Mathematics for Machine Learning and LLMs

Explore supervised learning by training a model on labeled fruit images to classify oranges versus non-oranges, using a training set and operator labels to map image patterns to probabilities.

Explore unsupervised learning by grouping fruits into clusters based on geometries, textures, volume, and colors, without labels, to reveal hidden patterns and customer segments.

Reinforcement learning trains an agent to maximize rewards from the environment by acting, observing feedback, and updating its policy through trial and error, with applications from games to robotics.

Explore when to use ML by covering binomial and multiclass classification, regression, clustering, and anomaly detection, and distinguish automation from ML based on data availability.

Select ML algorithms by problem type and data characteristics, balancing supervised and unsupervised tasks, linearity, features, interpretability, and training time.

Analyze data preparation and preliminary analysis of a dataset of 1460 homes with 79 predictors to estimate sale price, guided by CRISP-DM, exploring correlations, missing values, outliers, and feature engineering.

Investigate how the target variable sale price is assessed with nine predictor variables, examining skewness, relationships, correlations, multicollinearity, and predictor selection.

Explore how missing data arise, differentiate MCAR, MAR, and MNAR, and learn when to exclude predictors or apply imputation, including mean, median, or most frequent value in practice.

Apply log transformation to compress ranges, reduce outliers, and improve normality, then use log linear models to interpret coefficients as percentage changes and assess homoscedasticity.

Identify outliers and distinguish anomaly detection from outlier detection. Use isolation forest to detect and filter unusual points before applying models, in contexts like fraud, sales, and visual data.

Apply data transformation to convert data formats and encode categorical predictors as numeric variables, using log, normalization, standardization, and Box-Cox to meet distribution assumptions and improve model performance.

Explain box-cox transformations as a family of power transformations, and lambda selection to stabilize variance and approximate normality for regression, and compare the log transformation when lambda approaches zero.

Explore the key differences between statistics and machine learning, contrasting inferential focus and model interpretability with prediction performance and learning from data.

Explore descriptive statistics for concise data summaries, using numerical and graphical methods, and inferential statistics that generalize from a random sample to a population via probability theory.

Identify qualitative and quantitative variable types, convert categorical data with encoding, and summarize with mean, median, and mode; distinguish sample from population using standard deviation and standard error.

Explore dispersion and relationships by examining quartiles, percentiles, and the interquartile range, and compare covariance with Pearson correlation to assess linear associations in data.

Explore how probability quantifies uncertainty in machine learning, linking data noise, limited knowledge, and imperfect models to probabilistic predictions, training, and validation through concepts like MLE and confidence intervals.

Compare frequentist and Bayesian probabilities and their treatment of prior information. See how priors are updated with new data and applied in machine learning.

Explore discrete and continuous random variables and how probability distributions model uncertainty. Apply random sampling, cross-validation, bootstrap, and ensemble methods like random forests to improve learning.

Explore fundamental probability concepts by identifying sample spaces, events, and set operations, then apply unions, intersections, and complements to real scenarios like the birthday paradox.

Understand discrete, finite, and continuous sampling spaces from coin tosses to area measurements, and apply combinatorial analysis, discretization, and Gaussian models to classification and decision tasks.

Explore the axioms: nonnegativity, total probability, union, and intersection, and the independence notion between events. Independence helps avoid multicollinearity, boosts interpretability, and improves model performance in ml.

Explore conditional probability and independence, using p(a|b) relationships and real examples like dice sums and exam results. Visualize relations with a Venn diagram and apply the conditional probability theorem.

Explore Bayes theorem and the Naive Bayes algorithm, defining posterior, prior, likelihood, and marginal likelihood, with a drug test example and notes on independence assumptions and Gaussian Naive Bayes.

Understand expectation and expected value in uncertain outcomes, and differentiate chance, odds, and likelihood using practical examples. See how reinforcement learning maximizes expected cumulative reward to guide actions.

Apply maximum likelihood estimation to infer mu and sigma from data of a normal distribution, using log-likelihood and differentiation under independence to fit models.

Simulations fill missing data and generate synthetic datasets for ML models in autonomous driving, using random walks and Drunkard's Walk to illustrate time series, reinforcement learning, and anomaly detection.

Monte Carlo simulation uses repeated random sampling to estimate numerical results, while Markov chain Monte Carlo models probability distributions through state transitions for reinforcement learning and text generation.

Explore probability distributions to represent uncertainty and guide model selection, analyzing data to choose appropriate distributions like exponential or normal; identify pmf, pdf, and cdf for discrete and continuous variables.

Explore families of probability distributions, from fixed parameters to inference, including the exponential family, and learn to visualize them with histograms and density plots.

Explore normal distribution and its mean and standard deviation, including the standard normal, z-scores, and PDF that shape bell curves. Include moments, skewness, kurtosis, and ML relevance.

Explore how to test for normality using visual q-q plots and key statistical tests such as Shapiro-Wilk, Kolmogorov-Smirnov, Anderson-Darling, and D'agostino's K-squared, and interpret p-values in regression errors.

Explore the exponential distribution, its single parameter lambda, and waiting-time interpretation; examine its pdf and the mean equals standard deviation, with Python sampling, plotting, and Kolmogorov–Smirnov test or MLE.

Explore the Weibull and beta distributions and their use in survival analysis to model time-to-event data and remaining useful life with two parameters lambda and k.

Model binary outcomes with the binomial distribution, a generalization of Bernoulli trials, and apply it to binary classification tasks such as spam detection, using pmf and cdf.

Explore the Poisson distribution and Poisson processes, modeling random, independent events with a constant average rate lambda, and understand the pmf, inter-arrival times, and real-world examples.

Assess evidence about population parameters through hypothesis testing by formulating H0 and H1, computing p value and test statistics, and rejecting H0 when p value is less than alpha.

Explain the p value and its role in hypothesis testing, including null and alternative hypotheses, statistical significance, significance levels, and how p values guide rejecting the null.

Explore critical values, significance, and confidence, including one- and two-tailed tests, p-values, and confidence intervals, then connect the central limit theorem and law of large numbers to machine learning.

Explore z and t tests in ML, learn how to choose the right hypothesis test, and apply one-sample, two-sample, and paired t tests.

Explore how degrees of freedom define independent information in a data sample and use the F statistic, with df1 and df2, to assess variances in ANOVA and regression.

ANOVA uses the F-test to determine whether three or more group means differ, testing the null hypothesis by partitioning variance into between-group and within-group components in one-way and two-way designs.

Use the chi squared test to assess the relationship between two categorical variables with contingency tables, observed versus expected frequencies, and the null hypothesis of no association.

Statistical power connects sample size and effect size to detect true differences, guiding model comparisons via hypothesis tests, p values, and alpha thresholds for adequate power.

Understand robustness and statistical sufficiency in machine learning, showing how robust statistics resist outliers and noise, even when normality assumptions falter, and how sufficient statistics preserve information efficiently.

Explore time series decomposition and autoregressive models to forecast and analyze seasonality, trend, and residuals. Compare additive and multiplicative decompositions and use Python with statsmodels to extract trend and seasonality.

Explore autoregressive models that forecast time series from past values, assess stationarity, and use acf and pacf to identify ar order and arima adjustments for nonstationary data.

Arima analyzes and forecasts time series by modeling past values and autocorrelations, using differencing to achieve stationarity and incorporating lag effects with autoregressive and moving average terms.

Explore how linear models are defined by linearity in the parameters, with additivity and homogeneity, and how non-linear models differ, using polynomial terms for curved patterns in ML.