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Joseph Bradley

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5 papers

1 author row

JMLR Journal 2016 Journal Article

Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence

Nihar B. Shah
Sivaraman Balakrishnan
Joseph Bradley
Abhay Parekh
Kannan Ramchandran
Martin J. Wainwright

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a latent vector $w^* \in \mathbb{R}^d$ that represents the âqualitiesâ of the $d$ items being compared; this class of models includes the two most widely used parametric models---the Bradley-Terry-Luce (BTL) and the Thurstone models. Working within a standard minimax framework, we provide tight upper and lower bounds on the optimal error in estimating the quality score vector $w^*$ under this class of models. The bounds depend on the topology of the comparison graph induced by the subset of pairs being compared, via the spectrum of the Laplacian of the comparison graph. Thus, in settings where the subset of pairs may be chosen, our results provide principled guidelines for making this choice. Finally, we compare these error rates to those under cardinal measurement models and show that the error rates in the ordinal and cardinal settings have identical scalings apart from constant pre- factors. [abs] [ pdf ][ bib ] &copy JMLR 2016. ( edit, beta )

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JMLR Journal 2016 Journal Article

MLlib: Machine Learning in Apache Spark

Xiangrui Meng
Joseph Bradley
Burak Yavuz
Evan Sparks
Shivaram Venkataraman
Davies Liu
Jeremy Freeman
DB Tsai

Apache Spark is a popular open-source platform for large-scale data processing that is well-suited for iterative machine learning tasks. In this paper we present MLlib, Spark's open- source distributed machine learning library. MLlib provides efficient functionality for a wide range of learning settings and includes several underlying statistical, optimization, and linear algebra primitives. Shipped with Spark, MLlib supports several languages and provides a high-level API that leverages Spark's rich ecosystem to simplify the development of end-to-end machine learning pipelines. MLlib has experienced a rapid growth due to its vibrant open-source community of over 140 contributors, and includes extensive documentation to support further growth and to let users quickly get up to speed. [abs] [ pdf ][ bib ] [ code ] [ webpage ] &copy JMLR 2016. ( edit, beta )

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NeurIPS Conference 2016 Conference Paper

Yggdrasil: An Optimized System for Training Deep Decision Trees at Scale

Firas Abuzaid
Joseph Bradley
Feynman Liang
Andrew Feng
Lee Yang
Matei Zaharia
Ameet Talwalkar

Deep distributed decision trees and tree ensembles have grown in importance due to the need to model increasingly large datasets. However, PLANET, the standard distributed tree learning algorithm implemented in systems such as \xgboost and Spark MLlib, scales poorly as data dimensionality and tree depths grow. We present Yggdrasil, a new distributed tree learning method that outperforms existing methods by up to 24x. Unlike PLANET, Yggdrasil is based on vertical partitioning of the data (i. e. , partitioning by feature), along with a set of optimized data structures to reduce the CPU and communication costs of training. Yggdrasil (1) trains directly on compressed data for compressible features and labels; (2) introduces efficient data structures for training on uncompressed data; and (3) minimizes communication between nodes by using sparse bitvectors. Moreover, while PLANET approximates split points through feature binning, Yggdrasil does not require binning, and we analytically characterize the impact of this approximation. We evaluate Yggdrasil against the MNIST 8M dataset and a high-dimensional dataset at Yahoo; for both, Yggdrasil is faster by up to an order of magnitude.

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NeurIPS Conference 2014 Conference Paper

Parallel Double Greedy Submodular Maximization

Xinghao Pan
Stefanie Jegelka
Joseph Gonzalez
Joseph Bradley
Michael Jordan

Many machine learning problems can be reduced to the maximization of submodular functions. Although well understood in the serial setting, the parallel maximization of submodular functions remains an open area of research with recent results only addressing monotone functions. The optimal algorithm for maximizing the more general class of non-monotone submodular functions was introduced by Buchbinder et al. and follows a strongly serial double-greedy logic and program analysis. In this work, we propose two methods to parallelize the double-greedy algorithm. The first, coordination-free approach emphasizes speed at the cost of a weaker approximation guarantee. The second, concurrency control approach guarantees a tight 1/2-approximation, at the quantifiable cost of additional coordination and reduced parallelism. As a consequence we explore the trade off space between guaranteed performance and objective optimality. We implement and evaluate both algorithms on multi-core hardware and billion edge graphs, demonstrating both the scalability and tradeoffs of each approach.

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NeurIPS Conference 2007 Conference Paper

FilterBoost: Regression and Classification on Large Datasets

Joseph Bradley
Robert Schapire

We study boosting in the ﬁltering setting, where the booster draws examples from an oracle instead of using a ﬁxed training set and so may train efﬁciently on very large datasets. Our algorithm, which is based on a logistic regression technique proposed by Collins, Schapire, & Singer, requires fewer assumptions to achieve bounds equivalent to or better than previous work. Moreover, we give the ﬁrst proof that the algorithm of Collins et al. is a strong PAC learner, albeit within the ﬁltering setting. Our proofs demonstrate the algorithm’s strong theoretical proper- ties for both classiﬁcation and conditional probability estimation, and we validate these results through extensive experiments. Empirically, our algorithm proves more robust to noise and overﬁtting than batch boosters in conditional probability estimation and proves competitive in classiﬁcation.

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