Signed measures
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.
Probability and expectation · Describe random variables and their averages under a law.
Project vectors have two features; the training matrix has n rows and two columns. Mathematical tools may operate on these values when their assumptions apply.
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: 1.2.2 Can the network express the answer?
A signed measure assigns positive or negative values to sets. μ = 0 means it assigns zero to every measurable set.
Signed measures appear when describing continuous linear functionals on C(K).
Source formula example
illustration · A zero total alone does not imply a signed measure is zero: the first example has cancelling nonzero weights.
Symbols
- A compact set.
- A signed Borel measure on K.
- The zero measure.
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
K=[0, 1]weights=[1, -1]zeroWeights=[0, 0]
Calculated here
Result expression: {
K,
weights,
total: weights.reduce((a, b) => a + b, 0),
zeroMeasure: zeroWeights.every((w) => w === 0),
}
Returns
K- array (2 items): [0, 1]
weights- array (2 items): [1, -1]
total- 0
zeroMeasure- true
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented. A zero total alone does not imply a signed measure is zero: the first example has cancelling nonzero weights.
Source: Inline notation