[googleresoure][ml concepts] 02 descending into ml

Source: https://developers.google.com/machine-learning/crash-course/descending-into-ml/video-lecture

Linear regression is a method for finding the straight line or hyperplane that best fits a set of points. This module explores linear regression intuitively before laying the groundwork for a machine learning approach to linear regression.

Learning Objectives

• Refresh your memory on line fitting.

• Relate weights and biases in machine learning to slope and offset in line fitting.

• Understand “loss” in general and squared loss in particular.

Descending into ML: Linear Regression

The equation for a linear regression model.

$y’ = b + w_1x_1 $

where:

• $y’$: The predicted label (a desired output).

• $b$: The bias, sometimes referred to as $w_0$.

• $w_1$: The weight of feature 1.

• $x_1$: a feature (a known input).

A more sophisticated model might rely on multiple features, each having a separate weight ($w_1, w_2$, etc.)

$y’ = b + w_1x_1 + w_2x_2 + w_3x_3$

Descending into ML: Training and Loss

Training a model simply means learning(determining) good values for all the weights and the bias from labeled examples.

In supervised learning, a machine learning algorithm builds a model by examining many examples and attempting to find a model that minimizes loss; this is called empirical risk minimization.

Loss is the penalty for a bad prediction. That is, loss is a number indicating how bad the model’s prediction was on a single example. If the model’s prediction is perfect, the loss is zero; otherwise, the loss is greater.

The goal of training a model is to find a set of weights and biases that have low loss, on average, across all examples.

Squared Loss: a popular loss function

The linear regression models we’ll examine here use a loss function called squared loss (also known as L$_2$ loss).

= Square of the difference between prediction and label

= (Observation - prediction($x$))$^2$

= $(y-y’)^2$

Mean square error (MSE)

MSE is the average squared loss per example over the whole dataset.

$$MSE = frac{1}{N}sum_{(x,y)in D}(y-prediction(x))^2$$

where:

• $(x,y)$ is an example in which

  • $x$ is the set of features that the model uses to make predictions.

  • $y$ is the example’s label.

• $prediction(x)$ is a function of the weights and bias in combination with the set of features $x$.

• $D$ is a data set containing many labeled examples, which are $(x,y)$ pairs.

• $N$ is the number of examples in $D$

Although MSE is commonly-used in machine learning, it is neither the only practical loss function nor the best loss function for all circumstances.