AI for PHP Developers (examples)

Linear regression as a basic model

Case 1. Apartment valuation based on parameters


Implementation in pure PHP

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We will start without any libraries. This is useful not for production, but for building intuition. We will use gradient descent, a feature matrix $X$ of size $N$ x $4$, and a weight vector $w$ of length $4$. We will add the bias as an extra feature with value 1.

 
<?php

// Compute the dot product of two vectors: sum(a_i * b_i)
function dotProduct(array $a, array $b): float {
    $sum = 0.0;

    foreach ($a as $i => $v) {
        $sum += $v * $b[$i];
    }

    return $sum;
}

// Training data: each row is an apartment described by features
// X: [area, floor, distance to city center, building age, bias]
$X = [
    [50, 3, 5, 10, 1],
    [70, 10, 3, 5, 1],
    [40, 2, 8, 30, 1],
];

// Target values: apartment prices in dollars
$y = [
    66_000,
    95_000,
    45_000,
];

// Initialize model parameters (weights) and training hyperparameters
$weights = array_fill(0, 5, 0.0);
$learningRate = 0.000001;
$epochs = 5_000;

// n — number of training examples, m — number of features (including bias)
$n = count($X);
$m = count($weights);

// Gradient descent loop: repeat several passes over the dataset
for ($epoch = 0; $epoch < $epochs; $epoch++) {
    // Accumulate gradients for each weight over the whole dataset
    $gradients = array_fill(0, $m, 0.0);

    for ($i = 0; $i < $n; $i++) {
        // Model prediction: y_hat = w · x
        $prediction = dotProduct($weights, $X[$i]);
        // Error for this example: true - predicted
        $error = $y[$i] - $prediction;

        // Accumulate gradient for each weight (derivative of MSE w.r.t. w_j)
        for ($j = 0; $j < $m; $j++) {
            $gradients[$j] += -2 * $X[$i][$j] * $error;
        }
    }

    // Gradient descent update: move weights against the average gradient
    for ($j = 0; $j < $m; $j++) {
        $weights[$j] -= $learningRate * ($gradients[$j] / $n);
    }
}

// Describe a new apartment with the same set of features as in X
// [square footage, number of bedrooms, number of bathrooms, number of floors, bias]
$newApartment = [60, 5, 4, 12, 1];
// Use the trained model to predict its price
$predictedPrice = dotProduct($weights, $newApartment);

echo 'Apartment valuation: $' . number_format($predictedPrice) . "\n";

Charts:

Chart Type:
Result: Memory: 0.003 Mb Time running: 0.004 sec. 
Apartment valuation: $78,374

The block above shows the result of the script: the predicted apartment price for the following features:

  • Apartment area: 60 m²
  • Number of rooms: 5
  • Number of bathrooms: 4
  • Number of floors: 12
  • Deviation: 1