We propose two novel model architectures for computing continuous vector representations of words from very large data sets. The quality of these representations is measured in a word similarity task, and the results are compared to the previously best performing techniques based on different types of neural networks. We observe large improvements in accuracy at much lower computational cost, i.e. it takes less than a day to learn high quality word vectors from a 1.6 billion words data set. Furthermore, we show that these vectors provide state-of-the-art performance on our test set for measuring syntactic and semantic word similarities.

Efficient Estimation of Word Representations in Vector Space

The tutorial starts with an overview of the concepts of VC dimension and structural risk minimization. We then describe linear Support Vector Machines (SVMs) for separable and non-separable data, working through a non-trivial example in detail. We describe a mechanical analogy, and discuss when SVM solutions are unique and when they are global. We describe how support vector training can be practically implemented, and discuss in detail the kernel mapping technique which is used to construct SVM solutions which are nonlinear in the data. We show how Support Vector machines can have very large (even infinite) VC dimension by computing the VC dimension for homogeneous polynomial and Gaussian radial basis function kernels. While very high VC dimension would normally bode ill for generalization performance, and while at present there exists no theory which shows that good generalization performance is guaranteed for SVMs, there are several arguments which support the observed high accuracy of SVMs, which we review. Results of some experiments which were inspired by these arguments are also presented. We give numerous examples and proofs of most of the key theorems. There is new material, and I hope that the reader will find that even old material is cast in a fresh light.

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A Tutorial on Support Vector Machines for Pattern Recognition

Tree boosting is a highly effective and widely used machine learning method. In this paper, we describe a scalable end-to-end tree boosting system called XGBoost, which is used widely by data scientists to achieve state-of-the-art results on many machine learning challenges. We propose a novel sparsity-aware algorithm for sparse data and weighted quantile sketch for approximate tree learning. More importantly, we provide insights on cache access patterns, data compression and sharding to build a scalable tree boosting system. By combining these insights, XGBoost scales beyond billions of examples using far fewer resources than existing systems.

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XGBoost: A Scalable Tree Boosting System

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

LambdaMART is the boosted tree version of LambdaRank, which is based on RankNet. RankNet, LambdaRank, and LambdaMART have proven to be very successful algorithms for solving real world ranking problems: for example an ensemble of LambdaMART rankers won Track 1 of the 2010 Yahoo! Learning To Rank Challenge. The details of these algorithms are spread across several papers and reports, and so here we give a self-contained, detailed and complete description of them.

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From RankNet to LambdaRank to LambdaMART: An Overview

We present MCTest, a freely available set of stories and associated questions intended for research on the machine comprehension of text. Previous work on machine comprehension (e.g., semantic modeling) has made great strides, but primarily focuses either on limited-domain datasets, or on solving a more restricted goal (e.g., open-domain relation extraction). In contrast, MCTest requires machines to answer multiple-choice reading comprehension questions about fictional stories, directly tackling the high-level goal of open-domain machine comprehension. Reading comprehension can test advanced abilities such as causal reasoning and understanding the world, yet, by being multiple-choice, still provide a clear metric. By being fictional, the answer typically can be found only in the story itself. The stories and questions are also carefully limited to those a young child would understand, reducing the world knowledge that is required for the task. We present the scalable crowd-sourcing methods that allow us to cheaply construct a dataset of 500 stories and 2000 questions. By screening workers (with grammar tests) and stories (with grading), we have ensured that the data is the same quality as another set that we manually edited, but at one tenth the editing cost. By being open-domain, yet carefully restricted, we hope MCTest will serve to encourage research and provide a clear metric for advancement on the machine comprehension of text. 1 Reading Comprehension A major goal for NLP is for machines to be able to understand text as well as people. Several research disciplines are focused on this problem: for example, information extraction, relation extraction, semantic role labeling, and recognizing textual entailment. Yet these techniques are necessarily evaluated individually, rather than by how much they advance us towards the end goal. On the other hand, the goal of semantic parsing is the machine comprehension of text (MCT), yet its evaluation requires adherence to a specific knowledge representation, and it is currently unclear what the best representation is, for open-domain text. We believe that it is useful to directly tackle the top-level task of MCT. For this, we need a way to measure progress. One common method for evaluating someone’s understanding of text is by giving them a multiple-choice reading comprehension test. This has the advantage that it is objectively gradable (vs. essays) yet may test a range of abilities such as causal or counterfactual reasoning, inference among relations, or just basic understanding of the world in which the passage is set. Therefore, we propose a multiple-choice reading comprehension task as a way to evaluate progress on MCT. We have built a reading comprehension dataset containing 500 fictional stories, with 4 multiple choice questions per story. It was built using methods which can easily scale to at least 5000 stories, since the stories were created, and the curation was done, using crowd sourcing almost entirely, at a total of $4.00 per story. We plan to periodically update the dataset to ensure that methods are not overfitting to the existing data. The dataset is open-domain, yet restricted to concepts and words that a 7 year old is expected to understand. This task is still beyond the capability of today’s computers and algorithms.

