Academic References¶

This page is the canonical bibliography for the model families implemented in ml4t-models. Every claim that touches an estimator, a loss, or an architectural choice in the user guide should resolve here. Citations follow the Chicago author-date convention used throughout Machine Learning for Trading; the paper anchors mirror the bibliography in ~/ml4t/book/14_latent_factors/bibliography.json.

If a model adds a new mechanism, the corresponding paper should be added here first, then referenced from the user guide.

How To Read This Page¶

Each entry includes:

the implementation in ml4t-models it supports
the specific role the paper plays for that model (definition, identification, training procedure, evaluation diagnostic)
a short qualification when the library departs from the paper

The bibliography is grouped by model family. Cross-cutting references (factor zoo critique, weak-factor theory, replication evidence) live in the final section.

PCA on Asset Returns¶

Implementation: PCAModel.

Connor and Korajczyk (2009)¶

Factor Models of Asset Returns. Provides the canonical statement of static-loading approximate factor models for return panels and motivates the eigendecomposition of the demeaned return covariance as a structural extraction step (rather than a forecasting step).

Litterman and Scheinkman (1991)¶

Common Factors Affecting Bond Returns. The classical low-dimensional yield-curve PCA result: three components (level, slope, curvature) explain almost all variation in Treasury returns. Used in the chapter to justify component selection by economic interpretation rather than scree-elbow heuristics alone.

Avellaneda and Lee (2010)¶

Statistical Arbitrage in the US Equities Market. Establishes the eigenportfolio framing: principal-component vectors are tradable portfolios, and PCA residuals can be modeled with mean-reverting OU processes for stat-arb signals. The library’s PCAModel exposes the loadings that this paper interprets as portfolio weights.

Avellaneda (2019)¶

Hierarchical PCA and Applications to Portfolio Management. Develops sector-conditional PCA as a robustness fix for global equity decompositions. Out of scope for the v0.1 implementation but flagged in the Roadmap as a candidate refinement.

Baik, Ben Arous, and Péché (2005)¶

Phase Transition of the Largest Eigenvalue for Nonnull Complex Sample Covariance Matrices. The BBP threshold: a factor is recoverable from a sample covariance matrix only if its population eigenvalue exceeds \(1 + \sqrt{n/T}\). This bound governs how many components PCAModel can recover when \(n/T\) is non-trivial.

Paleologo (2025)¶

The Elements of Quantitative Investing. Chapter 7 collects the random-matrix-theory machinery (Marchenko–Pastur, BBP, eigenvalue shrinkage) that the chapter relies on for component selection.

RP-PCA¶

Implementation: RPPCAModel.

Lettau and Pelger (2020)¶

Estimating Latent Asset-Pricing Factors. Defines the RP-PCA objective as a weighted sum of unexplained variance and squared cross-sectional pricing errors, controlled by a single parameter \(\gamma\). The library exposes gamma, base_moment (covariance vs. second moment), scale_by_asset_volatility, and normalize_loadings as direct counterparts of the paper's design knobs. Out-of-sample Sharpe gains over standard PCA are reported there but are not reproduced inside the library — that is the case-study's job.

IPCA¶

Implementation: IPCAModel.

Kelly, Pruitt, and Su (2019)¶

Characteristics Are Covariances: A Unified Model of Risk and Return. The IPCA model: excess returns are explained by characteristic-implied conditional betas times latent factors,

\[ r^{e}_{i,t+1} = z_{i,t}^{\top} \Gamma f_{t+1} + \varepsilon_{i,t+1}. \]

The library’s alternating-least-squares solver mirrors the paper's identification: \(\Gamma\) is updated holding \(f_t\) fixed and vice versa, with ridge stabilizers on both sides (gamma_ridge, factor_ridge).

Didisheim et al. (2023)¶

Complexity in Factor Pricing Models. Shows theoretically and empirically that factor models with many parameters can outperform sparse ones out of sample, qualifying the "select a single optimal \(K\)" intuition. The library's IPCA defaults treat \(K\) as a swept argument, not a parsimony pick.

Conditional Autoencoder¶

Implementation: CAEModel.

Gu, Kelly, and Xiu (2021)¶

Autoencoder Asset Pricing Models. Defines the conditional autoencoder (CAE) as a non-linear generalization of IPCA: the linear \(\beta = \Gamma' z\) map is replaced by a feed-forward network \(\beta = g(z; W)\), and the factor-network input is the characteristic-managed-portfolio block

\[ x_t = (Z_{t-1}^{\top} Z_{t-1})^{-1} Z_{t-1}^{\top} r_t. \]

The library's CAEModel follows this dual-network structure (hidden_units controls the beta-network pyramid, n_ensemble averages over random initializations) and trains under MSE reconstruction loss with optional L1 regularization (lambda_l1). Reported GKX out-of-sample Sharpe figures (~1.53 value-weighted) are not reproduced inside the library.

Stochastic Discount Factor Network¶

Implementation: StochasticDiscountFactorModel.

Chen, Pelger, and Zhu (2021)¶

Deep Learning in Asset Pricing. The CPZ adversarial SDF: a neural network parameterizes the pricing kernel \(M_{t+1}\), a separate moment network learns the worst-case test-asset weighting, and the two networks train against each other so that the SDF is disciplined by the most-mispriced portfolio at every step. The library implements the three-phase training that the paper describes:

unconditional pre-training of the SDF network (n_epochs_unc),
moment-network fitting (n_epochs_moment),
conditional-SDF refinement under the adversarial signal (n_epochs_cond).

