Mixed Regression via Approximate Message Passing
Authors: Nelvin Tan, Ramji Venkataramanan
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The theoretical results are validated by numerical simulations for mixed linear regression, max-affine regression, and mixture-of-experts. For max-affine regression, we propose an algorithm that combines AMP with expectation-maximization to estimate the intercepts of the model along with the signals. The numerical results show that AMP significantly outperforms other estimators for mixed linear regression and max-affine regression in most parameter regimes. |
| Researcher Affiliation | Academia | Nelvin Tan EMAIL Department of Engineering, University of Cambridge Cambridge, CB2 1PZ, United Kingdom Ramji Venkataramanan EMAIL Department of Engineering, University of Cambridge Cambridge, CB2 1PZ, United Kingdom |
| Pseudocode | Yes | Algorithm 1 Expectation-maximization approximate message passing (EM-AMP) |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that the source code for the methodology described is publicly available or released. It mentions a preliminary version published in AISTATS 2023 but does not provide code access. |
| Open Datasets | No | The paper describes generating synthetic data for its simulations (e.g., "Xi i.i.d. N(0, Ip/n)", "ci i.i.d. Bernoulli(α)"). It does not refer to or provide access information for any existing public datasets. |
| Dataset Splits | No | The paper describes generating synthetic data for its numerical simulations and varies parameters like 'p' (signal dimension) and 'n' (number of observations) to control the sampling ratio 'δ = n/p'. It does not discuss conventional training/validation/test splits for specific datasets. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running the experiments, such as GPU/CPU models, processors, or memory specifications. |
| Software Dependencies | No | The paper does not explicitly mention any specific software dependencies or their version numbers that would be required to reproduce the experiments. |
| Experiment Setup | Yes | In Figures 1, 2, and 3, we set the Bernoulli parameter α = 0.7 and choose the two signals to be jointly Gaussian, with their entries generated as (β(1) j , β(2) j ) i.i.d. N( 0 0 , j [p]). The signal dimension p = 500 and vary the value of n in our experiments. For the soft-thresholding denoiser fk... The tuning parameter ζ set to 1.1402. ...we execute EM-AMP with mmax = 5 and kmax = 5. |