High Dimensional Linear Regression using Lattice Basis Reduction
Authors: Ilias Zadik, David Gamarnik
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we present an experimental analysis of the ELO and LBR algorithms. |
| Researcher Affiliation | Academia | David Gamarnik Sloan School of Management Massachussetts Institute of Technology Cambridge, MA 02139 gamarnik@mit.edu; Ilias Zadik Operations Research Center Massachussetts Institute of Technology Cambridge, MA 02139 izadik@mit.edu |
| Pseudocode | Yes | Algorithm 1 Extended Lagarias-Odlyzko (ELO) Algorithm; Algorithm 2 Lattice Based Regression (LBR) Algorithm |
| Open Source Code | No | The paper does not provide any links to open-source code or explicitly state that the code for the described methodology is publicly available. |
| Open Datasets | No | Each entry of β is iid Unif ({1, 2, . . . , R = 100}). For 10 values of α (0, 3), specifically α {0.25, 0.5, 0.75, 1, 1.3, 1.6, 1.9, 2.25, 2.5, 2.75}, we generate the entries of X iid Unif {1, 2, 3, . . . , 2N} for N = p2 /2αn. We generate each entry of β w.p. 0.5 equal to zero and w.p. 0.5, Unif ({1, 2, . . . , R = 100}). We generate the entries of X iid U(0, 1) and of W iid U( σ, σ) for σ {0, e 20, e 12, e 4}. |
| Dataset Splits | No | The paper describes generating synthetic data for experiments and does not specify traditional train/validation/test dataset splits. It generates independent instances for evaluation. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU/GPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper does not mention specific software dependencies with version numbers required to replicate the experiments. |
| Experiment Setup | Yes | ELO algorithm: We focus on p = 30 features sample sizes n = 1, n = 10 and n = 30, R = 100 and zero-noise W = 0. Each entry of β is iid Unif ({1, 2, . . . , R = 100}). For 10 values of α (0, 3), specifically α {0.25, 0.5, 0.75, 1, 1.3, 1.6, 1.9, 2.25, 2.5, 2.75}, we generate the entries of X iid Unif {1, 2, 3, . . . , 2N} for N = p2 /2αn. For each combination of n, α we generate 20 independent instances of inputs. LBR algorithm: We focus on p = 30 features, n = 10 samples, Q = 1 and R = 100. We generate each entry of β w.p. 0.5 equal to zero and w.p. 0.5, Unif ({1, 2, . . . , R = 100}). We generate the entries of X iid U(0, 1) and of W iid U( σ, σ) for σ {0, e 20, e 12, e 4}. We generate 20 independent instances for any combination of σ and truncation level N. |