Maths 1.3Lesson outlineLesson 3 of 3 in Module 1
Reading ML Notation
Read the formulas in ML papers and docs without stalling.
Free sample. Everything in this module opens with a free account.Video in production.
Learn
In this lesson11 parts
- 01Two symbols we used without reading
- 02Subscripts, superscripts and indices
- 03Sum and product notation
- 04Hats, bars and stars
- 05Bold vectors, capital matrices, the transpose and set notation
- 06argmin and argmax
- 07Checkpoint: the notation so far
- 08The mean squared error, term by term
- 09Reading the ridge objective and scikit-learn's documentation
- 10The notation in NumPy
- 11Recap, challenge, and next: vectors
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- index
- a letter that counts through rows (
i) or columns (j) |i = 1, 2, 3 - subscript
- a small index written below and to the right |
x₂₁ = 0 - superscript
- a small mark above and to the right |
x², orx⁽¹⁾for row 1 - summation
Σ - add an expression over an index |
Σᵢ₌₁³ i² = 14 - product notation
Π - multiply an expression over an index |
Πᵢ₌₁³ i = 6 - hat
- a value a model produced, an estimate |
ŷ = (5, −3, 10) - bar
- a mean |
x̄ = (2, 2),ȳ = 4.6667 - star
- the optimal value for an objective |
w* = (2.7667, −0.3333) - vector
- an ordered list of numbers, written bold |
𝐰 = (3, −1) - matrix
- a table of numbers, written as a capital |
X, shape(3, 2) - transpose
- rows and columns swapped |
Xᵀ, shape(2, 3) ∈- is a member of |
𝐰 ∈ ℝ² ℝᵈ- lists of
dreal numbers |X ∈ ℝ³ˣ² - argmin**, **argmax
- the input that gives the lowest, or highest, output |
argmin (w − 3)² + 1 = 3 - hyperparameter
- a number chosen before training that controls how a model is fitted |
λ = 0.1, scikit-learn'salpha - common mistake:
x⁽ⁱ⁾ - a bracketed superscript is row
i, not a power |x⁽¹⁾is row 1 - common mistake:
ŷandy - not interchangeable; the gap between them is what the model makes small | errors
(−1, 2, 1) - common mistake:
argmin argminreturns the input,minreturns the value |3against1
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.