Polynomial feature vector
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.
Features · Transform inputs into features used by a rule.
The project scales bill and flipper measurements using training-row means and scales; its feature vector has two entries.
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: 1.3 The questions ahead
The feature vector lists the constant 1 and powers of Z through Zᵈ.
These features permit a linear model in the features to express a polynomial in Z.
Source formula example
illustration · This evaluates a feature map for one value of Z; Z can be random in the source.
Symbols
- A scalar input.
- The nonnegative integer degree.
- A vector of d+1 polynomial features.
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
Z=2d=3
Calculated here
Result expression: { Z, d, X }
X=Array.from({ length: d + 1 }, (_, i) => Z ** i)Uses:d,Z
Returns
Z- 2
d- 3
X- array (4 items): [1, 2, 4, 8]
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented. This evaluates a feature map for one value of Z; Z can be random in the source.
Source: Inline notation