Learning to Rank

Contents

Overview

Often in the context of information retrieval, learning-to-rank aims to train a model that arranges a set of query results into an ordered list [1]. For supervised learning-to-rank, the predictors are sample documents encoded as feature matrix, and the labels are relevance degree for each sample. Relevance degree can be multi-level (graded) or binary (relevant or not). The training samples are often grouped by their query index with each query group containing multiple query results.

XGBoost implements learning to rank through a set of objective functions and performance metrics. The default objective is rank:ndcg based on the LambdaMART [2] algorithm, which in turn is an adaptation of the LambdaRank [3] framework to gradient boosting trees. For a history and a summary of the algorithm, see [5]. The implementation in XGBoost features deterministic GPU computation, distributed training, position debiasing and two different pair construction strategies.

Training with the Pairwise Objective

LambdaMART is a pairwise ranking model, meaning that it compares the relevance degree for every pair of samples in a query group and calculate a proxy gradient for each pair. The default objective rank:ndcg is using the surrogate gradient derived from the ndcg metric. To train a XGBoost model, we need an additional sorted array called qid for specifying the query group of input samples. An example input would look like this:

QID

Label

Features

1

0

\(x_1\)

1

1

\(x_2\)

1

0

\(x_3\)

2

0

\(x_4\)

2

1

\(x_5\)

2

1

\(x_6\)

2

1

\(x_7\)

Notice that the samples are sorted based on their query index in a non-decreasing order. In the above example, the first three samples belong to the first query and the next four samples belong to the second. For the sake of simplicity, we will use a synthetic binary learning-to-rank dataset in the following code snippets, with binary labels representing whether the result is relevant or not, and randomly assign the query group index to each sample. For an example that uses a real world dataset, please see Getting started with learning to rank.

from sklearn.datasets import make_classification
import numpy as np

import xgboost as xgb

# Make a synthetic ranking dataset for demonstration
seed = 1994
X, y = make_classification(random_state=seed)
rng = np.random.default_rng(seed)
n_query_groups = 3
qid = rng.integers(0, n_query_groups, size=X.shape[0])

# Sort the inputs based on query index
sorted_idx = np.argsort(qid)
X = X[sorted_idx, :]
y = y[sorted_idx]
qid = qid[sorted_idx]

The simplest way to train a ranking model is by using the scikit-learn estimator interface. Continuing the previous snippet, we can train a simple ranking model without tuning:

ranker = xgb.XGBRanker(tree_method="hist", lambdarank_num_pair_per_sample=8, objective="rank:ndcg", lambdarank_pair_method="topk")
ranker.fit(X, y, qid=qid[sorted_idx])

Please note that, as of writing, there’s no learning-to-rank interface in scikit-learn. As a result, the xgboost.XGBRanker class does not fully conform the scikit-learn estimator guideline and can not be directly used with some of its utility functions. For instances, the auc_score and ndcg_score in scikit-learn don’t consider query group information nor the pairwise loss. Most of the metrics are implemented as part of XGBoost, but to use scikit-learn utilities like sklearn.model_selection.cross_validation(), we need to make some adjustments in order to pass the qid as an additional parameter for xgboost.XGBRanker.score(). Given a data frame X (either pandas or cuDF), add the column qid as follows:

df = pd.DataFrame(X, columns=[str(i) for i in range(X.shape[1])])
df["qid"] = qid[sorted_idx]
ranker.fit(df, y)  # No need to pass qid as a separate argument

from sklearn.model_selection import StratifiedGroupKFold, cross_val_score
# Works with cv in scikit-learn, along with HPO utilities like GridSearchCV
kfold = StratifiedGroupKFold(shuffle=False)
cross_val_score(ranker, df, y, cv=kfold, groups=df.qid)

The above snippets build a model using LambdaMART with the NDCG@8 metric. The outputs of a ranker are relevance scores:

scores = ranker.predict(X)
sorted_idx = np.argsort(scores)[::-1]
# Sort the relevance scores from most relevant to least relevant
scores = scores[sorted_idx]

Position Bias

Added in version 2.0.0.

Note

The feature is considered experimental. This is a heated research area, and your input is much appreciated!

