Latent-Factor Models

This guide covers the structural latent-factor family:

• PCAModel
• RPPCAModel
• IPCAModel
• CAEModel

These models all estimate latent structure, but they do not all use the same data contract or economic assumptions.

The family splits into two groups:

• persistent-panel estimators: PCAModel, RPPCAModel
• dated cross-sectional estimators: IPCAModel, CAEModel

Overview

Model	Input contract	Native output	Main assumption	Predictive object
PCAModel	PersistentPanelBatch	LatentFactorState with static loadings and factor returns	stable asset IDs	beta × premium after a forecaster
RPPCAModel	PersistentPanelBatch	LatentFactorState with pricing-aware static loadings	stable asset IDs and meaningful cross-sectional means	beta × premium after a forecaster
IPCAModel	CrossSectionBatch	LatentFactorState with characteristic-implied betas	dated characteristics parameterize conditional exposures	beta × premium after a forecaster
CAEModel	CrossSectionBatch	LatentFactorState with nonlinear characteristic betas	nonlinear exposure map can be learned from cross-sections	beta × premium after a forecaster

PCA

PCAModel is the persistent-panel baseline.

Use it when:

• entity identity is stable through time
• variance decomposition is the primary structural task
• a simple low-dimensional baseline is more important than pricing-aware extraction

It estimates:

• static loadings
• factor returns from demeaned panel returns

It does not directly forecast expected returns. That requires:

1. a factor-premium forecast
2. an asset mapper

Do not use PCA when the asset axis is an unstable identifier field. PCA and RP-PCA rely on the same entity occupying the same panel slot through time.

RP-PCA

RPPCAModel extends PCA by letting expected-return information influence factor extraction.

Conceptually, it moves from:

• explaining covariance only

to:

• explaining covariance and cross-sectional mean differences

This makes it attractive when you want factors that matter for pricing rather than only for variance decomposition.

The model follows Lettau and Pelger (2020): the extraction criterion blends covariance structure with pricing information instead of treating those as separate downstream concerns.

Key config fields:

• gamma
• base_moment
• scale_by_asset_volatility
• normalize_loadings
• orthogonalize_factors

The gamma parameter in RPPCAConfig is the RP-PCA pricing-error weight, not an exposure matrix. The fitted loadings are returned in LatentFactorState.asset_betas.

IPCA

IPCAModel is the linear bridge between PCA and neural conditional factor models.

Economic idea:

• asset loadings are not static
• they are linear functions of observable characteristics

In the library, IPCAModel:

• consumes CrossSectionBatch
• alternates between factor estimation and gamma estimation
• returns a LatentFactorState with conditional betas and factor history
• reports ALS convergence metadata in LatentFactorState.metadata

The economic interpretation follows Kelly, Pruitt, and Su (2019): characteristics do not predict returns directly in an unconstrained way. They parameterize conditional factor exposures.

Predictive use:

• forecast factor premia from historical factor returns
• map current conditional betas times those premia back to assets

CAE

CAEModel is a conditional autoencoder structural extractor.

It should be interpreted as:

• a nonlinear extension of IPCA
• not as a direct supervised return predictor

The model learns:

• a nonlinear mapping from characteristics to betas
• latent factor returns from managed portfolios

The implementable return forecast is still a two-step object:

current nonlinear betas × ex ante factor-premium forecast

Current implementation features:

• configurable hidden units
• checkpoint-aware training
• optional ensemble averaging across saved checkpoints
• classification mode that still keeps factor construction tied to continuous returns

Checkpoint selection changes the extracted structural state. If you pass checkpoint=10, the betas and factor history come from the checkpoint saved at epoch 10, not from the final training epoch.

This is the right way to think about the model:

• CAEModel is a nonlinear extension of IPCA
• the fitted return uses realized latent factor returns
• the tradeable forecast replaces those realized factor returns with an ex ante premium estimate

That is exactly why CAEModel lives naturally inside LatentFactorForecastPipeline rather than exposing a monolithic end-to-end return-prediction API.

Persistent Vs Ragged

The split between panel and cross-sectional models is intentional.

Persistent-panel family

• PCAModel
• RPPCAModel

Ragged cross-sectional family

• IPCAModel
• CAEModel

This is not an implementation detail. It reflects the actual assumptions the models need.

If entity identity is unstable, use IPCAModel or CAEModel, not PCAModel or RPPCAModel.

Recommended Defaults

Simple baseline

• PCAModel or IPCAModel
• ExpandingMeanFactorForecaster
• BetaLambdaMapper

Pricing-aware linear baseline

• RPPCAModel
• ExpandingMeanFactorForecaster
• BetaLambdaMapper

Nonlinear latent-factor baseline

• CAEModel
• ExpandingMeanFactorForecaster
• BetaLambdaMapper

Better-than-mean factor forecasting

Swap in:

• AR1FactorForecaster
• EWMABaseFactorForecaster

without changing the structural model.