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What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Dealing With Ratio Metrics in A/B Testing at the Presence...
Keyu Nie, Yinfei Kong, Ted Tao Yuan, Pauline Berry Burke · 2019-11-09 · via math.ST updates on arXiv.org

We study ratio metrics in A/B testing at the presence of correlation among observations coming from the same user and provides practical guidance especially when two metrics contradict each other. We propose new estimating methods to quantitatively measure the intra-user correlation (within segments). With the accurately estimated correlation, a uniformly minimum-variance unbiased estimator of the population mean, called correlation-adjusted mean, is proposed to account for such correlation structure. It is proved theoretically and numerically better than the other two unbiased estimators, naive mean and normalized mean (averaging within users first and then across users). The correlation-adjusted mean method is unbiased and has reduced variance so it gains additional power. Several simulation studies are designed to show the estimation accuracy of the correlation structure, effectiveness in reducing variance, and capability of obtaining more power. An application to the eBay data is conducted to conclude this paper.