Prediction-Powered Ranking of Large Language Models

Large language models are often ranked according to their level of alignment with human preferences -- a model is better than other models if its outputs are more frequently preferred by humans. One of the most popular ways to elicit human preferences utilizes pairwise comparisons between the outputs provided by different models to the same inputs. However, since gathering pairwise comparisons by humans is costly and time-consuming, it has become a very common practice to gather pairwise comparisons by a strong large language model -- a model strongly aligned with human preferences. Surprisingly, practitioners cannot currently measure the uncertainty that any mismatch between human and model preferences may introduce in the constructed rankings. In this work, we develop a statistical framework to bridge this gap. Given a small set of pairwise comparisons by humans and a large set of pairwise comparisons by a model, our framework provides a rank-set -- a set of possible ranking positions -- for each of the models under comparison. Moreover, it guarantees that, with a probability greater than or equal to a user-specified value, the rank-sets cover the true ranking consistent with (the distribution of) human pairwise preferences. Our framework is computationally efficient, easy to use, and does not make any assumption about the distribution of human preferences nor about the degree of alignment between the pairwise comparisons by the humans and the strong large language model.

Diversity-aware clustering: Computational Complexity and Approximation Algorithms

In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution need to ensure that a minimum number of cluster centers are chosen from each group while simultaneously minimizing the clustering objective, which can be either $k$-median, $k$-means or $k$-supplier. We present parameterized approximation algorithms with approximation ratios $1+ \frac{2}{e}$, $1+\frac{8}{e}$ and $3$ for diversity-aware $k$-median, diversity-aware $k$-means and diversity-aware $k$-supplier, respectively. The approximation ratios are tight assuming Gap-ETH and FPT $\neq$ W[2]. For fair $k$-median and fair $k$-means with disjoint faicility groups, we present parameterized approximation algorithm with approximation ratios $1+\frac{2}{e}$ and $1+\frac{8}{e}$, respectively. For fair $k$-supplier with disjoint facility groups, we present a polynomial-time approximation algorithm with factor $3$, improving the previous best known approximation ratio of factor $5$.

Fair Column Subset Selection

We consider the problem of fair column subset selection. In particular, we assume that two groups are present in the data, and the chosen column subset must provide a good approximation for both, relative to their respective best rank-k approximations. We show that this fair setting introduces significant challenges: in order to extend known results, one cannot do better than the trivial solution of simply picking twice as many columns as the original methods. We adopt a known approach based on deterministic leverage-score sampling, and show that merely sampling a subset of appropriate size becomes NP-hard in the presence of two groups. Whereas finding a subset of two times the desired size is trivial, we provide an efficient algorithm that achieves the same guarantees with essentially 1.5 times that size. We validate our methods through an extensive set of experiments on real-world data.