R initialization for GP MAP¶

SearchConfig(r_init=True) initializes the first GP MAP restart with a bounded CPU R-MSRM fit. It is opt-in and off by default. The configuration guide describes its budgets, parameter translation, diagnostics and fallback. This preliminary fit is separate from NUTS warmup and does not replace sampler adaptation.

The measurements below are small synthetic cases. They show fewer iterations but no reduction in total time, and the empirical evaluation on a real five-participant recording did not reproduce the larger synthetic gain: it found as many iterations, a different lag basin, and two lags resting at their bounds. Treat enabling this as a per-analysis decision rather than a general recommendation.

Synthetic comparison¶

The committed benchmark script compares one historical data-based start with one R start. It generates three participants on unequal modality clocks with feature masks. The single-factor case learns a Gaussian response lag; the two-factor case uses Identity responses. Neither case includes empirical observations or tests SCR response recovery.

Each fit runs in a fresh process, with the same seed, priors, optimizer limits and physical-gradient tolerance. Both configurations receive up to 1,200 search iterations and 200 refinement iterations. Total time includes preparation, compilation, R initialization when enabled, optimization and diagnostics. The table reports medians across seeds 31, 32 and 33 for grouped algebra; dense and state-space checks use seed 31. Iterations include search and refinement.

All 16 fits passed the physical-gradient threshold of 1e-3. For Gaussian seed 31, the R start found a lower negative log posterior: approximately -84.79 versus -64.56, with agreement between dense and grouped algebra. The other paired fits agreed in objective to numerical precision. A single start does not establish global mode coverage; production searches retain the other configured prior-quantile starts.

These small cold fits show reduced optimizer work, with similar total time for dense/grouped algebra. Compilation dominates at this size. The state-space pair was about 7% faster, but one timing pair is insufficient for a general speedup claim. Larger data, GPU execution, SCR filters and empirical analyses require their own measurements. Fewer iterations do not guarantee a faster fit or better predictions.

Measurements were made on Linux CPU with float64, affinity restricted to eight cores and one BLAS/OpenMP thread. Exact runtime versions, CPU model and individual fit records are in the results file. Timings are observations from this run, not performance test thresholds.

Reproduce¶

Install the Bayesian extra, then run each configuration in a fresh process:

JAX_ENABLE_X64=true JAX_PLATFORM_NAME=cpu OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
  python scripts/benchmark_r_initialization.py --case gaussian --seed 31 --no-r-init
JAX_ENABLE_X64=true JAX_PLATFORM_NAME=cpu OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
  python scripts/benchmark_r_initialization.py --case gaussian --seed 31 --r-init

Repeat for seeds 32 and 33 and --case multifactor. Use --algebra dense for the Gaussian backend check or --algebra state_space --case multifactor for the Identity state-space check. On Linux, prefix the command with an appropriate taskset -c CPU list to reproduce a fixed affinity. Compare convergence and objectives alongside wall time, and keep thread settings and background load consistent.