Jiarui Qi | Search arXiv

arXiv2026

Shape without scale: an identifiability dichotomy for a bounded tail observed through a non-additive measurement kernel

A latent severity has a bounded lower tail with density of shape alpha and scale L. It is observed only through a fixed Markov kernel K that is biased and non-additive. The relative conditional spread of K diverges at the endpoint. Our sample is i.i.d. from the marginal Q alone, with no anchoring covariate or instrument. We prove a dichotomy. The shape index alpha is identifiable: for every admissible choice of the class constants, any two observationally equivalent members of a lean class share alpha, determined by a near-endpoint expansion of Q. The rate, namely L and the fixed-scale exceedance p_tau, does not survive. There exist admissible shared class constants and two members of a smaller regularity class whose observed laws coincide exactly. Across the pair alpha agrees, whereas L and p_tau move. A degenerate Le Cam two-point bound excludes any uniformly consistent estimator of either, and pointwise consistency fails at one member. Only the rate needs an anchor. We conjecture that a known kernel family with known edge map identifies the rate fiber by fiber if and only if the family satisfies a fixed-scale injectivity clause, and we prove the sufficiency direction. In surrogate safety, uncalibrated conflict data give the shape of near-crash risk, not its absolute rate.

math.ST↗

arXiv2020

Multi-task Learning for Low-resource Second Language Acquisition Modeling

Second language acquisition (SLA) modeling is to predict whether second language learners could correctly answer the questions according to what they have learned. It is a fundamental building block of the personalized learning system and has attracted more and more attention recently. However, as far as we know, almost all existing methods cannot work well in low-resource scenarios due to lacking of training data. Fortunately, there are some latent common patterns among different language-learning tasks, which gives us an opportunity to solve the low-resource SLA modeling problem. Inspired by this idea, in this paper, we propose a novel SLA modeling method, which learns the latent common patterns among different language-learning datasets by multi-task learning and are further applied to improving the prediction performance in low-resource scenarios. Extensive experiments show that the proposed method performs much better than the state-of-the-art baselines in the low-resource scenario. Meanwhile, it also obtains improvement slightly in the non-low-resource scenario.

cs.CL↗