Obtaining real relevance degrees for query results is an expensive and strenuous, requiring human labelers to label all results one by one. When such labeling task is infeasible, we might want to train the learning-to-rank model on user click data instead, as it is relatively easy to collect. Another advantage of using click data directly is that it can reflect the most up-to-date user preferences [1]. However, user clicks are often biased, as users tend to choose results that are displayed in higher positions. User clicks are also noisy, where users might accidentally click on irrelevant documents. To ameliorate these issues, XGBoost implements the Unbiased LambdaMART [4] algorithm to debias the position-dependent click data. The feature can be enabled by the lambdarank_unbiased parameter; see Parameters for learning to rank (rank:ndcg, rank:map, rank:pairwise) for related options and Getting started with learning to rank for a worked example with simulated user clicks.

Loss

XGBoost implements different LambdaMART objectives based on different metrics. We list them here as a reference. Other than those used as objective function, XGBoost also implements metrics like pre (for precision) for evaluation. See parameters for available options and the following sections for how to choose these objectives based of the amount of effective pairs.

  • NDCG

Normalized Discounted Cumulative Gain NDCG can be used with both binary relevance and multi-level relevance. If you are not sure about your data, this metric can be used as the default. The name for the objective is rank:ndcg.

  • MAP

Mean average precision MAP is a binary measure. It can be used when the relevance label is 0 or 1. The name for the objective is rank:map.

  • Pairwise

The LambdaMART algorithm scales the logistic loss with learning to rank metrics like NDCG in the hope of including ranking information into the loss function. The rank:pairwise loss is the original version of the pairwise loss, also known as the RankNet loss [7] or the pairwise logistic loss. Unlike the rank:map and the rank:ndcg, no scaling is applied (\(|\Delta Z_{ij}| = 1\)).

Whether scaling with a LTR metric is actually more effective is still up for debate; [8] provides a theoretical foundation for general lambda loss functions and some insights into the framework.

Constructing Pairs

There are two implemented strategies for constructing document pairs for \(\lambda\)-gradient calculation. The first one is the mean method, another one is the topk method. The preferred strategy can be specified by the lambdarank_pair_method parameter.

For the mean strategy, XGBoost samples lambdarank_num_pair_per_sample pairs for each document in a query list. For example, given a list of 3 documents and lambdarank_num_pair_per_sample is set to 2, XGBoost will randomly sample 6 pairs, assuming the labels for these documents are different. On the other hand, if the pair method is set to topk, XGBoost constructs about \(k \times |query|\) number of pairs with \(|query|\) pairs for each sample at the top \(k = lambdarank\_num\_pair\) position. The number of pairs counted here is an approximation since we skip pairs that have the same label.

Obtaining Good Result

Learning to rank is a sophisticated task and an active research area. It’s not trivial to train a model that generalizes well. There are multiple loss functions available in XGBoost along with a set of hyperparameters. This section contains some hints for how to choose hyperparameters as a starting point. One can further optimize the model by tuning these hyperparameters.

The first question would be how to choose an objective that matches the task at hand. If your input data has multi-level relevance degrees, then either rank:ndcg or rank:pairwise should be used. However, when the input has binary labels, we have multiple options based on the target metric. [6] provides some guidelines on this topic and users are encouraged to see the analysis done in their work. The choice should be based on the number of effective pairs, which refers to the number of pairs that can generate non-zero gradient and contribute to training. LambdaMART with MRR has the least amount of effective pairs as the \(\lambda\)-gradient is only non-zero when the pair contains a non-relevant document ranked higher than the top relevant document. As a result, it’s not implemented in XGBoost. Since NDCG is a multi-level metric, it usually generate more effective pairs than MAP.

However, when there are sufficiently many effective pairs, it’s shown in [6] that matching the target metric with the objective is of significance. When the target metric is MAP and you are using a large dataset that can provide a sufficient amount of effective pairs, rank:map can in theory yield higher MAP value than rank:ndcg.

The consideration of effective pairs also applies to the choice of pair method (lambdarank_pair_method) and the number of pairs for each sample (lambdarank_num_pair_per_sample). For example, the mean-NDCG considers more pairs than NDCG@10, so the former generates more effective pairs and provides more granularity than the latter. Also, using the mean strategy can help the model generalize with random sampling. However, one might want to focus the training on the top \(k\) documents instead of using all pairs, to better fit their real-world application.

