update (d2l-ai#595)

* update

* fix

* fix

* add references

chapter_recommender-systems/autorec.md

@@ -1,6 +1,6 @@
 # AutoRec: Rating Prediction with Autoencoders
 
-Although the matrix factorization model achieves decent performance on the rating prediction task, it is essentially a linear model. Thus, such models are not capable of capturing complex nonlinear and intricate relationships that may be predictive of users' preferences. In this section, we introduce a nonlinear neural network collaborative filtering model, AutoRec. It identifies collaborative filtering (CF) with an autoencoder architecture and aims to integrate nonlinear transformations into CF on the basis of explicit feedback. Neural networks have been proven to be capable of approximating any continuous function, making it suitable to address the limitation of matrix factorization and enrich the expressiveness of matrix factorization.
+Although the matrix factorization model achieves decent performance on the rating prediction task, it is essentially a linear model. Thus, such models are not capable of capturing complex nonlinear and intricate relationships that may be predictive of users' preferences. In this section, we introduce a nonlinear neural network collaborative filtering model, AutoRec :cite:`Sedhain.Menon.Sanner.ea.2015`. It identifies collaborative filtering (CF) with an autoencoder architecture and aims to integrate nonlinear transformations into CF on the basis of explicit feedback. Neural networks have been proven to be capable of approximating any continuous function, making it suitable to address the limitation of matrix factorization and enrich the expressiveness of matrix factorization.
 
 On one hand, AutoRec has the same structure as an autoencoder which consists of an input layer, a hidden layer, and a reconstruction (output) layer.  An autoencoder is a neural network that learns to copy its input to its output in order to code the inputs into the hidden (and usually low-dimensional) representations. In AutoRec, instead of explicitly embedding users/items into low-dimensional space, it uses the column/row of the interaction matrix as the input, then reconstructs the interaction matrix in the output layer.
 
@@ -122,7 +122,3 @@ d2l.train_recsys_rating(net, train_iter, test_iter, loss, trainer, num_epochs,
 ## References
 
 * Sedhain, Suvash, et al. "AutoRec: Autoencoders meet collaborative filtering." Proceedings of the 24th International Conference on World Wide Web. ACM, 2015.
-
-```{.python .input}
-
-```

chapter_recommender-systems/deepfm.md

@@ -2,7 +2,7 @@
 
 Learning effective feature combinations is critical to the success of click-through rate prediction task. Factorization machines model feature interactions in a linear paradigm (e.g., bilinear intearctions). This is often insufficient for real-world data where inherent feature crossing structures are usually very complex and nonlinear. What's worse, second-order feature interactions are generally used in factorization machines in practice. Modelling higher degress of feature combinations with factorization machines is possible theorectically but it is usuallt not adopted due to numerical instability and high computationla complexity.
 
-One effective solution is using deep neural networks. Deep neural networks are powerful in feature representation learning and have the potential to learn sophisticated feature interactions. As such, it is natural to integrate deep neural networks to factorization machines. Adding nonlinear transformation layers to factorization machines gives it the capability to model both low-order feature combinations and high-order feature combinations. Moreover, non-linear inherent structures from inputs can also be captured with deep neural networks. In this section, we will introduce a representative model named deep factorization machines (DeepFM) which combine FM and deep neural networks. 
+One effective solution is using deep neural networks. Deep neural networks are powerful in feature representation learning and have the potential to learn sophisticated feature interactions. As such, it is natural to integrate deep neural networks to factorization machines. Adding nonlinear transformation layers to factorization machines gives it the capability to model both low-order feature combinations and high-order feature combinations. Moreover, non-linear inherent structures from inputs can also be captured with deep neural networks. In this section, we will introduce a representative model named deep factorization machines (DeepFM) :cite:`Guo.Tang.Ye.ea.2017` which combine FM and deep neural networks. 
 
