Deep Learning Foundation : Linear Regression and Statistics

Explore linear regression with a scatter plot, the y = mx + c model, and how weights, biases, and mean squared error guide fitting a line to data.

Explore the three error types in linear regression, including SSD and SSR. Understand how the mean and the regression line illustrate these SSD and SSR with dotted lines.

Explore cost functions and 3d surfaces, and see how gradient descent finds linear and nonlinear minima while contrasting global versus local minima and discussing starting points.

Derive gradients of the loss function with respect to M and C for linear regression, then code from scratch to update parameters and reduce the loss.

Explore how gradient descent optimizes a linear regression model by iteratively reducing mean squared error, adjusting slope (m) and intercept (c) with a learning rate.

Code a linear regression model from scratch in Python using gradient descent to fit a line to random samples, updating parameters with learning rate to minimize cost of squared errors.

Predict King County house prices using linear regression with gradient descent from scratch, leveraging features such as square foot living area and other attributes in a Jupyter notebook dataset.

Explore adaptive learning rates in gradient descent for linear regression, starting with a high learning rate that decreases as the cost improves to speed convergence.

Explore multivariate linear regression by extending linear models to multiple features (x1, x2, x3), derive the expanded and vector forms, relate gradients to vector calculus, and prepare for Python implementation.

Compute unbiased sample estimates by calculating the mean for univariate data and the variance by squaring deviations, summing, and dividing by n minus one to measure variability.

Explore histograms to understand distributions, locate the mean, and assess normal-type patterns in data, using frequency plots to transition to probability distributions for data analysis.

Demonstrates how a histogram reveals the frequency of sample values and explains that 68%, 95.4%, and 99.7% lie within one, two, and three standard deviations of the mean.

Explore how to perform an independent two-sample t-test, assess equal versus unequal variances, compute t-statistics and degrees of freedom, and interpret a non-significant result for milk vs no-milk height data.

Learn how z-tests use known population mean and standard deviation, with the formula (x̄−μ)/(σ/√n) to test if a sample comes from the population, unlike t-tests that rely on sample estimates.

Apply the chi-square test to compare observed and expected frequencies, computing (observed minus expected)^2/expected, and assess the null hypothesis using degrees of freedom for categorical data.

Learn the basics of descriptive and inferential statistics, distinguishing samples from populations, and how tests like t-tests and chi-squared support confidence in estimates ahead of linear regression assumptions.

Learn how covariance and correlation quantify shared trends between variables, apply their formulas using means and standard deviations, and interpret positive and negative relationships.

Explore the five core assumptions of linear regression, from linear relationships and residuals to normality, homoscedasticity, and no multicollinearity or autocorrelation, with diagnostic plots and tests.

Explore how to detect multicollinearity in linear regression using the variance inflation factor (VIF) and its relation to R-squared; learn how VIF signals when a feature is redundant.

Learn logistic regression for binary classification by predicting the probability of clearing the job from study hours, using cross-entropy loss and gradient descent to fit M and C.

Explore multiclass logistic regression with three classes (cat, dog, lion), using height as input, and learn to compute class probabilities via softmax and optimize with cross-entropy loss and gradient descent.

Explore eigenvalues and eigenvectors through a matrix example, showing how certain directions scale without angular change and reveal principal directions tied to principal component analysis.

Solve a neural network on paper from scratch to understand forward propagation, matrix-based weight calculations, sigmoid and softmax activations, and gradient descent with backpropagation.

demonstrates live face and eye detection from a laptop webcam using python and opencv haar cascades, with grayscale processing and on-screen annotations.