Timezone: »
We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction approaches for constructing logarithmic depth trees. On the theoretical front, we formulate a new objective function, which is optimized at each node of the tree and creates dynamic partitions of the data which are both pure (in terms of class labels) and balanced. We demonstrate that under favorable conditions, we can construct logarithmic depth trees that have leaves with low label entropy. However, the objective function at the nodes is challenging to optimize computationally. We address the empirical problem with a new online decision tree construction procedure. Experiments demonstrate that this online algorithm quickly achieves improvement in test error compared to more common logarithmic training time approaches, which makes it a plausible method in computationally constrained large-k applications.
Author Information
Anna Choromanska (Courant Institute, NYU)
John Langford (Microsoft Research New York)
More from the Same Authors
-
2020 Poster: Empirical Likelihood for Contextual Bandits »
Nikos Karampatziakis · John Langford · Paul Mineiro -
2020 Poster: Efficient Contextual Bandits with Continuous Actions »
Maryam Majzoubi · Chicheng Zhang · Rajan Chari · Akshay Krishnamurthy · John Langford · Aleksandrs Slivkins -
2020 Poster: Learning the Linear Quadratic Regulator from Nonlinear Observations »
Zakaria Mhammedi · Dylan Foster · Max Simchowitz · Dipendra Misra · Wen Sun · Akshay Krishnamurthy · Alexander Rakhlin · John Langford -
2019 Poster: Efficient Forward Architecture Search »
Hanzhang Hu · John Langford · Rich Caruana · Saurajit Mukherjee · Eric Horvitz · Debadeepta Dey -
2018 Poster: On Oracle-Efficient PAC RL with Rich Observations »
Christoph Dann · Nan Jiang · Akshay Krishnamurthy · Alekh Agarwal · John Langford · Robert Schapire -
2018 Spotlight: On Oracle-Efficient PAC RL with Rich Observations »
Christoph Dann · Nan Jiang · Akshay Krishnamurthy · Alekh Agarwal · John Langford · Robert Schapire -
2017 Poster: Off-policy evaluation for slate recommendation »
Adith Swaminathan · Akshay Krishnamurthy · Alekh Agarwal · Miro Dudik · John Langford · Damien Jose · Imed Zitouni -
2017 Oral: Off-policy evaluation for slate recommendation »
Adith Swaminathan · Akshay Krishnamurthy · Alekh Agarwal · Miro Dudik · John Langford · Damien Jose · Imed Zitouni -
2016 Workshop: Nonconvex Optimization for Machine Learning: Theory and Practice »
Hossein Mobahi · Anima Anandkumar · Percy Liang · Stefanie Jegelka · Anna Choromanska -
2016 Poster: Efficient Second Order Online Learning by Sketching »
Haipeng Luo · Alekh Agarwal · Nicolò Cesa-Bianchi · John Langford -
2016 Poster: A Credit Assignment Compiler for Joint Prediction »
Kai-Wei Chang · He He · Stephane Ross · Hal DaumĂ© III · John Langford -
2016 Poster: PAC Reinforcement Learning with Rich Observations »
Akshay Krishnamurthy · Alekh Agarwal · John Langford -
2016 Poster: Search Improves Label for Active Learning »
Alina Beygelzimer · Daniel Hsu · John Langford · Chicheng Zhang -
2015 Poster: Efficient and Parsimonious Agnostic Active Learning »
Tzu-Kuo Huang · Alekh Agarwal · Daniel Hsu · John Langford · Robert Schapire -
2015 Spotlight: Logarithmic Time Online Multiclass prediction »
Anna Choromanska · John Langford -
2015 Spotlight: Efficient and Parsimonious Agnostic Active Learning »
Tzu-Kuo Huang · Alekh Agarwal · Daniel Hsu · John Langford · Robert Schapire -
2015 Poster: Deep learning with Elastic Averaging SGD »
Sixin Zhang · Anna Choromanska · Yann LeCun -
2015 Spotlight: Deep learning with Elastic Averaging SGD »
Sixin Zhang · Anna Choromanska · Yann LeCun -
2013 Workshop: Extreme Classification: Multi-Class & Multi-Label Learning with Millions of Categories »
Manik Varma · John Langford