Minimal ℓ_p-Minimization Interpolator (CVXPY + MOSEK)

This repository provides a minimal, extendable codebase to run experiments for minimum-ℓ_p interpolation in overparameterized linear regression.

• Solver: CVXPY with MOSEK (default).
• Design: i.i.d. Gaussian features.
• Ground truth w*: (i) spike e1, (ii) flat on a support of size s.
• Usage: HPC-friendly command line (python -m minlp ...) and plain python main.py.

Note: For MOSEK you need a valid license (student/academic free licenses available). Set the environment variable MOSEKLM_LICENSE_FILE to point to your license file (or use MOSEK's default license discovery).

Installation

python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt
# Optional (if not already provided by your environment)
pip install mosek

Quick start

Run a small n-sweep at fixed d:

python -m minlp \
  --d 50000 \
  --n_list 250 500 1000 2000 3000 4000 5000 \
  --p 1.9 \
  --r_list 1.1 1.5 1.9 \
  --sigma 0.5 \
  --w_mode e1 \
  --s 1 \
  --reps 2 \
  --n_test 20000 \
  --out results_n_sweep.csv

Or using the root script:

python main.py --help

HPC (example)

We intentionally avoid interactive plotting and produce CSV logs only. You can submit array jobs by varying --seed and/or --reps.

Example shell snippet (replace addqueue with your scheduler wrapper as needed):

#!/usr/bin/env bash
# scripts/addqueue_example.sh
set -e
MEM_GB=${1:-16}
OUT=${2:-"results.csv"}

# Example: one job
addqueue -m ${MEM_GB} /usr/bin/python -m minlp \
  --d 50000 \
  --n_list 500 1000 2000 3000 4000 5000 \
  --p 1.9 \
  --r_list 1.1 1.5 1.9 \
  --sigma 0.5 \
  --w_mode e1 \
  --s 1 \
  --reps 1 \
  --seed 0 \
  --n_test 20000 \
  --out ${OUT}

Files

• minlp/ — package with datasets, solver, experiment runner, CLI (__main__.py)
• main.py — convenience wrapper to run python main.py ...
• requirements.txt — Python dependencies
• scripts/ — example HPC submission script
• plot_results.py — optional quick plotting script once CSV exists

Extending

• New model classes (e.g., diagonal linear networks) can live under minlp/models/. Plug them into minlp/experiments.py following the interface in fit_min_lp.
• Custom data generators can be added to minlp/datasets.py.
• You can add new metrics to minlp/metrics.py and log them in experiments.py.

Reproducibility

We thread a single RNG seed through NumPy. The convex program solved by MOSEK is deterministic given the data (up to solver tolerances).

License

MIT License (see LICENSE).