Calibrated Multiple-Output Quantile Regression with Representation Learning
Authors: Shai Feldman, Stephen Bates, Yaniv Romano
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques. |
| Researcher Affiliation | Academia | Shai Feldman EMAIL Department of Computer Science Technion Israel Institute of Technology Technion City, Haifa 32000, Israel Stephen Bates EMAIL Departments of Electrical Engineering and Computer Science and of Statistics University of California, Berkeley Berkeley, CA 94720, USA Yaniv Romano EMAIL Departments of Electrical and Computer Engineering and of Computer Science Technion Israel Institute of Technology Technion City, Haifa 32000, Israel |
| Pseudocode | Yes | Algorithm 1: Spherically transformed DQR (ST-DQR) Algorithm 2: Calibrating Multivariate Quantile Regression |
| Open Source Code | Yes | Software implementing the proposed method and reproducing our experiments can be found at https://github.com/Shai128/mqr |
| Open Datasets | Yes | blog_data. Blogfeedback data set. https://archive.ics.uci.edu/ml/datasets/ Blog Feedback. Accessed: January, 2019. bio. Physicochemical properties of protein tertiary structure data set. https: //archive.ics.uci.edu/ml/datasets/Physicochemical+Properties+of+ Protein+Tertiary+Structure. Accessed: January, 2019. house. House sales in king county, USA. https://www.kaggle.com/harlfoxem/ housesalesprediction/metadata. Accessed: July, 2021. meps_19. Medical expenditure panel survey, panel 19. https://meps.ahrq.gov/ mepsweb/data_stats/download_data_files_detail.jsp?cbo Puf Number= HC-181. Accessed: January, 2019. |
| Dataset Splits | Yes | We split the data sets (both real and synthetic) into a training set (38.4%), calibration (25.6%), validation set (16%) used for early stopping, and a test set (20%) to evaluate performance. |
| Hardware Specification | Yes | CPU: Intel(R) Xeon(R) E5-2650 v4. GPU: Nvidia TITAN-X, 1080TI, 2080TI. OS: Ubuntu 18.04. |
| Software Dependencies | No | The optimizer is Adam (Kingma and Ba, 2015), and the batch size is 256 for all methods. using Gurobi solver (Gurobi Optimization, LLC, 2021). |
| Experiment Setup | Yes | The neural network consists of 3 layers of 64 hidden units, and a leaky Re LU activation function with parameter 0.2. The learning rate used is 1e-3, the optimizer is Adam (Kingma and Ba, 2015), and the batch size is 256 for all methods. The maximum number of epochs is 10000, but the training is stopped early if the validation loss does not improve for 100 epochs, and in this case, the model with the lowest loss is chosen. The number of distinct directions used in each gradient step is 32, and they are taken from a fixed collection of 2048 directions that were sampled once, before the training process. The number of directions used to determine the quantile region belonging is 256, and they are sampled from the same collection of directions. |