Linear Regression with Elixir, Phoenix and LiveView. Part I

The post walks through a basic linear regression example in Elixir with Phoenix and LiveView as the project setup. It defines a model with weights m and b, a data struct for training points, and a train function that updates the model from X and Y pairs.

It explains training as repeated prediction, error calculation, and weight adjustment with a learning rate. The example shows how multiple epochs bring the prediction closer to the expected line, and it ends by pointing to a second part that will make the example interactive with LiveView.

Reading notes

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• Phoenix 1.5 makes it easier to start a new app with LiveView by passing the --live flag.
• The example project is created with mix phx.new linreg --live --no-ecto.
• The model keeps two values, m and b, and predicts with b + m * x.
• Training depends on prediction, error measurement, and repeated adjustment of the weights.
• The training data is a list of (x, y) points stored in a %Data{} struct.
• The train/3 function computes average errors for m and b and subtracts them times the learning rate.
• The learning rate controls how small each update is so the model does not overshoot.
• One pass over the data is one epoch, and the post says multiple epochs are usually needed.
• The revised train/3 function uses a for comprehension with reduce to run through the full dataset many times.
• With more training, the example moves closer to Y = 2 * X + 0, though it does not reach exact values.
• The post says the remaining gap comes from the learning rate and floating point arithmetic.
• The next part will use Phoenix LiveView to let clicks on a SVG plane generate training data and show the fitted line.