Undirected graphical models or Markov random fields (MRFs) are widely used for modeling multivariate probability distributions. Much of the work on MRFs has focused on continuous variables, and nominal variables (that is, unordered categorical variables). However, data from many real world applications involve ordered categorical variables also known as ordinal variables, e.g., movie ratings on Netflix which can be ordered from 1 to 5 stars. With respect to univariate ordinal distributions, as we detail in the paper, there are two main categories of distributions; while there have been efforts to extend these to multivariate ordinal distributions, the resulting distributions are typically very complex, with either a large number of parameters, or with non-convex likelihoods. While there have been some work on tractable approximations, these do not come with strong statistical guarantees, and moreover are relatively computationally expensive. In this paper, we theoretically investigate two classes of graphical models for ordinal data, corresponding to the two main categories of univariate ordinal distributions. In contrast to previous work, our theoretical developments allow us to provide correspondingly two classes of estimators that are not only computationally efficient but also have strong statistical guarantees.
Author Information
Arun SUGGALA (Carnegie Mellon University)
Eunho Yang (KAIST / AItrics)
Pradeep Ravikumar (Carnegie Mellon University)
Related Events (a corresponding poster, oral, or spotlight)
-
2017 Talk: Ordinal Graphical Models: A Tale of Two Approaches »
Mon Aug 7th 01:30 -- 01:48 PM Room C4.9& C4.10
More from the Same Authors
-
2019 Poster: Spectral Approximate Inference »
Sejun Park · Eunho Yang · Se-Young Yun · Jinwoo Shin -
2019 Oral: Spectral Approximate Inference »
Sejun Park · Eunho Yang · Se-Young Yun · Jinwoo Shin -
2019 Poster: Trimming the $\ell_1$ Regularizer: Statistical Analysis, Optimization, and Applications to Deep Learning »
Jihun Yun · Peng Zheng · Eunho Yang · Aurelie Lozano · Aleksandr Aravkin -
2019 Oral: Trimming the $\ell_1$ Regularizer: Statistical Analysis, Optimization, and Applications to Deep Learning »
Jihun Yun · Peng Zheng · Eunho Yang · Aurelie Lozano · Aleksandr Aravkin -
2018 Poster: Deep Asymmetric Multi-task Feature Learning »
Hae Beom Lee · Eunho Yang · Sung Ju Hwang -
2018 Poster: Binary Classification with Karmic, Threshold-Quasi-Concave Metrics »
Bowei Yan · Sanmi Koyejo · Kai Zhong · Pradeep Ravikumar -
2018 Poster: Loss Decomposition for Fast Learning in Large Output Spaces »
En-Hsu Yen · Satyen Kale · Felix Xinnan Yu · Daniel Holtmann-Rice · Sanjiv Kumar · Pradeep Ravikumar -
2018 Oral: Binary Classification with Karmic, Threshold-Quasi-Concave Metrics »
Bowei Yan · Sanmi Koyejo · Kai Zhong · Pradeep Ravikumar -
2018 Oral: Deep Asymmetric Multi-task Feature Learning »
Hae Beom Lee · Eunho Yang · Sung Ju Hwang -
2018 Oral: Loss Decomposition for Fast Learning in Large Output Spaces »
En-Hsu Yen · Satyen Kale · Felix Xinnan Yu · Daniel Holtmann-Rice · Sanjiv Kumar · Pradeep Ravikumar -
2018 Poster: Deep Density Destructors »
David Inouye · Pradeep Ravikumar -
2018 Oral: Deep Density Destructors »
David Inouye · Pradeep Ravikumar -
2017 Poster: ProtoNN: Compressed and Accurate kNN for Resource-scarce Devices »
Chirag Gupta · ARUN SUGGALA · Ankit Goyal · Saurabh Goyal · Ashish Kumar · Bhargavi Paranjape · Harsha Vardhan Simhadri · Raghavendra Udupa · Manik Varma · Prateek Jain -
2017 Poster: Sparse + Group-Sparse Dirty Models: Statistical Guarantees without Unreasonable Conditions and a Case for Non-Convexity »
Eunho Yang · Aurelie Lozano -
2017 Talk: ProtoNN: Compressed and Accurate kNN for Resource-scarce Devices »
Chirag Gupta · ARUN SUGGALA · Ankit Goyal · Saurabh Goyal · Ashish Kumar · Bhargavi Paranjape · Harsha Vardhan Simhadri · Raghavendra Udupa · Manik Varma · Prateek Jain -
2017 Talk: Sparse + Group-Sparse Dirty Models: Statistical Guarantees without Unreasonable Conditions and a Case for Non-Convexity »
Eunho Yang · Aurelie Lozano -
2017 Poster: Doubly Greedy Primal-Dual Coordinate Descent for Sparse Empirical Risk Minimization »
Qi Lei · En-Hsu Yen · Chao-Yuan Wu · Inderjit Dhillon · Pradeep Ravikumar -
2017 Poster: Latent Feature Lasso »
En-Hsu Yen · Wei-Cheng Lee · Sung-En Chang · Arun Suggala · Shou-De Lin · Pradeep Ravikumar -
2017 Talk: Doubly Greedy Primal-Dual Coordinate Descent for Sparse Empirical Risk Minimization »
Qi Lei · En-Hsu Yen · Chao-Yuan Wu · Inderjit Dhillon · Pradeep Ravikumar -
2017 Talk: Latent Feature Lasso »
En-Hsu Yen · Wei-Cheng Lee · Sung-En Chang · Arun Suggala · Shou-De Lin · Pradeep Ravikumar