The output is weight-native: StochasticDiscountFactorState.asset_weights are the SDF portfolio weights; sdf_values are the realized \(M_{t+1}\) series. Expected-return-style projections require the optional beta-head network.

Gospodinov, Kan, and Robotti (2017)¶

Spurious Inference in Reduced-Rank Asset-Pricing Models. The cautionary counterpart to the CPZ adversarial machinery: cross-sectional GMM fit can be made arbitrarily good through weighting-matrix choices when the model is misspecified. The library does not encode this critique mechanically but the user guide calls out that pricing-error minimization alone does not certify economic validity.

Supervised Autoencoder¶

Implementation: SAEModel.

The SAE in this library is the supervised autoencoder of the Jane Street competition lineage — encoder, decoder, auxiliary head, and main predictive head trained jointly under a composite loss. It is not a sparse autoencoder and not a latent-factor model. The library treats SAEModel as a direct supervised cross-sectional predictor; predict() returns AssetSignalResult, not a beta-times-lambda decomposition.

The library's contract draws on the supervised-autoencoder pattern documented in:

the Jane Street Market Prediction competition winners' write-ups (encoder, denoising bottleneck, auxiliary classification head, MLP main head trained jointly),
and the broader literature on auxiliary-task regularization for tabular cross-sectional prediction.

Treat this section as a deliberate departure from chapter conventions: the chapter discusses SAE alongside latent-factor models because the architectures share a bottleneck, but in production they answer different questions and the library reflects that.

End-to-End Portfolio Learning¶

Implementations: LinearFeaturePortfolioModel, LSTMPortfolioModel, DeepPortfolioModel.

The portfolio family draws on two threads.

End-to-end portfolio learning¶

The Sharpe-ratio-as-loss training framework: optimize portfolio weights directly under a differentiable Sharpe-style or turnover-aware objective rather than chaining a return forecast into a separate optimizer. This is the design behind the linear and LSTM baselines, and motivates why portfolio costs (costs) and previous weights (prev_weights) appear in PortfolioSequenceBatch rather than only in a downstream backtester.

DeePM-style structured portfolio learning¶

DeepPortfolioModel implements a DeePM-style allocator: static context encoding, feature modulation, variable selection, an LSTM temporal backbone, temporal self-attention, cross-sectional attention, and optional macro-graph attention. The architecture choices come from the published end-to-end portfolio-learning literature (TFT-style encoders for context; DeePM-style multi-head architectures for cross-sectional structure). The library presents this as one structured allocator, not a generic Transformer wrapper.

Wood, Roberts, and Zohren (2026)¶

DeePM: Regime-Robust Deep Learning for Systematic Macro Portfolio Management. Provides the structured portfolio-learning blueprint behind DeepPortfolioModel: sequence encoding, cross-sectional interaction, graph-aware structure, and direct optimization of a robust risk-adjusted objective under transaction costs.

Kisiel et al. (2023)¶

Portfolio Transformer for Attention-Based Asset Allocation. Cited here as motivation for treating attention-based allocators as a separate family rather than a special case of return forecasting.

Cross-Cutting References¶

These papers do not pin a specific estimator but shape the library's framing.

Cochrane (2011)¶

Discount Rates. Frames the factor-zoo problem and the variance-vs-pricing distinction that motivates separating PCA / RP-PCA / IPCA / CAE from the SDF family.

Harvey, Liu, and Zhu (2016)¶

…and the Cross-Section of Expected Returns. The multiple-testing critique that justifies treating factor discovery as a disciplined model-selection problem rather than open-ended specification search. Cited in the user guide only when arguing for the RP-PCA / IPCA / CAE design's structural posture, not as a default citation.

Feng, Giglio, and Xiu (2020)¶

Taming the Factor Zoo: A Test of New Factors. Double-selection LASSO inference for new-factor evaluation. The library does not bundle this test; it is the recommended diagnostic when a user adds a new latent-factor model and wants robust incremental-significance evidence.

Jensen, Kelly, and Pedersen (2022)¶

Is There a Replication Crisis in Finance? Hierarchical Bayesian replication across 153 factors in 93 countries; finds that factors cluster into roughly 13 themes that hold up out of sample. Used in the user guide to qualify how aggressively to interpret factor-zoo critique when interpreting RPPCAModel and IPCAModel outputs.

Bryzgalova, Pelger, and Zhu (2025)¶

Forest through the Trees: Building Cross-Sections of Stock Returns. Endogenous test-asset construction. Cited as the design rationale for treating test-asset choice as a first-class evaluation knob rather than a neutral backdrop, and listed in the Roadmap as a future model addition.

Bagnara (2024)¶

Asset Pricing and Machine Learning: A Critical Review. Survey that organizes the IPCA / RP-PCA / CAE / SDF families along the same axes the library uses (variance maximization, variance plus pricing, no-arbitrage). Useful onboarding reading for anyone moving between the chapter and the library.

What This Bibliography Deliberately Excludes¶

Three classes of citations are kept out on purpose, in line with the user-guide voice rules:

Default trading-research citations (Harvey 2016 standalone, Lopez de Prado on PBO / triple-barrier / fractional differentiation). These are out of scope for ml4t-models; they shape ml4t-diagnostic and ml4t-engineer, not this library.
One-off application papers that do not generalize to a reusable model family. See ROADMAP.md for the explicit prioritization rule.
Numerical results from the chapter case studies. Those live with the case-study artifacts and the run_log/registry.db they are emitted to. Importing them here would create a maintenance liability the library cannot honor.