Justin Y. Chen

Anders Aamand, Justin Y. Chen, Allen Liu et al. · deepmind

Individual preference (IP) stability, introduced by Ahmadi et al. (ICML 2022), is a natural clustering objective inspired by stability and fairness constraints. A clustering is $α$-IP stable if the average distance of every data point to its own cluster is at most $α$ times the average distance to any other cluster. Unfortunately, determining if a dataset admits a $1$-IP stable clustering is NP-Hard. Moreover, before this work, it was unknown if an $o(n)$-IP stable clustering always \emph{exists}, as the prior state of the art only guaranteed an $O(n)$-IP stable clustering. We close this gap in understanding and show that an $O(1)$-IP stable clustering always exists for general metrics, and we give an efficient algorithm which outputs such a clustering. We also introduce generalizations of IP stability beyond average distance and give efficient, near-optimal algorithms in the cases where we consider the maximum and minimum distances within and between clusters.

Anders Aamand, Justin Y. Chen, Huy Lê Nguyen et al.

We give improved tradeoffs between space and regret for the online learning with expert advice problem over $T$ days with $n$ experts. Given a space budget of $n^δ$ for $δ\in (0,1)$, we provide an algorithm achieving regret $\tilde{O}(n^2 T^{1/(1+δ)})$, improving upon the regret bound $\tilde{O}(n^2 T^{2/(2+δ)})$ in the recent work of [PZ23]. The improvement is particularly salient in the regime $δ\rightarrow 1$ where the regret of our algorithm approaches $\tilde{O}_n(\sqrt{T})$, matching the $T$ dependence in the standard online setting without space restrictions.

Anders Aamand, Justin Y. Chen, Huy Lê Nguyen et al.

Estimating frequencies of elements appearing in a data stream is a key task in large-scale data analysis. Popular sketching approaches to this problem (e.g., CountMin and CountSketch) come with worst-case guarantees that probabilistically bound the error of the estimated frequencies for any possible input. The work of Hsu et al. (2019) introduced the idea of using machine learning to tailor sketching algorithms to the specific data distribution they are being run on. In particular, their learning-augmented frequency estimation algorithm uses a learned heavy-hitter oracle which predicts which elements will appear many times in the stream. We give a novel algorithm, which in some parameter regimes, already theoretically outperforms the learning based algorithm of Hsu et al. without the use of any predictions. Augmenting our algorithm with heavy-hitter predictions further reduces the error and improves upon the state of the art. Empirically, our algorithms achieve superior performance in all experiments compared to prior approaches.

Supriya Nagesh, Justin Y. Chen, Nina Mishra et al.

We explore how private synthetic text can be generated by suitably prompting a large language model (LLM). This addresses a challenge for organizations like hospitals, which hold sensitive text data like patient medical records, and wish to share it in order to train machine learning models for medical tasks, while preserving patient privacy. Methods that rely on training or finetuning a model may be out of reach, either due to API limits of third-party LLMs, or due to ethical and legal prohibitions on sharing the private data with the LLM itself. We propose Differentially Private Keyphrase Prompt Seeding (DP-KPS), a method that generates a private synthetic text corpus from a sensitive input corpus, by accessing an LLM only through privatized prompts. It is based on seeding the prompts with private samples from a distribution over phrase embeddings, thus capturing the input corpus while achieving requisite output diversity and maintaining differential privacy. We evaluate DP-KPS on downstream ML text classification tasks, and show that the corpora it generates preserve much of the predictive power of the original ones. Our findings offer hope that institutions can reap ML insights by privately sharing data with simple prompts and little compute.

Anders Aamand, Justin Y. Chen, Piotr Indyk

We propose a model for online graph problems where algorithms are given access to an oracle that predicts (e.g., based on modeling assumptions or on past data) the degrees of nodes in the graph. Within this model, we study the classic problem of online bipartite matching, and a natural greedy matching algorithm called MinPredictedDegree, which uses predictions of the degrees of offline nodes. For the bipartite version of a stochastic graph model due to Chung, Lu, and Vu where the expected values of the offline degrees are known and used as predictions, we show that MinPredictedDegree stochastically dominates any other online algorithm, i.e., it is optimal for graphs drawn from this model. Since the "symmetric" version of the model, where all online nodes are identical, is a special case of the well-studied "known i.i.d. model", it follows that the competitive ratio of MinPredictedDegree on such inputs is at least 0.7299. For the special case of graphs with power law degree distributions, we show that MinPredictedDegree frequently produces matchings almost as large as the true maximum matching on such graphs. We complement these results with an extensive empirical evaluation showing that MinPredictedDegree compares favorably to state-of-the-art online algorithms for online matching.

Justin Y. Chen, Gregory Valiant, Paul Valiant

We introduce a framework for statistical estimation that leverages knowledge of how samples are collected but makes no distributional assumptions on the data values. Specifically, we consider a population of elements $[n]={1,\ldots,n}$ with corresponding data values $x_1,\ldots,x_n$. We observe the values for a "sample" set $A \subset [n]$ and wish to estimate some statistic of the values for a "target" set $B \subset [n]$ where $B$ could be the entire set. Crucially, we assume that the sets $A$ and $B$ are drawn according to some known distribution $P$ over pairs of subsets of $[n]$. A given estimation algorithm is evaluated based on its "worst-case, expected error" where the expectation is with respect to the distribution $P$ from which the sample $A$ and target sets $B$ are drawn, and the worst-case is with respect to the data values $x_1,\ldots,x_n$. Within this framework, we give an efficient algorithm for estimating the target mean that returns a weighted combination of the sample values--where the weights are functions of the distribution $P$ and the sample and target sets $A$, $B$--and show that the worst-case expected error achieved by this algorithm is at most a multiplicative $π/2$ factor worse than the optimal of such algorithms. The algorithm and proof leverage a surprising connection to the Grothendieck problem. This framework, which makes no distributional assumptions on the data values but rather relies on knowledge of the data collection process, is a significant departure from typical estimation and introduces a uniform algorithmic analysis for the many natural settings where membership in a sample may be correlated with data values, such as when sampling probabilities vary as in "importance sampling", when individuals are recruited into a sample via a social network as in "snowball sampling", or when samples have chronological structure as in "selective prediction".