Bound on the first sequence value
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: 1.2 Learning from examples
The assumption a₁ ≤ 1/16 bounds the first term of the positive decreasing sequence.
It restricts the sequence used in the no-free-lunch statement.
Source formula example
illustration · This checks one value; it does not establish the theorem for every sequence.
Symbols
- The first term of a positive sequence.
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.
Calculated here
Result expression: { a1, bound, valid: a1 <= bound }
a1=1 / 32bound=1 / 16
Returns
a1- 0.03125
bound- 0.0625
valid- true
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented. This checks one value; it does not establish the theorem for every sequence.
Source: Inline notation