Neural Learning to Rank

Workshop on Recommender Systems
HEC Montréal, August 20-23, 2019
Neural Learning to Rank
Bhaskar Mitra
Principal Applied Scientist, Microsoft
PhD student, University College London
@UnderdogGeek

Objectives
A quick recap of neural networks
The fundamentals of learning to rank
A quick recap of deep neural networks
Learning to rank with deep neural networks

Reading material
An Introduction to
Neural Information Retrieval
Foundations and Trends® in Information Retrieval
(December 2018)
Download PDF: http://bit.ly/fntir-neural

Most information retrieval
(IR) systems present a ranked
list of retrieved artifacts

Learning to Rank (LTR)
”... the task to automatically construct a
ranking model using training data, such
that the model can sort new objects
according to their degrees of relevance,
preference, or importance.”
- Liu [2009]
Tie-Yan Liu. Learning to rank for information retrieval. Foundation and Trends in Information Retrieval, 2009.
Image source: https://storage.googleapis.com/pub-tools-public-publication-data/pdf/45530.pdf

A quick recap of
neural networks

Neural networks
Chains of parameterized linear transforms (e.g., multiply weight, add
bias) followed by non-linear functions (σ)
Popular choices for σ:
Parameters trained using backpropagation
E2E training over millions of samples in batched mode
Many choices of architecture and hyper-parameters
Non-linearity
Input
Linear transform
Non-linearity
Linear transform
Predicted output
forwardpass
backwardpass
Expected output
loss
Tanh ReLU

Goal: iteratively update the learnable parameters such that the loss 𝑙 is minimized
Compute the gradient of the loss 𝑙 w.r.t. each parameter (e.g., 𝑤1)
𝜕𝑙
𝜕𝑤1
=
𝜕𝑙
𝜕𝑦2
×
𝜕𝑦2
𝜕𝑦1
×
𝜕𝑦1
𝜕𝑤1
Update the parameter value based on the gradient with 𝜂 as the learning rate
𝑤1
𝑛𝑒𝑤
= 𝑤1
𝑜𝑙𝑑
− 𝜂 ×
𝜕𝑙
𝜕𝑤1
Stochastic Gradient Descent (SGD)
Task: regression
Training data: 𝑥, 𝑦 pairs
Model: NN (1 feature, 1 hidden layer, 1 hidden node)
Learnable parameters: 𝑤1, 𝑏1, 𝑤2, 𝑏2
𝑥 𝑦1 𝑦2
𝑙
𝑡𝑎𝑛ℎ 𝑤1. 𝑥 + 𝑏1
𝑦 − 𝑦2
2
𝑦
𝑡𝑎𝑛ℎ 𝑤2. 𝑦1 + 𝑏2
…and repeat

𝜕𝑙
𝜕𝑤1
=
𝜕 𝑦 − 𝑦2
2
𝜕𝑦2
×
𝜕𝑦2
𝜕𝑦1
×
𝜕𝑦1
𝜕𝑤1
𝑤1
𝑛𝑒𝑤
= 𝑤1
𝑜𝑙𝑑
− 𝜂 ×
𝜕𝑙
𝜕𝑤1
Task: regression
𝑥 𝑦1 𝑦2
𝑙
𝑦 − 𝑦2
2
𝑦
…and repeat

𝜕𝑙
𝜕𝑤1
= −2 × 𝑦 − 𝑦2 ×
𝜕𝑦2
𝜕𝑦1
×
𝜕𝑦1
𝜕𝑤1
𝑤1
𝑛𝑒𝑤
= 𝑤1
𝑜𝑙𝑑
− 𝜂 ×
𝜕𝑙
𝜕𝑤1
Task: regression
𝑥 𝑦1 𝑦2
𝑙
𝑦 − 𝑦2
2
𝑦
…and repeat

𝜕𝑙
𝜕𝑤1
= −2 × 𝑦 − 𝑦2 ×
𝜕𝑡𝑎𝑛ℎ 𝑤2. 𝑦1 + 𝑏2
𝜕𝑦1
×
𝜕𝑦1
𝜕𝑤1
𝑤1
𝑛𝑒𝑤
= 𝑤1
𝑜𝑙𝑑
− 𝜂 ×
𝜕𝑙
𝜕𝑤1
Task: regression
𝑥 𝑦1 𝑦2
𝑙
𝑦 − 𝑦2
2
𝑦
…and repeat

