Limits To (Machine) Learning
A new study reveals that standard machine learning models greatly underestimate how predictable financial markets are. Researchers introduce the Limits-to-Learning Gap (LLG), a universal lower bound showing that true predictability in stock returns, bond yields, and credit spreads can be up to 20 times higher than models suggest. Using advanced statistics and big data, the paper finds high-dimensional models face sample size limits, challenging the belief that markets are unpredictable and urging a rethink in economic modeling.
What it examines
This paper shows that machine learning models often underestimate how predictable financial data really is, due to limits from having only finite samples. The authors introduce a new correction, the Limits-to-Learning Gap (LLG), to better measure true predictability in asset pricing and financial forecasting.
What it concludes
The study finds that true predictability in financial data is much higher than standard methods suggest. The LLG correction helps researchers and investors identify hidden patterns, improve forecasting, and guide model selection. This approach can be used in finance, economics, and any field dealing with complex, high-dimensional data.
Evidence objects
Researchers reveal that standard machine learning models vastly underestimate financial market predictability, sometimes by up to 20 times, challenging the widespread belief that markets are inherently unpredictable and difficult to forecast.
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The study introduces the Limits-to-Learning Gap (LLG), a universal lower bound that quantifies the gap between what models can learn and true predictability, offering a practical diagnostic tool for financial data analysis.
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Using advanced statistical theory and big data, the authors show high-dimensional models face intrinsic limits due to finite samples, but their approach mainly addresses linear estimators, leaving nonlinear complexities less explored.
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This paper introduces the novel Limits-to-Learning Gap (LLG), a universal, data-driven lower bound quantifying the gap between empirical model fit and true population benchmarks in financial machine learning. Its originality lies in addressing underestimation of predictability, offering practical corrections, and influencing both academic research and real-world financial ML applications.
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Raw abstract and provenance
Abstract: Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG), quantifying the unavoidable discrepancy between a model's empirical fit and the population benchmark. Recovering the true population $R^2$, therefore, requires… ▽ More Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG), quantifying the unavoidable discrepancy between a model's empirical fit and the population benchmark. Recovering the true population $R^2$, therefore, requires correcting observed predictive performance by this bound. Using a broad set of variables, including excess returns, yields, credit spreads, and valuation ratios, we find that the implied LLGs are large. This indicates that standard ML approaches can substantially understate true predictability in financial data. We also derive LLG-based refinements to the classic Hansen and Jagannathan (1991) bounds, analyze implications for parameter learning in general-equilibrium settings, and show that the LLG provides a natural mechanism for generating excess volatility. △ Less
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