Ekaterina Zubova | Searcharxiv

arXiv2026

Approximate Minimax Estimation of a Bounded Normal Mean via Stochastic Mirror Ascent

This paper presents a computational approach to find an approximately minimax estimator for the classical Bounded Normal Mean problem. The suggested procedure is the Bayes estimator corresponding to an approximately least-favorable distribution obtained from a stochastic mirror ascent routine for concave maximization. The paper shows that both the approximately least-favorable distribution and the approximately minimax estimator are indeed close (in a sense we make precise) to their desired targets. Simulation evidence suggests that the approximately minimax estimator can yield, with a reasonable amount of compute, risk improvements from 6% to almost 18% relative to the minimax linear estimator (which is known to admit a maximal improvement of 20%). The approximately minimax estimator is then applied to the problem of how to best aggregate the information contained in local projections and vector autoregressions to estimate an impulse response coefficient.

econ.EM↗

arXiv2024

FOLIO: Natural Language Reasoning with First-Order Logic

Large language models (LLMs) have achieved remarkable performance on a variety of natural language understanding tasks. However, existing benchmarks are inadequate in measuring the complex logical reasoning capabilities of a model. We present FOLIO, a human-annotated, logically complex and diverse dataset for reasoning in natural language (NL), equipped with first-order logic (FOL) annotations. FOLIO consists of 1,430 examples (unique conclusions), each paired with one of 487 sets of premises used to deductively reason for the validity of each conclusion. The logical correctness of the premises and conclusions is ensured by their FOL annotations, which are automatically verified by an FOL inference engine. In addition to the main NL reasoning task, NL-FOL pairs in FOLIO constitute a new NL-FOL translation dataset. Our experiments on FOLIO systematically evaluate the FOL reasoning ability of supervised fine-tuning on medium-sized language models. For both NL reasoning and NL-FOL translation, we benchmark multiple state-of-the-art language models. Our results show that a subset of FOLIO presents a challenge for one of the most capable {Large Language Model (LLM)} publicly available, GPT-4.

cs.CL↗