The Modern Mathematics of Deep Learning

Different samples and risks

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.

Risk and assessment · Distinguish loss on a sample from expected loss.

The fitted rule is evaluated on 102 held-out observations, not used for fitting.

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

A learned function fₛ is fitted using sample s. Its average loss can be evaluated on s or a different sample s̃.

Comparing sample risks illustrates why training and evaluation data are distinguished.

Source formula example

f_{s}

illustration · The loss lists are invented; this comparison does not determine population risk.

Symbols

$s$: Training sample.
$s̃$: A different sample.
$f_{s}$: A learned function.
ℛₛ, ℛₛ̃: Average losses on the indicated samples.

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

Initial values in code

trainLosses = [0, 2]
otherLosses = [2, 4]

Calculated here

Result expression: { trainLosses, otherLosses, trainRisk: mean(trainLosses), otherRisk: mean(otherLosses), }

Returns

Example result

trainLosses: array (2 items): [0, 2]
otherLosses: array (2 items): [2, 4]
trainRisk: 1
otherRisk: 3

JavaScript

Read numbers from input and return the result. JavaScript basics.

Result

Enable JavaScript to run this example.

Technical statement

The numerical values are invented unless the source values are stated. The loss lists are invented; this comparison does not determine population risk.

Source: Inline notation