#pearsoncorrelation

The Pearson correlation coefficient measures the strength and direction of a linear relationship between two variables by comparing how they vary together relative to their individual variability. Its value ranges from negative one to positive one [-1, 1], where values close to the extremes indicate strong linear correlation and values near zero indicate weak or no linear relationship. In machine learning and AI, Pearson correlation is often used for feature analysis, helping identify which inputs are strongly related to a target or redundant with each other. Squaring this value gives the coefficient of determination, commonly called R squared, which represents the proportion of variance in the target that can be explained by a linear model, making it a key metric for evaluating regression algorithms. C: 3 minute data science Join our AI community for more posts like this @aibutsimple 🤖 #machinelearning #deeplearning #statistics #computerscience #coding #mathematics #math #physics #science #education Want to Learn Deep Learning? Join 7000+ Others in our Visually Explained Deep Learning Newsletter—learn industry knowledge with easy-to-read issues complete with math and visuals. It's completely FREE (link in bio 🔗).

The Secret to Understanding Correlation Coefficients #statistics #math #datascience #correlation #Manim Master the Pearson Correlation Coefficient in seconds! This video breaks down the complex world of statistics by visualizing how 'r' values change across different scatter plots. From strong positive correlations (+0.95) to strong negative correlations (-0.95), you will see exactly how data points align with the line of best fit.

The Central Limit Theorem (CLT) is a foundational statistical principle stating that the distribution made from sampling independent, identically distributed random variables will converge to a normal distribution as the sample size increases, regardless of the original population’s distribution. We can visualize this using the ball and peg example in the video. As we draw random variables (the ball’s final position), we notice that they slowly, over time, converge to a more and more normal-looking distribution. In machine learning, the CLT provides a theoretical foundation for many common practices and techniques. For instance, in model evaluation, the CLT allows us to construct confidence intervals around performance metrics like accuracy. By repeatedly sampling from a test set and calculating the mean accuracy, the distribution of these means will be approximately normal, enabling us to estimate the true performance of the model on unseen data and quantify the uncertainty of this estimate. This is crucial for A/B testing and determining if the observed difference in performance between two models is statistically significant. C: 3blue1brown #deeplearning #statistics #mathematics #math #physics #computerscience #coding #science #education #machinelearning #datascience

Linear regression is a simple and elegant machine learning algorithm used to model relationships between variables by fitting a straight line, or more generally a linear function, to data. It works by adjusting two or more parameters, such as weights and a bias term, to minimize the sum of squared errors between the model’s predictions and the actual target values. This squared-error objective makes the optimization mathematically tractable and leads to stable, efficient solutions. Because of its clear assumptions, straightforward training, and easily interpretable parameters, linear regression remains widely used as both a practical baseline model and a foundational concept in machine learning. C: 3 minute data science

Ever wondered how machines find patterns in data? 🤖 Pearson Correlation is one of the most fundamental tools in a data scientist's toolkit — it tells you how strongly two variables move together, and in which direction. From picking the right features to spotting multicollinearity, mastering this concept can seriously level up your ML game. And always remember — just because two things correlate doesn't mean one causes the other. ⚠️ Save this for your next data science project! 💾 #KoshurAI #MachineLearning #DataScience #PearsonCorrelation #Statistics

Principal Component Analysis (PCA) is a dimensionality reduction technique for simplifying data by projecting it onto a smaller set of orthogonal directions called principal components. These components capture the maximum possible variance in the data, meaning they preserve the most important patterns while discarding noise and redundancy. By keeping only the top components, high-dimensional data can be compressed into a lower-dimensional representation with minimal information loss. Follow for more @infusewithai C: deepia #machinelearning #deeplearning #statistics #computerscience #coding #mathematics #math #physics #science #education

Strong correlation can mislead you In AI and machine learning, Pearson correlation only measures linear movement between variables. It tells you how tightly two numbers rise or fall together. An r close to 1 feels powerful. An r near 0 feels useless. But r only sees straight lines. Anything curved, delayed, or hidden in interaction quietly disappears. That is why r² can look impressive while the real story stays invisible. Comment WAIT if this surprised you. C: 3 Minute Data Science #ai #datascience #builders

why not linear regression #machinelearning #datascience #statistics #mathematics #maths

Neural networks are best understood as powerful function approximators. They are given input data and the corresponding outputs, even when the true underlying rule connecting them is unknown. Their task is to capture and represent that hidden relationship as accurately as possible. Rather than writing a precise mathematical formula by hand, we let the network discover the pattern on its own. During training, it continuously adjusts internal parameters known as weights and biases, reducing the gap between its predictions and the correct answers. With enough examples, it gradually learns the mapping from inputs to outputs. This is why neural networks shine in areas where data is abundant but clear formulas are not. Whether it is recognizing images, understanding language, or classifying information, they excel in situations where patterns exist but are too complex to define explicitly.

The math behind PCA is pure linear algebra. 📐🧠 Principal Component Analysis works by re-expressing data in a new coordinate system where the axes are chosen mathematically, not intuitively. First, the data is mean-centered so variance is measured correctly. Next, PCA computes the covariance matrix, which captures how features vary together. From there, PCA performs an eigenvalue decomposition (or Singular Value Decomposition) to find: • Eigenvectors → the principal directions • Eigenvalues → how much variance each direction explains Projecting the data onto the top-k eigenvectors is just a matrix multiplication, producing a lower-dimensional representation that minimizes reconstruction error in the least-squares sense. Nothing heuristic. Nothing learned. Just geometry, projections, and optimal variance preservation. This is why PCA is foundational to machine learning, statistics, and numerical methods. Credit: deepia Follow @deeprag.ai for math-driven explanations behind modern AI. . . . . . . #PCA #LinearAlgebra #Eigenvectors #Eigenvalues #MatrixDecomposition SVD MathBehindAI MachineLearningMath Statistics DataScience DimensionalityReduction MLTheory STEM

Neural networks work as powerful tools for approximating functions when the true relationship between inputs and outputs is unknown. Rather than being programmed with a fixed formula, they are given examples of input and output data and learn to capture the hidden patterns that connect them. Their goal is to represent the underlying relationship within the data, even when the exact function cannot be written mathematically. During training, the network continuously adjusts its internal parameters, called weights and biases, to reduce the difference between its predictions and the correct results. By learning from many examples, it gradually improves its accuracy and builds a mapping from inputs to outputs. This is why neural networks are especially useful in areas like image recognition, natural language processing, and classification tasks, where large amounts of data exist but clear analytical models do not. Follow @datascience.swat for more daily videos like this Shared under fair use for commentary and inspiration. No copyright infringement intended. If you are the copyright holder and would prefer this removed, please DM me. I will take it down respectfully. ©️ All rights remain with the original creator (s)

Principal Component Analysis (PCA) is an unsupervised machine learning technique used for dimensionality reduction while preserving as much variance as possible in a dataset. It transforms the original correlated variables into a new set of uncorrelated variables called principal components. The process begins by centering the data (which is subtracting the mean), then computing the covariance matrix to capture the relationships between variables. Eigenvectors and their corresponding eigenvalues are then calculated from the covariance matrix. The eigenvectors represent the directions/principal components of the highest variance, while the eigenvalues quantify the amount of variance in each direction. By selecting the top “k” eigenvectors with the highest eigenvalues, PCA projects the data into a lower dimensional space, simplifying analysis and visualization while retaining the most important information. C: deepia