Comparison up to a constant
Penguin learning project
The project uses 342 complete Palmer penguin records: 240 training-pool and 102 held-out rows. The selected training rows determine feature scaling and model parameters. Source CSV
This project trains weights with softmax, unlike the homepage lab, which uses nearest species averages. Same penguin measurements; different classification methods. Predictions can differ.
Source assumptions and notation · Interpret symbols and assumptions in a source statement.
The project supplies finite observations and fitted parameters. A held-out sample does not establish population bounds or prove a theorem.
Consider this concept alongside the project; its source assumptions may differ. These observations do not prove a theorem.
Input: 12 × 2; Held-out evaluation: 102 · #58 · 40.6 mm, 193 mm. Known answer: Adélie; Prediction: Adélie · [≈0.7383, ≈0.2444, ≈0.01737].
Used in these source sections: 1.1 A note on symbols
f ≲ g means one positive constant c bounds f(x) by c g(x) for every x in the domain.
This comparison ignores a fixed multiplicative factor.
Source formula example
illustration · Checking a finite example does not prove the bound for an infinite domain.
Symbols
- Nonnegative functions on the same domain.
- A positive constant independent of x.
Source formula example
This source example uses its own inputs and assumptions. Editing it does not change the project.
Edit a value or the code, then run the example. This is a finite demonstration, not a proof of the paper’s theorem.
This example’s data flow
Code changed. Reset to restore this example’s data flow.
Initial values in code
domain=[1, 2, 3]c=2
Calculated here
Result expression: {
c,
f: domain.map((x) => 2 * x),
g: domain,
holdsOnExample: domain.every((x) => 2 * x <= c * x),
}
Returns
c- 2
f- array (3 items): [2, 4, 6]
g- array (3 items): [1, 2, 3]
holdsOnExample- true
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values in this example are invented. Checking a finite example does not prove the bound for an infinite domain.
Source: Inline notation