Paper: arXiv 2410.01831

Abstract

The advances and development of various machine learning techniques has lead to practical solutions in various areas of science, engineering, medicine and finance. The great choice of algorithms, their implementations and libraries has resulted in another challenge of selecting the right algorithm and tuning their parameters in order to achieve optimal or satisfactory performance in specific applications. Here we show how the value of information (V(I)) can be used in this task to guide the algorithm choice and parameter tuning process. After estimating the amount of Shannon’s mutual information between the predictor and response variables, V(I) can define theoretical upper bound of performance of any algorithm. The inverse function I(V) defines the lower frontier of the minimum amount of information required to achieve the desired performance. In this paper, we illustrate the value of information for the mean-square error minimization and apply it to forecasts of cryptocurrency log-returns.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is heavily theoretical, deriving complex relationships using Shannon’s mutual information, Lagrange multipliers, and Legendre-Fenchel duality, indicating high mathematical complexity. Conversely, the empirical section is limited to a high-level application to cryptocurrency returns without specific code, backtesting procedures, or statistical metrics, resulting in low empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: <br>Use Value of Information V(I) <br>for ML Algorithm & Parameter Selection"] --> B["Input Data: <br>Financial Time-Series <br>e.g., Cryptocurrency Log-Returns"]
  B --> C["Key Methodology: <br>Estimate Mutual Information <br>between Predictors and Response"]
  C --> D["Computational Process: <br>Calculate V(I) <br>Upper Bound (Max Performance) <br>& I(V) Lower Frontier"]
  D --> E{"Outcomes & Application"}
  E --> F1["Theoretical Limit: <br>Define max achievable <br>prediction accuracy"]
  E --> F2["Selection Criteria: <br>Identify algorithms & params <br>approaching the bound"]
  E --> F3["Practical Result: <br>Optimized forecasts <br>for financial time-series"]

Cited References (21)

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  2. Information trajectory of optimal learning (2010)
  3. Mutation and Optimal Search of Sequences in Nested H amming Spaces (2011)
  4. Dynamics of Information and Optimal Control of Mutation in Evolutionary Systems (2012)
  5. Optimal measures and M arkov transition kernels (2013)
  6. Asymmetry of Risk and Value of Information (2014)
  7. Relation Between the K antorovich- W asserstein Metric and the K ullback- L eibler Divergence (2018)
  8. Monotonicity of fitness landscapes and mutation rate control (2016)
and 13 more
  1. SIMPLS: An alternative approach to partial least squares regression (1993)
  2. Value of information and sufficient statistics during an observation of a stochastic process (1966)
  3. Conjugate Duality and Optimization (1974)
  4. A mathematical theory of communication (1948)
  5. Topics in the Theory of Random Noise (2014)
  6. Theory of Information and its Value (2020)
  7. On value of information (1965)
  8. Value of information during an observation of a stochastic process in systems with finite state automata (1966)
  9. Extreme problems of information theory and dynamic programming (1967)
  10. Theory of Information (1975)
  11. Value of information when an estimated random variable is hidden (1966)
  12. Game-theoretic problems with information constraints (1968)
  13. Analysis II (1990)

0 of 21 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.