arXiv subjects

Nayoon Kim

Publications and source records attributed to Nayoon Kim.

2 recordsLinked to original sources

arXiv2026

When Can One Obtain Certificates of Optimality Using Positivstellensaetze?

We study certificates of positivity and optimality for learning problems whose objectives and constraints need not be polynomial. We isolate an axiomatic core of Fischer's constructive strict and weak Positivstellensätze and prove the resulting theorems for abstract function algebras over ordered fields. The framework separates two roles that can otherwise be conflated: objective and constraint functions may be built from broad classes of continuous or definable operations, while the auxiliary primitives used to construct a certificate satisfy explicit scalar and closure axioms. We give instances over continuous and definable function algebras, including ordered fields not closed under square roots, derive lower-bound and global-optimality certificates, and analyze both expanded term length and shared computation-graph complexity.

cs.AI↗

arXiv2023

Learning to Maximize Mutual Information for Dynamic Feature Selection

Feature selection helps reduce data acquisition costs in ML, but the standard approach is to train models with static feature subsets. Here, we consider the dynamic feature selection (DFS) problem where a model sequentially queries features based on the presently available information. DFS is often addressed with reinforcement learning, but we explore a simpler approach of greedily selecting features based on their conditional mutual information. This method is theoretically appealing but requires oracle access to the data distribution, so we develop a learning approach based on amortized optimization. The proposed method is shown to recover the greedy policy when trained to optimality, and it outperforms numerous existing feature selection methods in our experiments, thus validating it as a simple but powerful approach for this problem.

cs.LG↗