Open workspace
Track 4 of 5 · Beginner

Statisticsand probability, on real data.

Every idea starts from a question about a dataset, and ends with what the number does and does not tell you.

See the syllabus
6modules
28lessons planned
0ready to study now
0quiz questions so far

The syllabus6 modules, one objective per lesson.

The course is being built in this order. Every lesson is listed, including the ones still in production, so you can see where the track goes. Open lessons have their parts, key terms and quiz free.

Module 1

Describing Data

6 lessons, in production

  1. 1.1Histograms and DensitySee the shape of one feature, and turn a histogram into a smooth density.
    What it will cover
    • Bins, and how the bin width changes the story
    • The probability density function (PDF): area is probability
    • Kernel density estimation, and the bandwidth
    In production
  2. 1.2The CDF, Percentiles and QuantilesRead the fraction of data below any value, and the value below any fraction.
    What it will cover
    • The cumulative distribution function (CDF) from a histogram
    • Percentiles, quartiles and quantiles
    • Reading thresholds off a CDF
    In production
  3. 1.3Mean, Median and ModeChoose the right "typical value", and see the mean pulled by one outlier.
    What it will cover
    • Mean, median, mode
    • The outlier test: one wrong row
    • Skew and the mean–median gap
    In production
  4. 1.4Variance, Standard Deviation, IQR and MADMeasure spread, robustly when the data has outliers.
    What it will cover
    • Variance and standard deviation
    • Interquartile range
    • Median absolute deviation
    • Robust against non-robust, on the same data
    In production
  5. 1.5Box Plots and Violin PlotsCompare distributions at a glance.
    What it will cover
    • The box plot: quartiles, whiskers, flagged points
    • The violin plot: a box plot with the density
    • Univariate, bivariate and multivariate views
    In production
  6. 1.6Covariance and CorrelationMeasure how two features move together, and know what correlation can never tell you.
    What it will cover
    • Covariance, and why its size is hard to read
    • Pearson correlation: linear association
    • Spearman rank correlation: monotonic association
    • Correlation is not causation: confounders, and spurious correlation
    • How to use correlations in ML
    In production
Module 2

Probability

4 lessons, in production

  1. 2.1Probability BasicsReason about chance with outcomes, events and the rules that combine them.
    What it will cover
    • Sample space, events, probability as a long-run fraction
    • The addition and complement rules
    • Joint probability
    In production
  2. 2.2Conditional Probability and IndependenceUpdate a probability given evidence, and tell independent events from mutually exclusive ones.
    What it will cover
    • P(A | B) as restricting the population, with whole-number counts
    • Independence
    • Independent against mutually exclusive
    In production
  3. 2.3Bayes' TheoremTurn "how likely is the evidence given the class" into "how likely is the class given the evidence".
    What it will cover
    • The theorem from the counts
    • Base rates: the rare-disease test
    • Prior, likelihood, posterior
    • Chaining evidence: the posterior becomes the next prior
    In production
  4. 2.4Random Variables, Expectation and VarianceDescribe an uncertain quantity by its distribution, its average and its spread.
    What it will cover
    • Discrete and continuous random variables
    • Expected value as a long-run average
    • Variance of a random variable; rules for sums
    In production
Module 3

Distributions

6 lessons, in production

  1. 3.1Uniform Distributions and Random SamplingDraw fair random samples, including proportional samples.
    What it will cover
    • Discrete and continuous uniform
    • Sampling with and without replacement
    • Proportional (weighted) sampling
    In production
  2. 3.2Bernoulli, Binomial and PoissonModel yes/no outcomes and counts.
    What it will cover
    • Bernoulli: one trial
    • Binomial: the number of successes in n trials
    • Poisson: counts in an interval
    In production
  3. 3.3The Normal DistributionKnow the Gaussian's shape, its rules of thumb, and z-scores.
    What it will cover
    • The PDF and its two parameters
    • The CDF; the 68–95–99.7 rule
    • The standard normal variate: z-scores and standardisation
    • Chebyshev's inequality: a guarantee for any distribution
    In production
  4. 3.4Skew, Kurtosis and the Q-Q PlotTell whether a feature is normal, and how it is not.
    What it will cover
    • Symmetry, skewness and kurtosis
    • The Q-Q plot, read against known shapes
    In production
  5. 3.5Log-Normal, Power Laws and Box-CoxRecognise heavy-tailed data and transform it toward normal.
    What it will cover
    • The log-normal: incomes, prices, durations
    • Power laws and the 80/20 pattern
    • The Box-Cox transform
    • Where non-Gaussian distributions show up in ML
    In production
  6. 3.6The Multivariate NormalExtend the Gaussian to several features, and read its contours.
    What it will cover
    • The mean vector and the covariance matrix
    • Contour plots as ellipses
    • Correlation as the tilt of the ellipse
    In production
Module 4

