So how do we create a TensorFlow model to use WALS? Well, fortunately, there's a WALS Estimator. Using this, we simply just need to structure the inputs correctly, so we feed in the estimator, and it takes care of most of the rest. This begins with the training_input function, where we simply define our features. But wait, aren't they usually labels? In this case, we are alternating some of our features has labels, that is where the alternating comes from in alternating squares. We fixed the rows and install for the columns, and it takes the columns and install for the rows. The rows might begin as our features, where we're predicting the columns, and compare it with the actual column values as our labels from the radia matrix, and vice versa when alternating. Also, remember the W in WALS is for Weighted. That means we can customize our problem, it's not just for managing missing observations. We can add weights for specific entries if we want. One reason might be to encode our profit margin on items and use that as a weight. This way, more profitable items will be recommended more. We're ignoring this, here. But if you wanted to, it's just another the key in the features dictionary that you can add. Note here that input rows and input columns are both from a batch. Not all the rows. We'll dive deeper into this later, but now, let's take a look at the ALS algorithm. Here is the pseudocode for the alternating least squares algorithm. Remember, with matrix factorization, we iteratively learn U and V, which are multiplied together, hopefully reconstructs a close approximation to our original user item interaction matrix, however, it won't be perfect. With alternating least squares, we can get very close, though. Let's walk through it a bit to build a deeper intuition of what is happening under the hood. First, we initialize the u and v factor matrices. These are our learned row and column factors, which based on our previous examples, could be the users u and movies for v. Just as how we would normally treat an embedding, these start of as typically random, normal noise. Our goal is to calculate these two embeddings simultaneously. Next, we're going to enter a loop that will run until we reach the law's conversion, usually within some tolerance. This is our alternation loop. Let's enter and see just exactly what is alternating back and forth. In the first phase of the alternation, we are solving for the row factors u by looping through all the rows, which in our example, would be the users. Does the equation look familiar? Well, of course. It's the ordinary least squares normal equation with L-curve regularization added, with regularization constant lambda. We are used to seeing this with x's and y's, but it's essentially the same. This means that the Ui's we are solving for are analogous to the coefficients, or weight factor learned from linear regression. The normal equation's gram matrix is using v, our column factors, instead of x. Admini auto regularization, we then take the inverse, as usual, which gives us the inverse regularized grand matrix. Last but not the least, we multiply by the moment matrix to find out weight factors. As before, our usual access from a place for the column factors B, and instead of our labels, y, we had the ithro of the radiance matrix, r, as our labels. Now that we have solved for all the row factors using the column factors as features, and the ready matrix rows as our labels, we're going to alternate gears and do the same. But now, we will iterate over all the columns and solve for all the column factors using the row factors that we have just solved for as our features, and the radiance matrix columns as our labels. ALS is an alternating least squares algorithm. In ordinary least squares, we have the analytic solution of the normal equation. Beta equals the inverse of X transpose X, plus lambda, times the identity matrix, all multiplied by X transpose Y. In ALS, during the row-factor solving phase, where we fix column-factors, row factors u are analogous to blank. Column-factor v are analogous to, blank, and ratings matrix R is analogous to, blank. Choose the answer that best fills in the blanks. The correct answer is C. We're solving for the row-factors u with which the column-factors of V. We are solving for the latent variable embedding waste, which is analagous to what beta represents in linear regression. The coefficients or weights are predictive variables. In linear regression, our predictors are often denoted by the matrix X, which this case are our column-factors V, which are holding the fix for this cycle. Lastly, whether solving for ρ factors or column factors, our ratings matrix R is analogous to labels of linear regression, usually denoted y. Now, since we are solving for vectors, we are not using the entire ratings matrix R, we are only using the Ith row of the ratings matrix when solving for the Ith row factor. Remember, when solving for the column factors for the next half cycle of the ALS algorithm the variable analogies flip. With v now being solved for like beta, u is now fixed like the predictors x, and y is still the ratings matrix, but now the jth column of it is being used to solve for the jth column factor. All of this happening with factors that represent the user and item embeddings into k-dimensional spaces for both.
