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Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive with respect to memory and computation even with automatic differentiation. As a typical example in generative modeling, score matching~(SM) involves the optimization of the trace of a Hessian. To improve computing efficiency, we rewrite the SM objective and its variants in terms of directional derivatives, and present a generic strategy to efficiently approximate any-order directional derivative with finite difference~(FD). Our approximation only involves function evaluations, which can be executed in parallel, and no gradient computations. Thus, it reduces the total computational cost while also improving numerical stability. We provide two instantiations by reformulating variants of SM objectives into the FD forms. Empirically, we demonstrate that our methods produce results comparable to the gradient-based counterparts while being much more computationally efficient.
Author Information
Tianyu Pang (Tsinghua University)
Kun Xu (Tsinghua University)
Chongxuan LI (Tsinghua University)
Assistant Professor @ RUC
Yang Song (Stanford University)
Stefano Ermon (Stanford)
Jun Zhu (Tsinghua University)
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2017 Poster: A-NICE-MC: Adversarial Training for MCMC »
Jiaming Song · Shengjia Zhao · Stefano Ermon -
2017 Poster: InfoGAIL: Interpretable Imitation Learning from Visual Demonstrations »
Yunzhu Li · Jiaming Song · Stefano Ermon -
2017 Poster: Population Matching Discrepancy and Applications in Deep Learning »
Jianfei Chen · Chongxuan LI · Yizhong Ru · Jun Zhu -
2017 Poster: Neural Variational Inference and Learning in Undirected Graphical Models »
Volodymyr Kuleshov · Stefano Ermon -
2016 Poster: Solving Marginal MAP Problems with NP Oracles and Parity Constraints »
Yexiang Xue · zhiyuan li · Stefano Ermon · Carla Gomes · Bart Selman -
2016 Poster: Kernel Bayesian Inference with Posterior Regularization »
Yang Song · Jun Zhu · Yong Ren -
2016 Poster: Generative Adversarial Imitation Learning »
Jonathan Ho · Stefano Ermon -
2016 Poster: Variational Bayes on Monte Carlo Steroids »
Aditya Grover · Stefano Ermon -
2016 Poster: Stochastic Gradient Geodesic MCMC Methods »
Chang Liu · Jun Zhu · Yang Song -
2016 Poster: Conditional Generative Moment-Matching Networks »
Yong Ren · Jun Zhu · Jialian Li · Yucen Luo -
2016 Poster: Adaptive Concentration Inequalities for Sequential Decision Problems »
Shengjia Zhao · Enze Zhou · Ashish Sabharwal · Stefano Ermon -
2015 Poster: Max-Margin Majority Voting for Learning from Crowds »
TIAN TIAN · Jun Zhu -
2015 Poster: Max-Margin Deep Generative Models »
Chongxuan Li · Jun Zhu · Tim Shi · Bo Zhang -
2014 Poster: Distributed Bayesian Posterior Sampling via Moment Sharing »
Minjie Xu · Balaji Lakshminarayanan · Yee Whye Teh · Jun Zhu · Bo Zhang -
2014 Poster: Spectral Methods for Supervised Topic Models »
Yining Wang · Jun Zhu -
2014 Poster: Robust Bayesian Max-Margin Clustering »
Changyou Chen · Jun Zhu · Xinhua Zhang -
2013 Poster: Embed and Project: Discrete Sampling with Universal Hashing »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman -
2013 Poster: Scalable Inference for Logistic-Normal Topic Models »
Jianfei Chen · Jun Zhu · Zi Wang · Xun Zheng · Bo Zhang -
2012 Poster: Monte Carlo Methods for Maximum Margin Supervised Topic Models »
Qixia Jiang · Jun Zhu · Maosong Sun · Eric Xing -
2012 Poster: Density Propagation and Improved Bounds on the Partition Function »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman -
2012 Poster: Bayesian Nonparametric Maximum Margin Matrix Factorization for Collaborative Prediction »
Minjie Xu · Jun Zhu · Bo Zhang -
2011 Poster: Accelerated Adaptive Markov Chain for Partition Function Computation »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman -
2011 Spotlight: Accelerated Adaptive Markov Chain for Partition Function Computation »
Stefano Ermon · Carla Gomes · Ashish Sabharwal · Bart Selman -
2011 Poster: Infinite Latent SVM for Classification and Multi-task Learning »
Jun Zhu · Ning Chen · Eric Xing -
2010 Poster: Large Margin Learning of Upstream Scene Understanding Models »
Jun Zhu · Li-Jia Li · Li Fei-Fei · Eric Xing -
2010 Poster: Predictive Subspace Learning for Multi-view Data: a Large Margin Approach »
Ning Chen · Jun Zhu · Eric Xing -
2010 Poster: Adaptive Multi-Task Lasso: with Application to eQTL Detection »
Seunghak Lee · Jun Zhu · Eric Xing -
2010 Poster: Efficient Relational Learning with Hidden Variable Detection »
Ni Lao · Jun Zhu · Liu Xinwang · Yandong Liu · William Cohen -
2008 Poster: Partially Observed Maximum Entropy Discrimination Markov Networks »
Jun Zhu · Eric Xing · Bo Zhang