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.

Define the cost function as mean squared error between predicted and actual values; minimize it with gradient descent to obtain best fit, noting convex curves and local versus global minima.

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.

Learn to implement multivariate linear regression from scratch using a house price dataset, defining X and y, applying gradient descent with a learning rate, cost, and updates, and visualizing convergence.

Clarify the assumptions and prerequisites of linear regression by exploring descriptive and inferential statistics. Distinguish samples from the population and introduce tests like t-test and chi-square to assess estimates.

Understand what a hypothesis is and why we test it. See how a sample tests the idea that a force attracts objects to the ground, illustrating basic hypothesis testing.

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.

Compute null and alternate hypotheses using a gravity example, interpret p-values below 0.05, and recognize measurement errors and outliers in sample data.

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.

Perform a two-sample t-test in Python to compute p-values and t-statistics, compare equal-variance and unequal-variance cases, and interpret results against the null hypothesis.

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.

Watch the lecture series develop and gain access to all upcoming lectures over the next few weeks.

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.

Learn to make moving charts with Python by generating many plots from World Bank GDP data using matplotlib, interpolation, and video creation from image sequences.

Explore principal component analysis to reduce two features into a single predictive component, using eigenvalues, eigenvectors, and covariance matrices to capture maximum variance.

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.

Learn how transfer learning reuses pre-trained weights and biases to jump-start new models, guiding gradient descent toward optimal solutions and avoiding local minima.

Explore entropy as a measure of randomness and its role in decision trees, including probability, information gain, and entropy reduction when splitting data.

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