𝜕𝑙
𝜕𝑤1
= −2 × 𝑦 − 𝑦2 × 1 − 𝑡𝑎𝑛ℎ2
𝑤2. 𝑥 + 𝑏2 × 𝑤2 ×
𝜕𝑦1
𝜕𝑤1
𝑤1
𝑛𝑒𝑤
= 𝑤1
𝑜𝑙𝑑
− 𝜂 ×
𝜕𝑙
𝜕𝑤1
Task: regression
𝑥 𝑦1 𝑦2
𝑙
𝑦 − 𝑦2
2
𝑦
…and repeat

𝜕𝑙
𝜕𝑤1
= −2 × 𝑦 − 𝑦2 × 1 − 𝑡𝑎𝑛ℎ2
𝑤2. 𝑥 + 𝑏2 × 𝑤2 ×
𝜕𝑡𝑎𝑛ℎ 𝑤1. 𝑥 + 𝑏1
𝜕𝑤1
𝑤1
𝑛𝑒𝑤
= 𝑤1
𝑜𝑙𝑑
− 𝜂 ×
𝜕𝑙
𝜕𝑤1
Task: regression
𝑥 𝑦1 𝑦2
𝑙
𝑦 − 𝑦2
2
𝑦
…and repeat

𝜕𝑙
𝜕𝑤1
= −2 × 𝑦 − 𝑦2 × 1 − 𝑡𝑎𝑛ℎ2
𝑤2. 𝑥 + 𝑏2 × 𝑤2 × 1 − 𝑡𝑎𝑛ℎ2
𝑤1. 𝑥 + 𝑏1 × 𝑥
𝑤1
𝑛𝑒𝑤
= 𝑤1
𝑜𝑙𝑑
− 𝜂 ×
𝜕𝑙
𝜕𝑤1
Task: regression
𝑥 𝑦1 𝑦2
𝑙
𝑦 − 𝑦2
2
𝑦
…and repeat

Neural models for
non-ranking tasks

The softmax function
In neural classification models, the softmax function is popularly used
to normalize the neural network output scores across all the classes

Cross entropy
The cross entropy between two
probability distributions 𝑝 and 𝑞
over a discrete set of events is
given by,
If 𝑝 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 = 1and 𝑝𝑖 = 0 for all
other values of 𝑖 then,

Cross entropy with
softmax loss
Cross entropy with softmax is a popular loss
function for classification

Questions?

The fundamentals of
learning to rank

Problem formulation
LTR models represent a rankable item—e.g., a document or a movie or a
song—given some context—e.g., a user-issued query or user’s historical
interactions with other items—as a numerical vector 𝑥 ∈ ℝ 𝑛
The ranking model 𝑓: 𝑥 → ℝ is trained to map the vector to a real-valued
score such that relevant items are scored higher.

Examples of ranking metrics
Discounted Cumulative Gain (DCG)
𝐷𝐶𝐺@𝑘 =
𝑖=1
𝑘
2 𝑟𝑒𝑙𝑖
− 1
𝑙𝑜𝑔2 𝑖 + 1
Reciprocal Rank (RR)
𝑅𝑅@𝑘 = max
1<𝑖<𝑘
𝑟𝑒𝑙𝑖
𝑖

Why is ranking challenging?
Rank based metrics, such as DCG or MRR, are
non-smooth/non-differentiable

Approaches
Pointwise approach
Relevance label 𝑦 𝑞,𝑑 is a number—derived from binary or graded human
judgments or implicit user feedback (e.g., CTR). Typically, a regression or
classification model is trained to predict 𝑦 𝑞,𝑑 given 𝑥 𝑞,𝑑.
Pairwise approach
Pairwise preference between documents for a query (𝑑𝑖 ≻ 𝑑𝑗 w.r.t. 𝑞) as
label. Reduces to binary classification to predict more relevant document.
Listwise approach
Directly optimize for rank-based metric, such as NDCG—difficult because
these metrics are often not differentiable w.r.t. model parameters.
Liu [2009] categorizes
different LTR approaches
based on training objectives:
Tie-Yan Liu. Learning to rank for information retrieval. Foundation and Trends in Information Retrieval, 2009.

