Profile Likelihood F1 Confidence Interval Method

A Profile Likelihood F1 Confidence Interval Method is a likelihood-based confidence interval method that finds F1 score bounds by inverting likelihood ratio tests through parameter space search.

• AKA: Likelihood Ratio F1 Interval Method, Profile-Based F1 CI Method, LR Test Inversion F1 Method, Maximum Likelihood F1 Interval Method.
• Context:
  • It can typically search for F1 values where -2log(LR) < χ²(1,α) critical value.
  • It can typically maximize likelihood over nuisance parameters for each fixed F1 value.
  • It can typically produce asymmetric intervals that respect parameter constraints naturally.
  • It can often provide optimal coverage propertys based on likelihood principle.
  • It can often handle complex models with multiple parameters affecting F1.
  • It can often require iterative optimization making it computationally intensive.
  • It can range from being a Exact Profile Likelihood F1 Confidence Interval Method to being an Approximate Profile Likelihood F1 Confidence Interval Method, depending on its likelihood computation.
  • It can range from being a Univariate Profile Likelihood F1 Confidence Interval Method to being a Multivariate Profile Likelihood F1 Confidence Interval Method, depending on its parameter dimension.
  • It can range from being a Constrained Profile Likelihood F1 Confidence Interval Method to being an Unconstrained Profile Likelihood F1 Confidence Interval Method, depending on its parameter space.
  • It can range from being a Grid-Search Profile Likelihood F1 Confidence Interval Method to being a Gradient-Based Profile Likelihood F1 Confidence Interval Method, depending on its optimization method.
  • ...
• Example(s):
  • Binary Classification Profile CIs, such as:
    • F1=0.85: Search range [0.7,0.95], find LR cutoff at [0.79, 0.89].
    • Asymmetric: lower bound 0.06 from estimate, upper 0.04.
    • More precise than Wald [0.78, 0.92] with same coverage.
  • Multi-Parameter Models, such as:
    • Logistic regression with 10 predictors affecting F1.
    • Profile over regression coefficients for each F1 value.
    • Captures model uncertainty beyond sampling variance.
  • Computational Implementations, such as:
    • Grid search: 100 F1 values, optimize likelihood at each.
    • Binary search: narrow interval iteratively, 10-15 iterations.
    • Parallel computation: profile multiple parameters simultaneously.
  • ...
• Counter-Example(s):
  • Wald F1 Confidence Interval Method, which uses quadratic approximation.
  • Score-Based Interval Method, which inverts score tests.
  • Bootstrap F1 Interval Method, which uses resampling.
• See: Likelihood-Based Inference Method, Confidence Interval Method, Likelihood Ratio Test, Profile Likelihood, F1 Score, Parameter Space Search, Nuisance Parameter, Optimization Method, F1 Confidence Interval Construction Method, Asymmetric Confidence Interval, Maximum Likelihood Estimation.

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