When using the mean strategy for generating pairs, where the target metric (like NDCG) is computed over the whole query list, users can specify how many pairs should be generated per each document, by setting the lambdarank_num_pair_per_sample. XGBoost will randomly sample lambdarank_num_pair_per_sample pairs for each element in the query group (\(|pairs| = |query| \times num\_pairsample\)). Often, setting it to 1 can produce reasonable results. In cases where performance is inadequate due to insufficient number of effective pairs being generated, set lambdarank_num_pair_per_sample to a higher value. As more document pairs are generated, more effective pairs will be generated as well.

On the other hand, if you are prioritizing the top \(k\) documents, the lambdarank_num_pair_per_sample should be set slightly higher than \(k\) (with a few more documents) to obtain a good training result. Lastly, XGBoost employs additional regularization for learning to rank objectives, which can be disabled by setting the lambdarank_normalization to False.

Summary If you have large amount of training data:

  • Use the target-matching objective.

  • Choose the topk strategy for generating document pairs (if it’s appropriate for your application).

On the other hand, if you have comparatively small amount of training data:

  • Select NDCG or the RankNet loss (rank:pairwise).

  • Choose the mean strategy for generating document pairs, to obtain more effective pairs.

For any method chosen, you can modify lambdarank_num_pair_per_sample to control the amount of pairs generated.

Distributed Training

XGBoost implements distributed learning-to-rank with integration of multiple frameworks including Dask, Spark, and PySpark. The interface is similar to the single-node counterpart. Please refer to document of the respective XGBoost interface for details. Scattering a query group onto multiple workers is theoretically sound but can affect the model accuracy. For most of the use cases, the small discrepancy is not an issue, as the amount of training data is usually large when distributed training is used. As a result, users don’t need to partition the data based on query groups. As long as each data partition is correctly sorted by query IDs, XGBoost can aggregate sample gradients accordingly.

Reproducible Result

Like any other tasks, XGBoost should generate reproducible results given the same hardware and software environments (and data partitions, if distributed interface is used). Even when the underlying environment has changed, the result should still be consistent. However, when the lambdarank_pair_method is set to mean, XGBoost uses random sampling, and results may differ depending on the platform used. The random number generator used on Windows (Microsoft Visual C++) is different from the ones used on other platforms like Linux (GCC, Clang) [1], so the output varies significantly between these platforms.

References

[1] Tie-Yan Liu. 2009. “Learning to Rank for Information Retrieval”. Found. Trends Inf. Retr. 3, 3 (March 2009), 225–331.

[2] Christopher J. C. Burges, Robert Ragno, and Quoc Viet Le. 2006. “Learning to rank with nonsmooth cost functions”. In Proceedings of the 19th International Conference on Neural Information Processing Systems (NIPS’06). MIT Press, Cambridge, MA, USA, 193–200.

[3] Wu, Q., Burges, C.J.C., Svore, K.M. et al. “Adapting boosting for information retrieval measures”. Inf Retrieval 13, 254–270 (2010).

[4] Ziniu Hu, Yang Wang, Qu Peng, Hang Li. “Unbiased LambdaMART: An Unbiased Pairwise Learning-to-Rank Algorithm”. Proceedings of the 2019 World Wide Web Conference.

[5] Burges, Chris J.C. “From RankNet to LambdaRank to LambdaMART: An Overview”. MSR-TR-2010-82

[6] Pinar Donmez, Krysta M. Svore, and Christopher J.C. Burges. 2009. “On the local optimality of LambdaRank”. In Proceedings of the 32nd international ACM SIGIR conference on Research and development in information retrieval (SIGIR ‘09). Association for Computing Machinery, New York, NY, USA, 460–467.

[7] Chris Burges, Tal Shaked, Erin Renshaw, Ari Lazier, Matt Deeds, Nicole Hamilton, and Greg Hullender. 2005. “Learning to rank using gradient descent”. In Proceedings of the 22nd international conference on Machine learning (ICML ‘05). Association for Computing Machinery, New York, NY, USA, 89–96.

[8] Xuanhui Wang and Cheng Li and Nadav Golbandi and Mike Bendersky and Marc Najork. 2018. “The LambdaLoss Framework for Ranking Metric Optimization”. Proceedings of The 27th ACM International Conference on Information and Knowledge Management (CIKM ‘18).