 
 ## Model Architectures 
@@ -21,7 +21,7 @@ $$
 \mathbf{z}^{(l)}  = \alpha(\mathbf{W}^{(l)}\mathbf{z}^{(l-1)} + \mathbf{b}^{(l)}),
 $$
 
-where $\alpha$ is the activation function.  $\mathbf{W}_{l}$ and $ \mathbf{b}_{l}$ are the weight and bias at the $l^\mathrm{th}$ layer. Let $y_{DNN}$ denote the output of the prediction. The ultimate prediction of DeepFM is the summation of the outputs from both FM and DNN. So we have: 
+where $\alpha$ is the activation function.  $\mathbf{W}_{l}$ and $\mathbf{b}_{l}$ are the weight and bias at the $l^\mathrm{th}$ layer. Let $y_{DNN}$ denote the output of the prediction. The ultimate prediction of DeepFM is the summation of the outputs from both FM and DNN. So we have: 
 
 $$
 \hat{y} = \sigma(\hat{y}^{(FM)} + \hat{y}^{(DNN)}),

chapter_recommender-systems/fm.md

@@ -1,17 +1,17 @@
 # Factorization Machines
 
-Factorization machines (FM), proposed by Steffen Rendle in 2010,  is a supervised algorithm that can be used for classification, regression, and ranking tasks. It quickly took notice and became a popular and impactful method for making predictions and recommendations. Particularly, it is a generalization of the linear regression model and the matrix factorization model. Moreover, it is reminiscent of support vector machines with a polynomial kernel. The strengths of factorization machines over the linear regression and matrix factorization are: (1) it can model $\chi$-way variable interactions, where $\chi$ is the number of polynomial order and is usually set to two. (2) A fast optimization algorithm asociated with factorization machines can reduce the polynomial computation time to linear complexity, making it extremely efficient especially for high dimensional sparse inputs.  For these reasons, factorization machines are widely employed in mordern advertisement and products recommendations. The technical details and implemetations are described below.
+Factorization machines (FM) :cite:`Rendle.2010` , proposed by Steffen Rendle in 2010,  is a supervised algorithm that can be used for classification, regression, and ranking tasks. It quickly took notice and became a popular and impactful method for making predictions and recommendations. Particularly, it is a generalization of the linear regression model and the matrix factorization model. Moreover, it is reminiscent of support vector machines with a polynomial kernel. The strengths of factorization machines over the linear regression and matrix factorization are: (1) it can model $\chi$-way variable interactions, where $\chi$ is the number of polynomial order and is usually set to two. (2) A fast optimization algorithm asociated with factorization machines can reduce the polynomial computation time to linear complexity, making it extremely efficient especially for high dimensional sparse inputs.  For these reasons, factorization machines are widely employed in mordern advertisement and products recommendations. The technical details and implemetations are described below.
 
 
-## 2-Way Factorization machines
+## 2-Way Factorization Machines
 
 Formally, let $x \in \mathbb{R}^d$ denote the feature vectors of one sample, and $y$ denote the corresponding label which can be real-valued label or class label such as binary class "click/non-click". The model for a factorization machine of degree two is defined as:
 
 $$
 \hat{y}(x) = \mathbf{w}_0 + \sum_{i=1}^d \mathbf{w}_i x_i + \sum_{i=1}^d\sum_{j=i+1}^d \langle\mathbf{v}_i, \mathbf{v}_j\rangle x_i x_j
 $$
 