Estimation

4 lessons, in production

  1. 4.1Samples, Sampling Distributions and the Central Limit TheoremSee why sample means behave predictably even when the data does not.
    What it will cover
    • Population against sample
    • The sampling distribution of the mean
    • The central limit theorem, simulated
    • The standard error
    In production
  2. 4.2Maximum Likelihood EstimationChoose the parameters that make the observed data most probable, and see familiar losses fall out.
    What it will cover
    • The likelihood as a function of the parameters
    • The log-likelihood, and why the log
    • The MLE of a coin, and of a Gaussian's mean and variance
    • Squared error from Gaussian noise; log loss from Bernoulli labels
    In production
  3. 4.3Confidence IntervalsReport an estimate with its uncertainty, and say what the interval does and does not mean.
    What it will cover
    • Intervals from a known distribution
    • The interval for the mean of a normal variable
    • The frequentist reading, and the common misreading
    In production
  4. 4.4The BootstrapGet an interval for any statistic by resampling the data you have.
    What it will cover
    • Resampling with replacement
    • The bootstrap distribution
    • Percentile intervals, for a median and for a model score
    In production
Module 5

Hypothesis Testing

5 lessons, in production

  1. 5.1Hypothesis Testing and the p-ValueTest a claim against chance, and read a p-value correctly.
    What it will cover
    • The null hypothesis and the test statistic
    • The coin-toss example
    • The p-value: what it is and what it is not
    • Type I and Type II errors; significance level and power
    In production
  2. 5.2Permutation and Resampling TestsTest a difference by shuffling labels, with no distribution assumed.
    What it will cover
    • Shuffling breaks the link the null says does not exist
    • The permutation distribution; the p-value as a fraction
    • Two worked examples
    In production
  3. 5.3The t-Test and the Chi-Square TestUse the two classical tests ML practitioners meet most.
    What it will cover
    • The two-sample t-test for means
    • The chi-square test for counts and independence
    • The assumptions, and when to prefer a permutation test
    In production
  4. 5.4Comparing Distributions: The KS TestTest whether two samples come from the same distribution.
    What it will cover
    • The largest gap between two empirical CDFs
    • Running it in code
    • Use in train/test comparison and drift detection
    In production
  5. 5.5Using Tests WellAvoid the ways hypothesis testing misleads in practice.
    What it will cover
    • Statistical against practical significance; effect size
    • Multiple testing, and the corrections
    • Peeking and stopping early
    • How to use hypothesis testing in ML work
    In production
Module 6

Information Theory

3 lessons, in production

  1. 6.1EntropyMeasure uncertainty in bits, and see why a pure node has zero entropy.
    What it will cover
    • Surprise as −log p
    • Entropy as average surprise
    • Maximum for uniform, zero for certain
    • Gini impurity as a cousin
    In production
  2. 6.2Cross-Entropy and Log LossSee log loss as the cost of coding the truth with the model's probabilities.
    What it will cover
    • Cross-entropy between a true and a predicted distribution
    • Binary and multi-class log loss
    • Why confident mistakes cost so much
    In production
  3. 6.3KL DivergenceMeasure how different two distributions are, and why the direction matters.
    What it will cover
    • KL divergence as cross-entropy minus entropy
    • Asymmetry, pictured
    • Where it appears: t-SNE, variational methods (later), drift
    In production

What you’ll learnby the end of the track.

  • Summarise a dataset and spot what a summary hides.
  • Reason with conditional probability and Bayes' theorem.
  • Estimate a quantity with an honest interval around it.
  • Know when a difference in results is real.

Before you startand how the lessons work.

  • School algebra and basic Python. Code examples use pandas, from the Data Tools track.
  • Every open lesson shows its parts, key terms and quiz for free. Sign in to check your answers and save your progress.
  • While the course is being recorded, the practice problems, common mistakes, self-checking notebooks, cheat sheets and project checks are free with an account too.

Where it leadslive roles this track prepares you for.

Openings from companies’ own career pages, updated continuously.

Questionsabout this track.

Why does machine learning need statistics?

To describe data before modelling it, to know how sure a result is, and to understand the loss functions models are trained on.

The other tracksand the order to take them in.

See the learning path