Less is More: Adaptive Coverage for Synthetic Training Data

Synthetic training data generation with Large Language Models (LLMs) like Google's Gemma and OpenAI's GPT offer a promising solution to the challenge of obtaining large, labeled datasets for training classifiers. When rapid model deployment is critical, such as in classifying emerging social media trends or combating new forms of online abuse tied to current events, the ability to generate training data is invaluable. While prior research has examined the comparability of synthetic data to human-labeled data, this study introduces a novel sampling algorithm, based on the maximum coverage problem, to select a representative subset from a synthetically generated dataset. Our results demonstrate that training a classifier on this contextually sampled subset achieves superior performance compared to training on the entire dataset. This "less is more" approach not only improves accuracy but also reduces the volume of data required, leading to potentially more efficient model fine-tuning.

Fair Polylog-Approximate Low-Cost Hierarchical Clustering

Research in fair machine learning, and particularly clustering, has been crucial in recent years given the many ethical controversies that modern intelligent systems have posed. Ahmadian et al. [2020] established the study of fairness in \textit{hierarchical} clustering, a stronger, more structured variant of its well-known flat counterpart, though their proposed algorithm that optimizes for Dasgupta's [2016] famous cost function was highly theoretical. Knittel et al. [2023] then proposed the first practical fair approximation for cost, however they were unable to break the polynomial-approximate barrier they posed as a hurdle of interest. We break this barrier, proposing the first truly polylogarithmic-approximate low-cost fair hierarchical clustering, thus greatly bridging the gap between the best fair and vanilla hierarchical clustering approximations.

An Improved Relaxation for Oracle-Efficient Adversarial Contextual Bandits

We present an oracle-efficient relaxation for the adversarial contextual bandits problem, where the contexts are sequentially drawn i.i.d from a known distribution and the cost sequence is chosen by an online adversary. Our algorithm has a regret bound of $O(T^{\frac{2}{3}}(K\log(|\Pi|))^{\frac{1}{3}})$ and makes at most $O(K)$ calls per round to an offline optimization oracle, where $K$ denotes the number of actions, $T$ denotes the number of rounds and $\Pi$ denotes the set of policies. This is the first result to improve the prior best bound of $O((TK)^{\frac{2}{3}}(\log(|\Pi|))^{\frac{1}{3}})$ as obtained by Syrgkanis et al. at NeurIPS 2016, and the first to match the original bound of Langford and Zhang at NeurIPS 2007 which was obtained for the stochastic case.

Optimal Sparse Recovery with Decision Stumps

Decision trees are widely used for their low computational cost, good predictive performance, and ability to assess the importance of features. Though often used in practice for feature selection, the theoretical guarantees of these methods are not well understood. We here obtain a tight finite sample bound for the feature selection problem in linear regression using single-depth decision trees. We examine the statistical properties of these "decision stumps" for the recovery of the $s$ active features from $p$ total features, where $s \ll p$. Our analysis provides tight sample performance guarantees on high-dimensional sparse systems which align with the finite sample bound of $O(s \log p)$ as obtained by Lasso, improving upon previous bounds for both the median and optimal splitting criteria. Our results extend to the non-linear regime as well as arbitrary sub-Gaussian distributions, demonstrating that tree based methods attain strong feature selection properties under a wide variety of settings and further shedding light on the success of these methods in practice. As a byproduct of our analysis, we show that we can provably guarantee recovery even when the number of active features $s$ is unknown. We further validate our theoretical results and proof methodology using computational experiments.