The Modern Mathematics of Deep Learning

Sample average

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.

Vectors and matrices · Combine numbers using vector and matrix operations.

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: 4.2 Approximating with random pieces

Evaluate a function at each sampled input and average the results. The sample here is a fixed invented list.

Sampling can approximate an average over a distribution.

Source formula example

\frac{1}{m}\sum_{i=1}^{m}f(x_i)

approximation · A finite sample mean is not generally the population expectation. This fixed toy sample does not establish a convergence rate.

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.

Third value

This example’s data flow

You choose

input.last = 2

Calculated here

Result expression: { values, mean: values.reduce((a, b) => a + b, 0) / values.length }

values = [0, 1, input.last] Uses: input.last

Returns

Example result

values: array (3 items): [0, 1, 2]
mean: 1

JavaScript

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

Result

Enable JavaScript to run this example.

Technical statement

Change the input and run the same code again. The displayed result uses the values shown above.

Source: Sample average