Features
They can often be categorized as:
Query-independent or static features
e.g., incoming link count and document length
Query-dependent or dynamic features
e.g., BM25
Query-level features
e.g., query length
Traditional L2R models employ
hand-crafted features that
encode IR insights

Features
Tao Qin, Tie-Yan Liu, Jun Xu, and Hang Li. LETOR: A Benchmark Collection for Research on Learning to Rank for Information Retrieval, Information Retrieval Journal, 2010

Pointwise objectives
Regression loss
Given 𝑞, 𝑑 predict the value of 𝑦 𝑞,𝑑
e.g., square loss for binary or categorical
labels,
where, 𝑦 𝑞,𝑑 is the one-hot representation
[Fuhr, 1989] or the actual value [Cossock and
Zhang, 2006] of the label
Norbert Fuhr. Optimum polynomial retrieval functions based on the probability ranking principle. ACM TOIS, 1989.
David Cossock and Tong Zhang. Subset ranking using regression. In COLT, 2006.
labels
prediction
0 1 1

Pointwise objectives
Classification loss
Given 𝑞, 𝑑 predict the class 𝑦 𝑞,𝑑
e.g., cross-entropy with softmax over
categorical labels 𝑌 [Li et al., 2008],
where, 𝑠 𝑦 𝑞,𝑑
is the model’s score for label 𝑦 𝑞,𝑑
labels
prediction
0 1
Ping Li, Qiang Wu, and Christopher J Burges. Mcrank: Learning to rank using multiple classification and gradient boosting. In NIPS, 2008.

Pairwise objectives Pairwise loss generally has the following form [Chen et al., 2009],
where, 𝜙 can be,
• Hinge function 𝜙 𝑧 = 𝑚𝑎𝑥 0, 1 − 𝑧 [Herbrich et al., 2000]
• Exponential function 𝜙 𝑧 = 𝑒−𝑧
[Freund et al., 2003]
• Logistic function 𝜙 𝑧 = 𝑙𝑜𝑔 1 + 𝑒−𝑧
[Burges et al., 2005]
• Others…
Pairwise loss minimizes the average number of
inversions in ranking—i.e., 𝑑𝑖 ≻ 𝑑𝑗 w.r.t. 𝑞 but 𝑑𝑗 is
ranked higher than 𝑑𝑖
Given 𝑞, 𝑑𝑖, 𝑑𝑗 , predict the more relevant document
For 𝑞, 𝑑𝑖 and 𝑞, 𝑑𝑗 ,
Feature vectors: 𝑥𝑖 and 𝑥𝑗
Model scores: 𝑠𝑖 = 𝑓 𝑥𝑖 and 𝑠𝑗 = 𝑓 𝑥𝑗
Wei Chen, Tie-Yan Liu, Yanyan Lan, Zhi-Ming Ma, and Hang Li. Ranking measures and loss functions in learning to rank. In NIPS, 2009.
Ralf Herbrich, Thore Graepel, and Klaus Obermayer. Large margin rank boundaries for ordinal regression. 2000.
Yoav Freund, Raj Iyer, Robert E Schapire, and Yoram Singer. An efficient boosting algorithm for combining preferences. In JMLR, 2003.
Chris Burges, Tal Shaked, Erin Renshaw, Ari Lazier, Matt Deeds, Nicole Hamilton, and Greg Hullender. Learning to rank using gradient descent. In ICML, 2005.

Pairwise objectives
RankNet loss
Pairwise loss function proposed by Burges et al. [2005]—an industry favourite
[Burges, 2015]
Predicted probabilities: 𝑝𝑖𝑗 = 𝑝 𝑠𝑖 > 𝑠𝑗 ≡
𝑒 𝛾.𝑠 𝑖
𝑒 𝛾.𝑠 𝑖 +𝑒
𝛾.𝑠 𝑗
=
1
1+𝑒
−𝛾. 𝑠 𝑖−𝑠 𝑗
Desired probabilities: 𝑝𝑖𝑗 = 1 and 𝑝𝑗𝑖 = 0
Computing cross-entropy between 𝑝 and 𝑝
ℒ 𝑅𝑎𝑛𝑘𝑁𝑒𝑡 = − 𝑝𝑖𝑗. 𝑙𝑜𝑔 𝑝𝑖𝑗 − 𝑝𝑗𝑖. 𝑙𝑜𝑔 𝑝𝑗𝑖 = −𝑙𝑜𝑔 𝑝𝑖𝑗 = 𝑙𝑜𝑔 1 + 𝑒−𝛾. 𝑠 𝑖−𝑠 𝑗
pairwise
preference
score
0 1
Chris Burges, Tal Shaked, Erin Renshaw, Ari Lazier, Matt Deeds, Nicole Hamilton, and Greg Hullender. Learning to rank using gradient descent. In ICML, 2005.
Chris Burges. RankNet: A ranking retrospective. https://www.microsoft.com/en-us/research/blog/ranknet-a-ranking-retrospective/. 2015.

