arXiv subjects

Fangyuan Lin

Publications and source records attributed to Fangyuan Lin.

5 recordsLinked to original sources

arXiv2026

Mitigating the Winner's Curse While Controlling Multiplicity: e-Process Methods for Anytime-Valid Inference in Dose-Ranging Trials

Phase II dose-ranging trials often report the largest observed dose-control effect while inspecting accumulating data repeatedly. This creates two coupled distortions: selection optimism from choosing the empirical winner, known as the winner's curse, and Type I error inflation from multiplicity across doses and interim looks. We develop an anytime-valid procedure for testing whether the best true dose effect exceeds a clinically meaningful margin. The mathematical starting point is a recent selection-premium identity for the running maximum: for dose-control scores, the expected gain from re-selecting the current leader becomes a predictable selection charge. Subtracting this charge gives a residual with nonpositive drift under the composite null; applying a one-sided mixture-exponential construction then yields an e-process and hence an anytime-valid global test. The resulting rule has a transparent ledger form: raw best effect minus selection charge minus monitoring margin, and a ``GO'' decision is made only when the remaining evidence still exceeds the clinical margin. We give plug-in implementations for Gaussian and binary outcomes, prove finite-sample Type I control and anytime lower confidence bounds for the best dose effect, and illustrate the method through a worked example and simulations.

stat.ME↗

arXiv2026

Bounded Difference Concentration for Infinitely Exchangeable Sequences with Applications to AI Benchmark Uncertainty

We consider the concentration properties of functions of infinitely exchangeable random variables. By conditioning on the de Finetti directing measure, we show that the deviation of any function with bounded-difference constants $c_1, \dots, c_n$ decomposes into a conditional sampling fluctuation and a latent mixture fluctuation. When this latent mixture is $\sigma_{\mathrm{mix}}^2$-subgaussian, we establish a concentration inequality with an effective variance proxy of $\frac{1}{4}\sum_i c_i^2 + \sigma_{\mathrm{mix}}^2$. Crucially, we demonstrate that for zero-sum linear contrasts, such as the difference between a subsample mean and a full population mean, the latent mixture term cancels exactly. This cancellation yields a tight, mixture-free Hoeffding-type bound that provides a direct de Finetti mechanism for the infinite-extendibility limit of recent finite-exchangeable concentration results. We apply this framework to quantify uncertainty in composite AI benchmarks, such as MMLU, where question items naturally exhibit exchangeable dependence across domains. Our results provide both a domain-stratified hierarchical model for bounding the uncertainty of accuracy scores, and a distribution-free, cost-saving statistical guarantee for accurately estimating full benchmark scores from random subsets.

stat.ML↗

arXiv2026

A Selection Premium Decomposition for the Expected Maximum of Random Walks

When $K$ models are evaluated on the same validation set of size $n$, the selected winner's apparent performance is biased upward. Suppose $K$ models are evaluated on a shared sequence of i.i.d. observations $X_1,\dots, X_n$, where model $k$ achieves response $f_k(X_i)$ with mean $\mu_k = \mathbb E[f_k(X)]$. Writing $Y_{i,k} = f_k(X_i)-\mu_k$ for the centered increment and $S_{n,k} = \sum_{i=1}^n Y_{i,k}$ for the centered cumulative score, the expected maximum satisfies $0\le\mathbb E\bigl[\max_k S_{n,k}\bigr] = \sum_{i=1}^n \mathbb E\bigl[\varphi_K(S_{i-1})\bigr]$ where $\varphi_K(u) = \mathbb{E}\bigl[\max_k(u_k + Y_k)\bigr] - \max_k u_k$, $u\in \mathbb R^K$, is the selection premium function. This formula corresponds to the null hypothesis case (all models are equal in the sense that they have the same mean), which clarifies that the bias arises from selection. While this decomposition follows from elementary conditioning and telescoping, we develop the analytical consequences in five directions. (i) structural properties of $\varphi_K$; (ii) extension to stopping times, recovering Wald's equation at $K=1$; (iii) a winner's curse decomposition for heterogeneous means; (iv) a universal bias concentration law showing that the first $\alpha$-fraction of observations generates a $\sqrt\alpha$-fraction of total bias.

math.ST↗

arXiv2024

Revisiting the Unicity Distance through a Channel Transmission Perspective

This paper revisits the classical notion of unicity distance from an enlightening perspective grounded in information theory, specifically by framing the encryption process as a noisy transmission channel. Using results from reliable communication theory, we derive a simple information-theoretic proof of the same unicity distance formula as in Shannon's classical result and a channel transmission interpretation of the unicity distance.

cs.IT↗

arXiv2023

Applications of the Theory of Aggregated Markov Processes in Stochastic Learning Theory

A stochastic process that arises by composing a function with a Markov process is called an aggregated Markov process (AMP). The purpose of composing a Markov process with a function can be a reduction of dimensions, e.g., a projection onto certain coordinates. The theory around AMP has been extensively studied e.g. by Dynkin, Cameron, Rogers and Pitman, and Kelly, all of whom provided sufficient conditions for an AMP to remain Markov. In another direction, Larget provided a canonical representation for AMP, which can be used to verify the equivalence of two AMPs. The purpose of this paper is to describe how the theory of AMP can be applied to stochastic learning theory as they learn a particular task.

stat.ML↗