-where $\mathbf{w}_0 \in \mathbb{R}$ is the global bias; $\mathbf{w} \in \mathbb{R}^d$ denotes the weights of the i-th variable; $\mathbf{V} \in \mathbb{R}^{d\times k}$ represents the feature embeddings; $\mathbf{v}_i$ represet the $i^\mathrm{th}$ row of $\mathbf{V}$; $k$ is the dimensionality of latent factors; $\langle\cdot, \cdot \rangle$ is the dot product of two vectors.  $\langle\mathbf{v}_i, \mathbf{v}_j\rangle $ model the interaction between the $i^\mathrm{th}$ and $j^\mathrm{th}$ feature. Some feature interactions can be easily understood so they can be designed by experts. However, most other feature interactions are hidden in data and difficult to identify. So modelling feature interactions automatically can greatly reduce the efforts in feature engineering. It is obvious that the first two terms correspond to the linear regression model and the last term is an extension of the matrix factorization model. If the feature $i$ represents a item and the feature $j$ represents a user, the thid term is exactly the dot product between user and item embeddings. It is worth noting that FM can also generalize to higher orders (degree > 2). Nevertheless, the numerical stability might weaken the generalization.  
+where $\mathbf{w}_0 \in \mathbb{R}$ is the global bias; $\mathbf{w} \in \mathbb{R}^d$ denotes the weights of the i-th variable; $\mathbf{V} \in \mathbb{R}^{d\times k}$ represents the feature embeddings; $\mathbf{v}_i$ represet the $i^\mathrm{th}$ row of $\mathbf{V}$; $k$ is the dimensionality of latent factors; $\langle\cdot, \cdot \rangle$ is the dot product of two vectors.  $\langle \mathbf{v}_i, \mathbf{v}_j \rangle$ model the interaction between the $i^\mathrm{th}$ and $j^\mathrm{th}$ feature. Some feature interactions can be easily understood so they can be designed by experts. However, most other feature interactions are hidden in data and difficult to identify. So modelling feature interactions automatically can greatly reduce the efforts in feature engineering. It is obvious that the first two terms correspond to the linear regression model and the last term is an extension of the matrix factorization model. If the feature $i$ represents a item and the feature $j$ represents a user, the thid term is exactly the dot product between user and item embeddings. It is worth noting that FM can also generalize to higher orders (degree > 2). Nevertheless, the numerical stability might weaken the generalization.  
 
 
 ## An Efficient Optimization Criterion

chapter_recommender-systems/index.md

@@ -4,7 +4,10 @@
 
 **Shuai Zhang** (*Amazon*), **Aston Zhang** (*Amazon*), and **Yi Tay** (*Nanyang Technological University*)
 
-Recommender systems are widely employed in industry and are ubiquitous in our daily lives. These systems are utilized in a number of areas such as online shopping sites (e.g., amazon.com), music/movie services site (e.g., Netflix and Spotify), mobile application stores (e.g., IOS app store and google play), online advertising, just to name a few. As such, recommender systems are central to not only our everyday lives but also highly critical to an amazing user experience.
+Recommender systems are widely employed in industry and are ubiquitous in our daily lives. These systems are utilized in a number of areas such as online shopping sites (e.g., amazon.com), music/movie services site (e.g., Netflix and Spotify), mobile application stores (e.g., IOS app store and google play), online advertising, just to name a few. 
+
+The major goal of recommeder systems is to help users discover relevant items such as movies to watch, text to read or products to buy, so as to create a delightful user experience. Moreover, recommeder systems are among the most powerful machine learning systems that online retailers implement in order to drive incremental revenue. Recommender systems are replacements of search engines by reducing the efforts in proactive searches and suprising users with offers they never serached for. Many companies managed to position themselves ahead of their competitors with the help of more effective recommender systems. As such, recommender systems are central to not only our everyday lives but also highly indispensable in some industries.
+
 
 In this chapter, we will cover the fundamentals and advancements of recommender systems, along with exploring some common fundamental techniques for building recommender systems with different data sources available and their implementations. Specifically, you will learn how to predict the rating a user might give to a prospective item, how to generate a recommendation list of items and how to predict the click-through rate from abundant features. These tasks are commonplace in real-world applications. By studying this chapter, you will get hands-on experience pertaining to solving real world recommendation problems with not only classical methods but the more advanced deep learning based models as well.
 

chapter_recommender-systems/mf.md

@@ -1,6 +1,6 @@
 # Matrix Factorization
 
-Matrix Factorization is a well-established algorithm in the recommender systems literature. The first version of matrix factorization model is proposed by Simon Funk in a famous [blog
+Matrix Factorization :cite:`Koren.Bell.Volinsky.2009` is a well-established algorithm in the recommender systems literature. The first version of matrix factorization model is proposed by Simon Funk in a famous [blog
 post](https://sifter.org/~simon/journal/20061211.html) in which he described the idea of factorizing the interaction matrix. It then became widely known due to the Netflix contest which was held in 2006. At that time, Netflix, a media-streaming and video-rental company, announced a contest to improve its recommender system performance. The best team that can improve on the Netflix baseline, i.e., Cinematch), by 10 percent would win a one million USD prize.  As such, this contest attracted
 a lot of attention to the field of recommender system research. Subsequently, the grand prize was won by the BellKor's Pragmatic Chaos team, a combined team of BellKor, Pragmatic Theory, and BigChaos (you do not need to worry about these algorithms now). Although the final score was the result of an ensemble solution (i.e., a combination of many algorithms), the matrix factorization algorithm played a critical role in the final blend. The technical report [the Netflix Grand Prize solution](https://www.netflixprize.com/assets/GrandPrize2009_BPC_BigChaos.pdf) provides a detailed introduction to the adopted model. In this section, we will dive into the details of the matrix factorization model and its implementation.
 
