Statistics & Linear Algebra for Machine Learning

Analyze central tendency and dispersion to reveal data insights for machine learning with mean, median, mode, range, and standard deviation, plus percentiles, distribution shape, and data types.

Identify outliers with box plots by computing percentiles, Q1 and Q3, and the interquartile range to set lower and upper bounds for informed process analysis.

Explore how sampling extrapolates analysis from a sample to the population, emphasizing representativeness and randomness to avoid bias in data analysis and machine learning.

Learn how hypothesis testing validates extrapolation from sample to population by comparing null and alternate hypotheses using p values and a 0.05 significance level, recognizing type I and II errors.

Apply one-sample, two-sample, and paired t tests to assess hypotheses about population means using sample data, t statistics, and p-values, with manual and Python-based approaches.

Explore the analysis of variance to compare means across multiple groups, learn one-factor and two-factor ANOVA, and interpret F tests and p-values using Python and Excel.

Compare confidence level, confidence interval, and significance level within hypothesis testing, linking population versus sample and p-values to practical plant growth examples.

Explore simple and multiple linear regression, the line of best fit, and the equation y equals m times x plus c, then assess models with r squared and absolute error.

Explore how linear algebra expresses data as vectors and learning as transformations, using matrix operations, dot products, and inverses to fit linear regression and scale to larger data.

Explore eigenvectors and eigenvalues, how linear transformations scale vectors without changing direction, and how the determinant guides solving for eigenvalues, with applications in PCA and feature extraction.

Explore how matrix multiplication underpins deep learning, linking linear algebra to neural networks with input, hidden, and output layers and weight matrices.

Explore vector projections for dimensionality reduction and image processing, using dot products, magnitudes, and angles to project vectors and implement in NumPy.

Apply linear algebra to measure sentence similarity with cosine similarity, comparing to Euclidean and Manhattan distances, and use tokenization, vector embeddings, and tf-idf for semantic search.

Analyze the jacobian matrix and partial derivatives to see how inputs affect outputs in multivariable models, and use the chain rule with backpropagation to train neural networks via gradient descent.

Contrast machine learning and deep learning by abstraction levels, with ML relying on handcrafted features and DL learning layered representations end to end, via dot products and activations.

Explore the mathematics of logistic regression, including the logit function, probability estimation, and iterative coefficient updates via gradient and learning rate using the Titanic dataset.

Learn how to build a decision tree to predict heart disease from blood pressure, sugar, and cholesterol using binary splits. Explore root node selection and Gini index evaluation.

Learn unsupervised learning and clustering with k nearest neighbors, using Euclidean distance to identify customer segments and detect anomalies in marketing and fraud applications.

Apply Bayes theorem and Naive Bayes to update beliefs from observed data in classification tasks. Explain posterior with prior, likelihood, and evidence, and illustrate Laplace smoothing and conditional independence.

Explore how neural networks process information by weighting factors, applying an activation function, and learning to minimize loss through backpropagation and gradient descent to optimize predictions.

Explore activation functions used in machine learning and deep learning, including sigmoid, ReLU, leaky ReLU, tanh, softmax, and ELU. See how they introduce non-linearity and support learning and classification.

Explore convex optimization to find the global minimum of a convex function, illustrated by y = x^2, and apply gradient descent via derivatives to minimize the cost or loss function.

Explore how convolutional layers in CNN extract edges and features from images using kernels, activation, pooling and padding, producing a condensed feature vector for final classification.

Intro to RNN explains how looping networks preserve context with a hidden state, enabling memory for sequential data and tasks like time series forecasting and predicting the next word.

Explore the math behind rnn as the hidden state, or memory, updates from h_{t-1} to h_t using x_t and weights w_h, w_x, then compute y_t with softmax.

Celebrate completing the course by downloading a resource with curated links to other statistics and machine learning courses, available via the instructor's Udemy profile.