Fast and Accurate Least-Mean-Squares Solvers
Authors: Alaa Maalouf, Ibrahim Jubran, Dan Feldman
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Extensive experimental results and complete open source code are also provided. Extensive experimental results on synthetic and real-world data for common LMS solvers of Scikit-learn library with either CPython or Intel s Python distributions. In this section we apply our fast construction of the Carathoodory Set S from the previous section to boost the running time of common LMS solvers in Table 1 by a factor of tens to hundreds, or to improve their numerical accuracy by a similar factor to support, e.g., 32 bit floating point representation as in Fig. 2v. |
| Researcher Affiliation | Academia | The Robotics and Big Data Lab, Department of Computer Science, University of Haifa, Haifa, Israel |
| Pseudocode | Yes | Algorithm 1 FAST-CARATHEODORY-SET(P, u, k); see Theorem 3.1; Algorithm 2 CARATHEODORY-MATRIX(A, k); see Theorem 3.2; Algorithm 3 LMS-CORESET(A, b, m, k); Algorithm 4 LINREG-BOOST(A, b, m, k); Algorithm 5 RIDGECV-BOOST(A, b, A, m, k); Algorithm 6 LASSOCV-BOOST(A, b, A, m, k); Algorithm 7 ELASTICCV-BOOST(A, b, m, A, ρ, k) |
| Open Source Code | Yes | Extensive experimental results and complete open source code are also provided. Open code for our algorithms is provided [29]. [29] Alaa Maalouf, Ibrahim Jubran, and Dan Feldman. Open source code for all the algorithms presented in this paper, 2019. Link for open-source code. |
| Open Datasets | Yes | (i) 3D Road Network (North Jutland, Denmark) [24]. (ii) Individual household electric power consumption [1]. (iii) House Sales in King County, USA [2]. |
| Dataset Splits | Yes | m-folds cross validation (CV). We briefly discuss the CV technique which is utilized in common LMS solvers. Given a parameter m and a set of real numbers A, to select the optimal value α A of the regularization term, the existing Python s LMS solvers partition the rows of A into m folds (subsets) and run the solver m |A| times, each run is done on a concatenation of m 1 folds (subsets) and α A, and its result is tested on the remaining test fold . |
| Hardware Specification | Yes | All the experiments were conducted on a standard Lenovo Z70 laptop with an Intel i7-5500U CPU @ 2.40GHZ and 16GB RAM. |
| Software Dependencies | No | The paper mentions "Scikit-learn library" and "CPython or Intel s Python distributions" but does not provide specific version numbers for these software components. |
| Experiment Setup | Yes | The chosen number of clusters in Algorithm 3 is k = 2(d + 1)2 + 2 in order to have O(log n) iterations in Algorithm 1, and ρ = 0.5 for Algorithm 7. |