LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements
Authors: CHRISTOS THRAMPOULIDIS, Ehsan Abbasi, Babak Hassibi
NeurIPS 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Figure 1: Squared error of the ℓ1-regularized LASSO with non-linear measurements ( ) and with corresponding linear ones ( ) as a function of the regularizer parameter λ; both compared to the asymptotic prediction. Here, gi(x) = sign(x + 0.3zi) with zi N(0, 1). The unknown signal x0 is of dimension n = 768 and has 0.15n non-zero entries (see Sec. 2.2.2 for details). The different curves correspond to 0.75n and 1.2n number of measurements, respectively. Simulation points are averages over 20 problem realizations.Figure 2: Squared error of the LASSO as a function of the regularizer parameter compared to the asymptotic predictions. Simulation points represent averages over 20 realizations. |
| Researcher Affiliation | Academia | Christos Thrampoulidis, Department of Electrical Engineering Caltech cthrampo@caltech.edu Ehsan Abbasi Department of Electrical Engineering Caltech eabbasi@caltech.edu Babak Hassibi Department of Electrical Engineering Caltech hassibi@caltech.edu |
| Pseudocode | No | The paper presents mathematical derivations, theorems, and proofs but does not include any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement about making its source code publicly available, nor does it include links to a code repository. |
| Open Datasets | No | The paper discusses generating synthetic data based on probability distributions (e.g., "x0 is ρn-sparse on average and has unit Euclidean norm", "q X0 being Gaussian and Bernoulli"), but it does not utilize or provide access to a pre-existing public dataset for training purposes. |
| Dataset Splits | No | The paper describes its evaluation process using "Simulation points are averages over 20 problem realizations" but does not specify a training/validation/test split for a dataset, as it relies on generating problem instances. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used to conduct the simulations or experiments. |
| Software Dependencies | No | The paper does not specify any software dependencies with version numbers (e.g., programming languages, libraries, or solvers). |
| Experiment Setup | Yes | Here, gi(x) = sign(x + 0.3zi) with zi N(0, 1). The unknown signal x0 is of dimension n = 768 and has 0.15n non-zero entries (see Sec. 2.2.2 for details). The different curves correspond to 0.75n and 1.2n number of measurements, respectively. Simulation points are averages over 20 problem realizations. Illustration of Thm. 2.3 for g(x) = sign(x), n = 512, p X0(+1) = p X0(+1) = 0.05, p X0(+1) = 0.9 and two values of δ, namely 0.75 and 1.2. Illustration of Thm. 2.2 for x0 being group-sparse as in Section 2.2.3 and gi(x) = sign(x + 0.3zi). In particular, x0 is composed of t = 512 blocks of block size b = 3. Each block is zero with probability 0.95, otherwise its entries are i.i.d. N(0, 1). Finally, δ = 0.75. |