He suggests that "English" (pseudo-code) be used instead, such as the following:
residuals_squared = (actual_values - predictions) ^ 2
RSS = sum( residuals_squared )
Although there are some flaws in this particular comparison (1. the first example includes an unnecessary middle portion, 2. it also features the linear model definition, while the pseudo-code example does not, and 3. the indexing variable in the summation is straightforward in this case, but is not always so), I tend to agree. Despite my own familiarity with the math jargon, I agree with him that, in many cases, pseudo-code is easier to understand.
Pseudo-code is certainly simpler syntactically since it tends to make heavy use of (sometimes deeply-nested) functions, as opposed to floating subscripts, superscripts and baroque symbols. Pseudo-code often employs real names for parameters, variables and constants, as opposed to letters. It is also closer to computer code that one actually writes, which is the point of this post.
Given the convention in MATLAB to store variables as column vectors, here is my MATLAB implementation of Givre's pseudo-code:
residuals_squared = (actual_values - predictions) .^ 2;
RSS = sum( residuals_squared );
Only two minor changes were needed: 1. The MATLAB .^ operator raises each individual element in an input matrix to a power, while the MATLAB ^ operator raises the entire matrix to a power (through matrix multiplication). 2. The semicolons prevent echoing the result of each calculation to the console: They are not strictly necessary, but will typically be included in a MATLAB program. Note that, unlike some object-oriented languages we could name, no extra code is needed to lay the groundwork of overloaded operators.
Consider an example I have given in the past, for the forward calculation of a feedforward neural network using a hyperbolic tangent transfer function:
HiddenLayer = tanh(Input * HiddenWeights);
OutputLayer = tanh(HiddenLayer * OutputWeights);
Note that this code recalls the neural network over all observations stored in the matrix Input.That's it: Two lines of code, without looping, which execute efficiently (quickly) in MATLAB. The addition of bias nodes, jump connections and scaling of the output layer would require more code, but even such changes would leave this code easy to comprehend.