a function that gives the probability of each individual value of a discrete random variable. If is a discrete random variable, then its PMF is: It tells you: A PMF…
Types of random variables
Most random variables fall into two big categories: Everything else is a refinement of these two. 🎯 1. Discrete Random Variables A discrete random variable takes countable values — usually integers. Key features Examples Common…
independent vs mutually exclusive
Independent vs. Mutually Exclusive 🎯 Mutually Exclusive (Disjoint) Events Two events are mutually exclusive if they cannot happen at the same time. Example:Rolling a die: 🎯 Independent Events Two events are independent if knowing one…
general addition rule
⭐ General Addition Rule The general addition rule tells you how to find the probability that A or B happens — even when the events overlap. 📌 The formula Why subtract the intersection?Because if A…
Independent event
⭐ Independent Events Two events are independent when one happening does not change the probability of the other. That’s the whole heart of it. 📌 Formal definition Events and are independent if This equation is…
Complementary events
⭐ Complementary Events Two events are complements when they cover the entire sample space together and cannot happen at the same time. If is an event, then its complement is: 📌 Key properties 🎯 Examples…
Sample and Event
⭐ Sample vs. Event Think of probability as a story with two levels: 🎯 Sample Space (S) The sample space is the complete list of everything that could happen in an experiment. Examples Key idea…
Downsampling Techniques for Custom Batches in training Machine Learning Models
Downsampling techniques can be used to create custom batches for training a machine learning model. These custom batches can be tailored to specific needs, such as improving training efficiency, handling imbalanced data, or focusing on…
downsampling for hyperparameter tuning
Downsampling for hyperparameter tuning reduces the dataset size to speed up model training and experimentation while preserving key data characteristics. Here’s a concise overview: Why Downsample for Hyperparameter Tuning? Key Considerations Practical Steps Pitfalls to…
How to reduce catastrophic forgetting when fine-tuning neural networks
Catastrophic forgetting occurs when a neural network “overwrites” what it learned in a previous task while training on a new one. This happens because the weights optimized for the first task are changed to minimize…
Textbooks Are All You Need
The central idea of the paper “Textbooks Are All You Need” is that data quality is significantly more important than data quantity or model size when training large language models (LLMs), particularly for code generation.…
The “Speed” Myth of sloths
Baby sloths are born with their eyes open, all their teeth, and the ability to climb immediately.
Sloth’s Extreme Digestion & Bathroom Habits
Extreme Digestion & Bathroom Habits A Walking Ecosystem
Geckos’ amazing feet
Geckos are arguably the most charismatic and bizarre family in the reptile world. They are the only lizards that can vocalize, many can climb glass, and some have superpowers that seem pulled straight from a…
Iguanas’ third eye
Here are some fun and fascinating facts about iguanas, ranging from their superhero-like senses to their quirky survival habits. They Have a “Third Eye” One of the weirdest facts about iguanas is that they have…
Komodo dragons with stinky breath
Komodo dragons are the closest thing we have to real-life dinosaurs. They are the heaviest lizards on Earth, but their size is just the beginning of what makes them interesting. Here are the most fascinating…
What’s Cache Augmented Generation (CAG)
Cache Augmented Generation (CAG) is an architecture for Large Language Models (LLMs) that removes the need for real-time data retrieval by pre-loading a knowledge base directly into the model’s active memory. In practical terms, while…
Relationship Between MAE, MSE, RMSE
📐 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?…
Similarity Metrics for MR Image-to-Image Translation
The major conclusion of the paper Similarity Metrics for MR Image-to-Image Translation is that relying on the most commonly used metrics, specifically SSIM and PSNR, is insufficient for validating Magnetic Resonance (MR) image-to-image translation models…
Polynomial regression in Python
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…
Why is contrastive learning?
Contrastive learning is a technique used in machine learning, particularly in the field of self-supervised and unsupervised learning. It focuses on learning to distinguish between similar and dissimilar pairs of data points by contrasting them…
Choosing a Boyfriend Explained: Dating as a Maximum Likelihood Problem with the EM Algorithm
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…
An overview of explainable AI techniques
Explainable AI (XAI) techniques are methods and processes used to make AI models and their predictions understandable to humans. These techniques are critical for building trust, ensuring ethical use, and meeting regulatory requirements in AI…
Common distance measures in machine learning and their properties
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…