Learning from (Almost) Nothing: An Exact Theory of Projection Learning in Finance
A new study explains why complex machine learning models with thousands of parameters can excel in financial markets, even with tiny datasets. The key is 'projection learning,' where models improve by projecting the unknown return function onto observable features, not by learning the true function. The author provides exact formulas for bias, variance, and Sharpe ratios, showing that more complexity boosts performance. The findings challenge classical theory but rely on assumptions like independent and identically distributed (i.i.d.) data.
What it examines
This paper explains why complex machine learning models can perform well in finance even with very little data. It introduces 'projection learning,' showing that these models succeed by finding better projections of the true return function, not by learning the function itself, using exact mathematical formulas.
What it concludes
The study shows that increasing model complexity helps capture more useful financial signals, even with small datasets. This approach enables faster, more accurate portfolio decisions. The findings can improve financial forecasting, risk management, and investment strategies, and suggest new directions for research in data-scarce environments.
Evidence objects
A new study explains why highly complex machine learning models, with thousands of parameters, can excel in finance even with tiny datasets, challenging classical theory and resolving a longstanding paradox in the field.
key_findings bullet 1 · key_findings · validation V0
The paper introduces 'projection learning,' showing these models succeed by projecting the return function onto observable features, not by learning the true functionimproving risk-adjusted returns (Sharpe ratios) as complexity increases.
key_findings bullet 2 · key_findings · validation V0
Using advanced random matrix theory and kernel methods, the author provides exact formulas for bias, variance, and performance, enabling millisecond calculations, though results depend on assumptions like i.i.d. data and specific regularity conditions.
key_findings bullet 3 · key_findings · validation V0
This paper uniquely resolves a major paradox in machine learning for finance by introducing 'projection learning,' a novel framework with exact finite-sample theory and closed-form expressions. It compellingly explains why highly complex models ($12{,}000$ parameters, $12$ observations) succeed, reconciling empirical results with theory and offering significant practical and theoretical impact.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
- … machine learning in finance succeeds not by learning the true function f∗ (left panel), a task called Function Learning… this paper formalizes as Projection Learning. The left …
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