Bayesian Imputation with Optimal Look-Ahead-Bias and Variance Tradeoff
Bayesian Imputation with Optimal Look-Ahead-Bias and Variance Tradeoff
This paper addresses the overlooked problem of look-ahead-bias in imputation for downstream out-of-sample tasks, using portfolio allocation with missing asset returns as a leading example. The authors propose a Bayesian framework that fuses multiple posterior distributions derived from different temporal layers of data (e.g., training-only vs. full panel) via a consensus mechanism. The consensus posterior is obtained by minimizing a weighted sum of divergences (KL or Wasserstein) to the individual posteriors, with weights optimized to balance variance and look-ahead-bias. Under Gaussian assumptions and conjugate priors, tractable two-step optimization procedures are derived. Simulations and an empirical study demonstrate that the optimal consensus imputation significantly improves the out-of-sample performance of mean-variance portfolios compared to using only training data or the full panel, validating the practical relevance of the bias-variance trade-off in imputation.
Highlights
- 1Identifies and formalizes the look-ahead-bias problem in imputation for downstream tasks, proposing a novel Bayesian framework to optimally trade off bias and variance.
- 2Introduces a consensus posterior mechanism that fuses multiple Bayesian posteriors from different temporal information layers using KL divergence or Wasserstein distance.
- 3Provides tractable two-step optimization procedures for finding optimal consensus posteriors under Gaussian assumptions and simultaneous diagonalizability.
- 4Empirically demonstrates improved portfolio allocation performance (lower regret) compared to naive imputation using only training data or full panel data.
Methods
- MBayesian imputation with conjugate Gaussian priors and posteriors for the mean parameter θ.
- MConsensus posterior via weighted barycenter optimization using forward/backward Kullback-Leibler divergence and Wasserstein distance.
- MTwo-step optimization: first find consensus distribution given weights, then optimize weights to minimize variance under a look-ahead-bias constraint.
- MMultiple imputation sampler that generates imputed datasets from the consensus posterior for downstream portfolio optimization.
Results
- RThe optimal consensus posterior achieves a better bias-variance trade-off than using only training data (high variance) or full panel data (high look-ahead-bias).
- RForward KL divergence and Wasserstein distance yield tractable convex optimization problems under simultaneous diagonalizability, while backward KL leads to non-convex problems.
- RSimulations show that the proposed method reduces expected conditional mean squared error (regret) in portfolio allocation across various missing patterns (MAR, block missing, missing by values).
- REmpirical study on real financial data confirms improved out-of-sample portfolio performance relative to naive imputation baselines.
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