pyGPCCA Speedup Analysis

Benchmarks for pyGPCCA optimization improvements: gradient-based optimization (L-BFGS-B), multi-start via SO(k) rotation perturbation, and Krylov scaling.

Setup

All repos must live in the same parent directory:

Projects/
├── pygpcca_speedup_analysis/   # this repo
├── pyGPCCA/                    # feature/gradient-optimization branch
└── cellrank/                   # with optimizer passthrough

pixi install
pixi run test   # verify setup

The pixi environment provides PETSc/SLEPc for Krylov-based Schur decomposition (needed for m > ~20).

Benchmarks

Directory	What it tests	Datasets
analysis/01_synthetic/	NM vs L-BFGS-B/BFGS/CG runtime & crispness scaling in m	Synthetic block-diagonal (n=5000, k=30)
analysis/02_pancreas/	NM vs L-BFGS-B on real data (Tables A/B/C)	CellRank pancreas (~2500 cells)
analysis/03_dual_dataset/	NM(1 start) vs L-BFGS-B(10 starts, eps=0.1)	Pancreas + bone marrow (~5800 cells)
analysis/04_scaling/	Feasibility at m=50 with Krylov	Pancreas + bone marrow

Run any benchmark:

pixi run python analysis/01_synthetic/benchmark_gradient_opt.py
pixi run python analysis/02_pancreas/benchmark_pancreas.py [--mini]
pixi run python analysis/03_dual_dataset/benchmark_dual.py
pixi run python analysis/04_scaling/benchmark_m50.py

Key findings so far

• L-BFGS-B matches or beats NM at every m tested on two real datasets
• Gap grows with m: ties at m≤5, +50–135% crispness at m≥10
• NM fails outright at bone marrow m=12 (degenerate solution); L-BFGS-B succeeds
• Multi-start (10 starts, eps=0.1) reliably finds better basins at negligible wall-time cost
• Dense Schur decomposition limits m to ~20; Krylov (SLEPc) needed beyond that