Training Procedures

ml4t-models does not hide all estimators behind one generic trainer because the model families do not train the same way.

Some estimators are closed form. Some emit neural checkpoints every few epochs. The stochastic discount factor family has phased adversarial training. Portfolio learners optimize a turnover-aware objective directly. The library keeps those differences explicit and makes checkpoint reporting part of the public contract.

Why Checkpoints Are First-Class

In the book and case studies, neural estimators are often evaluated at several training horizons rather than only at the last epoch. The library therefore treats checkpoint emission as configuration, not as hidden trainer behavior.

The practical rule is:

• estimators emit the checkpoints you configured
• downstream code decides how to score or compare them
• prediction defaults stay explicit through default_checkpoint

This keeps model semantics and evaluation semantics separate.

Closed-Form And Alternating Estimators

PCAModel, RPPCAModel, and IPCAModel do not expose an epoch grid in the same sense as neural models.

• PCAModel and RPPCAModel are eigendecomposition-based estimators
• IPCAModel uses an alternating least-squares loop with convergence controls
• all three report structural output at epoch = 0

That convention matters in cross-family comparisons: epoch = 0 means "no neural training timeline applies here," not "the model was left untrained."

Checkpointed Neural Estimators

CAEModel, SAEModel, and the portfolio learners expose explicit checkpoint controls.

Typical knobs are:

• n_epochs or max_iters
• checkpoint_interval / checkpoint_every
• checkpoint_epochs / checkpoint_steps
• default_checkpoint

Use interval checkpoints when training horizons are short and dense comparison is cheap. That is a good default for CAEModel, SAEModel, and lighter portfolio learners.

Conditional Autoencoder Training

CAEModel follows the conditional autoencoder structure of Gu, Kelly, and Xiu (2021):

• a beta network maps characteristics to conditional exposures
• managed portfolios summarize the realized cross-section
• a factor side turns those managed portfolios into latent factor returns
• reconstruction loss ties the two together

Checkpointing is especially useful here because the structural state extracted at epoch 10 can lead to a different factor-premium forecast than the state extracted at epoch 50.

Phase-Aware Stochastic Discount Factor Training

StochasticDiscountFactorModel has a different protocol entirely. Following Chen, Pelger, and Zhu (2021), training is split into three phases:

1. unconditional SDF warm-up
2. moment-network fitting
3. conditional SDF refinement

This is why the config has n_epochs_unc, n_epochs_moment, and n_epochs_cond instead of one generic n_epochs.

The optional beta-network head has its own smaller checkpoint grid. That separation matters: the structural SDF fit is expensive and should usually be evaluated at sparse named milestones, while the beta head can often be trained on a shorter schedule.

For long phased models, prefer:

• explicit checkpoint_epochs
• explicit beta_checkpoint_epochs

over dense interval checkpointing.

Portfolio-Learning Training

Portfolio learners optimize allocation objectives directly rather than stopping at a return forecast.

Shared portfolio controls include:

• checkpoint_every or checkpoint_steps
• eval_every
• early_stopping_patience
• turnover_penalty
• gamma_cost

Those controls are part of the public model config because they change the learned policy, not just the reporting surface.

Reporting Rules

The library keeps three reporting rules consistent across families:

1. Emitted checkpoints are configuration, not hidden trainer state.
2. default_checkpoint controls what predict() or extract() returns by default.
3. Selection logic belongs outside the estimator.

That last rule is important. If you want to compare checkpoints by cross-sectional IC, Sharpe, or any other metric, do it in ml4t-diagnostic or in your case-study orchestration, not inside the model class.

Practical Defaults

Use these defaults unless there is a clear reason not to:

• PCA, RP-PCA, IPCA: no checkpoint sweep; report epoch = 0
• CAE, SAE: moderate training horizon with interval or explicit checkpoint lists
• StochasticDiscountFactorModel: sparse structural checkpoints and a smaller beta-head grid
• portfolio learners: checkpoint every few optimization steps, with early stopping and cost-aware validation

Where To Go Next

• Latent-Factor Pipelines
• Latent-Factor Models
• Stochastic Discount Factor
• Portfolio Learning