A generalized cross-entropy loss
An alternative loss function assumes a single relevant document 𝑑+ and compares it
against the full collection 𝐷
Predicted probabilities: p 𝑑+|𝑞 =
𝑒 𝛾.𝑠 𝑞,𝑑+
𝑑∈𝐷 𝑒 𝛾.𝑠 𝑞,𝑑
The cross-entropy loss is then given by,
ℒ 𝐶𝐸 𝑞, 𝑑+, 𝐷 = −𝑙𝑜𝑔 p 𝑑+|𝑞 = −𝑙𝑜𝑔
𝑒 𝛾.𝑠 𝑞,𝑑+
𝑑∈𝐷 𝑒 𝛾.𝑠 𝑞,𝑑
Computing the softmax over the full collection is prohibitively expensive—LTR models
typically consider few negative candidates [Huang et al., 2013, Shen et al., 2014, Mitra et al., 2017]
Po-Sen Huang, Xiaodong He, Jianfeng Gao, Li Deng, Alex Acero, and Larry Heck. Learning deep structured semantic models for web search using clickthrough data. In CIKM, 2013.
Yelong Shen, Xiaodong He, Jianfeng Gao, Li Deng, and Gregoire Mesnil. A latent semantic model with convolutional-pooling structure for information retrieval. In CIKM, 2014.
Bhaskar Mitra, Fernando Diaz, and Nick Craswell. Learning to match using local and distributed representations of text for web search. In WWW, 2017.

Blue: relevant Gray: non-relevant
NDCG and ERR higher for left but pairwise
errors less for right
Due to strong position-based discounting in
IR measures, errors at higher ranks are much
more problematic than at lower ranks
But listwise metrics are non-continuous and
non-differentiable
LISTWISE
OBJECTIVES
Christopher JC Burges. From ranknet to lambdarank to lambdamart: An overview. Learning, 2010.
[Burges, 2010]

Listwise objectives
Burges et al. [2006] make two observations:
1. To train a model we don’t need the costs
themselves, only the gradients (of the costs
w.r.t model scores)
2. It is desired that the gradient be bigger for
pairs of documents that produces a bigger
impact in NDCG by swapping positions
Christopher JC Burges, Robert Ragno, and Quoc Viet Le. Learning to rank with nonsmooth cost functions. In NIPS, 2006.
LambdaRank loss
Multiply actual gradients with the change in
NDCG by swapping the rank positions of the
two documents

Listwise objectives
According to the Luce model [Luce, 2005],
given four items 𝑑1, 𝑑2, 𝑑3, 𝑑4 the probability
of observing a particular rank-order, say
𝑑2, 𝑑1, 𝑑4, 𝑑3 , is given by:
where, 𝜋 is a particular permutation and 𝜙 is a
transformation (e.g., linear, exponential, or
sigmoid) over the score 𝑠𝑖 corresponding to
item 𝑑𝑖
R Duncan Luce. Individual choice behavior. 1959.
Zhe Cao, Tao Qin, Tie-Yan Liu, Ming-Feng Tsai, and Hang Li. Learning to rank: from pairwise approach to listwise approach. In ICML, 2007.
Fen Xia, Tie-Yan Liu, Jue Wang, Wensheng Zhang, and Hang Li. Listwise approach to learning to rank: theory and algorithm. In ICML, 2008.
ListNet loss
Cao et al. [2007] propose to compute the
probability distribution over all possible
permutations based on model score and ground-
truth labels. The loss is then given by the K-L
divergence between these two distributions.
This is computationally very costly, computing
permutations of only the top-K items makes it
slightly less prohibitive.
ListMLE loss
Xia et al. [2008] propose to compute the
probability of the ideal permutation based on the
ground truth. However, with categorical labels
more than one permutation is possible.

Listwise objectives
Mingrui Wu, Yi Chang, Zhaohui Zheng, and Hongyuan Zha. Smoothing DCG for learning to rank: A novel approach using smoothed hinge functions. In CIKM, 2009.
Smooth DCG
Wu et al. [2009] compute a “smooth” rank of
documents as a function of their scores
This “smooth” rank can be plugged into a
ranking metric, such as MRR or DCG, to
produce a smooth ranking loss

A quick recap of
deep neural networks

Types of vector representations
Local (or one-hot) representation
Every term in vocabulary T is represented by a
binary vector of length |T|, where one position in
the vector is set to one and the rest to zero
Distributed representation
Every term in vocabulary T is represented by a
real-valued vector of length k. The vector can be
sparse or dense. The vector dimensions may be
observed (e.g., hand-crafted features) or latent
(e.g., embedding dimensions).

