Finding k in Latent $k-$ polytope
Authors: Chiranjib Bhattacharyya, Ravindran Kannan, Amit Kumar
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | The paper introduces the notion of Interpolative Convex Rank(ICR) of a matrix, and shows that k = ICR of a subset smoothed data matrix where k is the number of vertices in Lk P (see details in Theorem 1). The paper introduces new techniques based on the hyperplane separator theorem for proving lower bounds on the ICR of a matrix (see details in Section 3.4). Under standard assumptions, the paper gives a polynomial time algorithm for finding the correct value of the number of vertices of the polytope K (see Theorem 18). |
| Researcher Affiliation | Collaboration | 1Department of Computer Science and Automation, IISc Bangalore, India 2Microsoft Research India Lab., Bangalore, India 3Department of Computer Science and Engineering, IIT Delhi, India. |
| Pseudocode | Yes | Algorithm 1 Algorithm for finding the number of extreme points of K. Algorithm 2 Algorithm for finding the approximations to the vertices of K. |
| Open Source Code | No | The paper does not provide any statement or link regarding the availability of open-source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not describe experiments using a dataset, public or otherwise. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments or dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any specific hardware used for experiments. |
| Software Dependencies | No | The paper is theoretical and does not specify software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any experimental setup or hyperparameters. |