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MCTest: A Challenge Dataset for the Open-Domain Machine Comprehension of Text

The quality measures used in information retrieval are particularly difficult to optimize directly, since they depend on the model scores only through the sorted order of the documents returned for a given query. Thus, the derivatives of the cost with respect to the model parameters are either zero, or are undefined. In this paper, we propose a class of simple, flexible algorithms, called LambdaRank, which avoids these difficulties by working with implicit cost functions. We describe LambdaRank using neural network models, although the idea applies to any differentiable function class. We give necessary and sufficient conditions for the resulting implicit cost function to be convex, and we show that the general method has a simple mechanical interpretation. We demonstrate significantly improved accuracy, over a state-of-the-art ranking algorithm, on several datasets. We also show that LambdaRank provides a method for significantly speeding up the training phase of that ranking algorithm. Although this paper is directed towards ranking, the proposed method can be extended to any non-smooth and multivariate cost functions.

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Learning to Rank with Nonsmooth Cost Functions

We present a new ranking algorithm that combines the strengths of two previous methods: boosted tree classification, and LambdaRank, which has been shown to be empirically optimal for a widely used information retrieval measure. Our algorithm is based on boosted regression trees, although the ideas apply to any weak learners, and it is significantly faster in both train and test phases than the state of the art, for comparable accuracy. We also show how to find the optimal linear combination for any two rankers, and we use this method to solve the line search problem exactly during boosting. In addition, we show that starting with a previously trained model, and boosting using its residuals, furnishes an effective technique for model adaptation, and we give significantly improved results for a particularly pressing problem in web search--training rankers for markets for which only small amounts of labeled data are available, given a ranker trained on much more data from a larger market.

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Adapting boosting for information retrieval measures

A Support Vector Machine SVM is a uni versal learning machine whose decision sur face is parameterized by a set of support vec tors and by a set of corresponding weights An SVM is also characterized by a kernel function Choice of the kernel determines whether the resulting SVM is a polynomial classi er a two layer neural network a ra dial basis function machine or some other learning machine SVMs are currently considerably slower in test phase than other approaches with sim ilar generalization performance To address this we present a general method to signif icantly decrease the complexity of the deci sion rule obtained using an SVM The pro posed method computes an approximation to the decision rule in terms of a reduced set of vectors These reduced set vectors are not support vectors and can in some cases be computed analytically We give ex perimental results for three pattern recogni tion problems The results show that the method can decrease the computational com plexity of the decision rule by a factor of ten with no loss in generalization perfor mance making the SVM test speed com petitive with that of other methods Fur ther the method allows the generalization performance complexity trade o to be di rectly controlled The proposed method is not speci c to pattern recognition and can be applied to any problem where the Sup port Vector algorithm is used for example regression INTRODUCTION SUPPORT VECTOR MACHINES Consider a two class classi er for which the decision rule takes the form

Christopher J. C. Burges

Papers

From RankNet to LambdaRank to LambdaMART: An Overview

MCTest: A Challenge Dataset for the Open-Domain Machine Comprehension of Text

Learning to Rank with Nonsmooth Cost Functions

Adapting boosting for information retrieval measures

Simplified support vector decision rules