Different modalities of input text representation

Shift-invariant
neural operations
Detecting a pattern in one part of the input space is similar to
detecting it in another
Leverage redundancy by moving a window over the whole
input space and then aggregate
On each instance of the window a kernel—also known as a
filter or a cell—is applied
Different aggregation strategies lead to different architectures

Convolution
Move the window over the input space each time applying
the same cell over the window
A typical cell operation can be,
ℎ = 𝜎 𝑊𝑋 + 𝑏
Full Input [words x in_channels]
Cell Input [window x in_channels]
Cell Output [1 x out_channels]
Full Output [1 + (words – window) / stride x out_channels]

Pooling
Move the window over the input space each time applying an
aggregate function over each dimension in within the window
ℎ𝑗 = 𝑚𝑎𝑥𝑖∈𝑤𝑖𝑛 𝑋𝑖,𝑗 𝑜𝑟 ℎ𝑗 = 𝑎𝑣𝑔𝑖∈𝑤𝑖𝑛 𝑋𝑖,𝑗
Full Input [words x channels]
Cell Input [window x channels]
Cell Output [1 x channels]
Full Output [1 + (words – window) / stride x channels]
max -pooling average -pooling

Convolution w/
Global Pooling
Stacking a global pooling layer on top of a convolutional layer
is a common strategy for generating a fixed length embedding
for a variable length text
Full Output [1 x out_channels]

Recurrent neural
network
Similar to a convolution layer but additional dependency on
previous hidden state
A simple cell operation shown below but others like LSTM and
GRUs are more popular in practice,
ℎ𝑖 = 𝜎 𝑊𝑋𝑖 + 𝑈ℎ𝑖−1 + 𝑏
Cell Input [window x in_channels] + [1 x out_channels]
Cell Output [1 x out_channels]
Full Output [1 x out_channels]

Learning to rank with
deep neural networks

Representation
learning for IR
Many IR scenarios—e.g., web search and content-based
filtering for recommender systems—involve matching
items based on their descriptions
Deep learning models can be useful
for learning good representation of
items for matching
i.e., LTR with raw inputs instead of
hand-engineered features

DNN for YouTube
recommendation
Input: user profile
Output: probability distribution over
items to be recommended
Paul Covington, Jay Adams, and Emre Sargin. Deep neural networks for youtube recommendations. In RecSys, 2016.

Siamese networks
Relevance estimated by cosine similarity
between item embeddings
Input: character trigraph counts (bag of
words assumption)
Minimizes cross-entropy loss against
randomly sampled negative documents
Po-Sen Huang, Xiaodong He, Jianfeng Gao, Li Deng, Alex Acero, and Larry Heck. Learning deep structured semantic models for web search using clickthrough data. In CIKM, 2013.

Wide and deep model
Deep model for representation
learning and wide model for
memorization
Heng-Tze Cheng, Levent Koc, Jeremiah Harmsen, Tal Shaked, et al. Wide & deep learning for recommender systems. In workshop on deep learning for recommender systems, 2016.

Lexical and semantic
matching networks
Mitra et al. [2016] argue that both lexical and
semantic matching is important for
document ranking
Duet model is a linear combination of two
DNNs—focusing on lexical and semantic
matching, respectively—jointly trained on
labelled data
code: http://bit.ly/duetv2code
Bhaskar Mitra, Fernando Diaz, and Nick Craswell. Learning to match using local and distributed representations of text for web search. In WWW, 2017.
GET THE CODE

Large scale pretrained
language models
BERT (and other large-scale unsupervised
language models) are demonstrating dramatic
performance improvements on many IR tasks
Jacob Devlin, Ming-Wei Chang, et al. Bert: Pre-training of deep bidirectional transformers for language understanding. In NAACL, 2018.
Nogueira, Rodrigo, and Kyunghyun Cho. Passage Re-ranking with BERT. In arXiv, 2019.

Dealing with
multiple fields
Real world items have multiple sources of
descriptions—creates unique challenges for
representation learning models
Hamed Zamani, Bhaskar Mitra, Xia Song, Nick Craswell, and Saurabh Tiwary. Neural ranking models with multiple document fields. In WSDM, 2018.
Juan Li, Zhicheng Dou, Yutao Zhu, Xiaochen Zuo, and Ji-Rong Wen. Deep cross-platform product matching in e-commerce. In IRJ, 2019.

Key takeaways
• Learning to Rank is effective on a broad range of IR tasks
• Optimization of non-smooth rank-based metrics is challenging but loss functions, such
as RankNet and LambdaRank, are effective in practice
• Learning to rank models can operate over hand-engineered features or employ deep
architectures to learn useful representations from raw input
• Large scale pretraining of language models demonstrate strong performance on tasks
that involve text matching

Thank you
@UnderdogGeek bmitra@microsoft.com

Neural Learning to Rank

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