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Choosing SAGA Tolerance for Sparse Multiclass Logistic Regression

Code Machine Learning for Trading

Summary

This configuration note explains why an L1-penalized, three-class logistic regression uses SAGA with an explicitly tightened tolerance. It compares SAGA with liblinear on a Nasdaq 100 microstructure prediction panel, reporting faster fits and better out-of-sample log loss and accuracy for SAGA in the measured runs. It also describes why liblinear is unsuitable under the project’s scikit-learn version constraints.

The central methodological point is that loose convergence tolerance can leave coefficients numerically near zero rather than exactly zero, distorting feature sparsity counts. At the selected penalty strength, tightening tolerance makes SAGA’s exact-zero count align with its count of coefficients below a small magnitude threshold. The note reports timing and sparsity measurements across several penalty values, but cautions that full-panel runtime is uncertain because its estimate relies on limited scaling evidence.

Key ideas

  • SAGA supports the three-class setup under the stated scikit-learn compatibility constraints.
  • Measured SAGA runs were faster and had better out-of-sample scores than liblinear on the cited panel.
  • A tighter tolerance improves the reliability of exact-zero counts for an L1 sparsity sweep.
  • The full-panel runtime for this configuration remains uncertain and should be observed directly.

Tags

Machine learningStatisticsEquitiesUS markets
Full text
# logistic_l1_C0.01.yaml


```yaml
# L1 logistic regression. The solver is `saga` rather than `liblinear`, and the tolerance
# is set explicitly rather than left at scikit-learn's 1e-4 default.
#
# Two reasons, and the first one is not optional. These labels are three-class (-1, 0, 1),
# and scikit-learn 1.8 makes multiclass `liblinear` a hard error; #740 already moved our
# floor to 1.7. `OneVsRestClassifier(liblinear)` would reproduce the current objective
# exactly - liblinear multiclass IS one-vs-rest - and would keep the problem below.
#
# The second is that `liblinear` does not finish. It is single-threaded coordinate descent
# and scales about N^1.4 here. Measured on nasdaq100_microstructure's `fwd_dir_15m` panel:
#
#     rows      liblinear 1000/1e-4     saga 200/1e-2
#     400,000     144.4s  converged      11.0s  converged
#   1,200,000     716.9s  converged      44.8s  converged
#
# which extrapolates to roughly eight hours per configuration at the full 16.9M rows against
# about twenty minutes. That is not a projection: `06_linear` ran 7h23m at 100% of one core
# on 2026-09-05 and was killed with two of thirteen configurations still unfinished, both of
# them these L1 ones.
#
# saga is also better out of sample at every C measured here: log loss 1.0273-1.0276 against
# liblinear's 1.0293-1.0294, and accuracy 0.415-0.420 against 0.404-0.410.
#
# `tol: 0.001` here rather than the 0.01 the weakly-penalised configurations use, because
# this is where the penalty binds and exact sparsity is the point of the sweep. At 1e-2 saga
# leaves coefficients stranded NEAR zero instead of AT zero, which `coef_ != 0` then counts
# as live. Measured on the same panel, exact zeros against coefficients below 1e-8, out of
# 198:
#
#     C        liblinear 1e-4     saga 1e-2        saga 1e-3
#     0.001      128 / 128         148 / 149        157 / 157
#     0.01        40 /  40          24 /  52         87 /  87
#     0.1          8 /   8           3 /   4         24 /  26
#
# The 24-against-52 at C=0.01 is the defect: twenty-eight coefficients below 1e-8 that are
# not zero. At 1e-3 the two counts agree and saga is *more* sparse than liblinear at every C
# here, so the tighter tolerance is not a concession - it is what makes the L1 solution an
# L1 solution.
#
# Cost at 1.2M rows: 226s, 352s and 287s for C=0.001, 0.01 and 0.1 against liblinear's 30s,
# 202s and 499s. **The full-panel cost of this arm is not established** - the 16.9M-row
# extrapolation is uncertain because it rests on a single scaling estimate taken from the
# tol=1e-2 timings. Watch it on the first run rather than assuming it is small.
model_class: LogisticRegression
params:
  C: 0.01
  max_iter: 200
  penalty: l1
  solver: saga
  tol: 0.001

```

Shown in full with attribution under the source's licence. Licence: MIT

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.