@@ -171,6 +171,3 @@ scores
 * Vary the size of latent factors. How does the size of latent factors influence the model performance?
 * Try different optimizers, learning rates, and weight decay rates.
 * Check the predicted rating scores of other users for a specific movie.
-
-## Reference
-* Koren, Yehuda, Robert Bell, and Chris Volinsky. "Matrix factorization techniques for recommender systems." Computer 8 (2009): 30-37.

chapter_recommender-systems/neumf.md

@@ -1,6 +1,6 @@
 # Neural Collaborative Filtering for Personalized Ranking
 
-This section moves beyond explicit feedback, introducing the neural collaborative filtering (NCF) framework for recommendation with implicit feedback. Implicit feedback is pervasive in recommender systems. Actions such as Clicks, buys, and watches are common implicit feedback which are easy to collect and indicative of users' preferences. The model we will introduce, titled NeuMF, short for neural matrix factorization, aims to address the personalized ranking task with implicit feedback. This model leverages the flexibility and non-linearity of neural networks to replace dot products of matrix factorization, aiming at enhancing the model expressiveness. In specific, this model is structured with two subnetworks including generalized matrix factorization (GMF) and multilayer perceptron (MLP) and models the interactions from two pathways instead of simple inner products. The outputs of these two networks are concatenated for the final prediction scores calculation. Unlike the rating prediction task in AutoRec, this model generates a ranked recommendation list to each user based on the implicit feedback. We will use the personalized ranking loss introduced in the last section to train this model. 
+This section moves beyond explicit feedback, introducing the neural collaborative filtering (NCF) framework for recommendation with implicit feedback. Implicit feedback is pervasive in recommender systems. Actions such as Clicks, buys, and watches are common implicit feedback which are easy to collect and indicative of users' preferences. The model we will introduce, titled NeuMF :cite:`He.Liao.Zhang.ea.2017`, short for neural matrix factorization, aims to address the personalized ranking task with implicit feedback. This model leverages the flexibility and non-linearity of neural networks to replace dot products of matrix factorization, aiming at enhancing the model expressiveness. In specific, this model is structured with two subnetworks including generalized matrix factorization (GMF) and multilayer perceptron (MLP) and models the interactions from two pathways instead of simple inner products. The outputs of these two networks are concatenated for the final prediction scores calculation. Unlike the rating prediction task in AutoRec, this model generates a ranked recommendation list to each user based on the implicit feedback. We will use the personalized ranking loss introduced in the last section to train this model. 
 
 ## The NeuMF model
 

chapter_recommender-systems/ranking.md

@@ -6,7 +6,7 @@ To this end, a class of recommendation models targeting at generating ranked rec
 
 ## Bayesian Personalized Ranking Loss and its Implementation
 
-Bayesian personalized ranking (BPR) is a pairwise personalized ranking loss that is derived from the maximum posterior estimator. It has been widely used in many existing recommendation models. The training data of BPR consists of both positive and negative pairs (missing values). It assumes that the user prefers the positive item over all other non-observed items.
+Bayesian personalized ranking (BPR) :cite:`Rendle.Freudenthaler.Gantner.ea.2009` is a pairwise personalized ranking loss that is derived from the maximum posterior estimator. It has been widely used in many existing recommendation models. The training data of BPR consists of both positive and negative pairs (missing values). It assumes that the user prefers the positive item over all other non-observed items.
 
 In formal, the training data is constructed by tuples in the form of $(u, i, j)$, which represents that the user $u$ prefers the item $i$ over the item $j$. The Bayesian formulation of BPR which aims to maximize the posterior probability is given below: