Alex Kulesza

Travis Dick, Alex Kulesza, Ziteng Sun et al.

We propose a new definition of instance optimality for differentially private estimation algorithms. Our definition requires an optimal algorithm to compete, simultaneously for every dataset $D$, with the best private benchmark algorithm that (a) knows $D$ in advance and (b) is evaluated by its worst-case performance on large subsets of $D$. That is, the benchmark algorithm need not perform well when potentially extreme points are added to $D$; it only has to handle the removal of a small number of real data points that already exist. This makes our benchmark significantly stronger than those proposed in prior work. We nevertheless show, for real-valued datasets, how to construct private algorithms that achieve our notion of instance optimality when estimating a broad class of dataset properties, including means, quantiles, and $\ell_p$-norm minimizers. For means in particular, we provide a detailed analysis and show that our algorithm simultaneously matches or exceeds the asymptotic performance of existing algorithms under a range of distributional assumptions.

Alex Bie, Travis Dick, Alex Kulesza et al.

Modern AI systems have been successfully deployed to win medals at international math competitions, assist with research workflows, and prove novel technical lemmas. However, despite their progress at advanced levels of mathematics, they remain stubbornly bad at basic arithmetic, consistently failing on the simple task of adding two numbers. We present a systematic investigation of this phenomenon. We demonstrate empirically that all frontier models suffer significantly degraded accuracy for integer addition as the number of digits increases. Furthermore, we show that most errors made by these models are highly interpretable and can be attributed to either operand misalignment or a failure to correctly carry; these two error classes explain 87.9%, 62.9%, and 92.4% of Claude Opus 4.1, GPT-5, and Gemini 2.5 Pro errors, respectively. Finally, we show that misalignment errors are frequently related to tokenization, and that carrying errors appear largely as independent random failures.

Kareem Amin, Jennifer Gillenwater, Matthew Joseph et al.

Differential privacy has become the standard for private data analysis, and an extensive literature now offers differentially private solutions to a wide variety of problems. However, translating these solutions into practical systems often requires confronting details that the literature ignores or abstracts away: users may contribute multiple records, the domain of possible records may be unknown, and the eventual system must scale to large volumes of data. Failure to carefully account for all three issues can severely impair a system's quality and usability. We present Plume, a system built to address these problems. We describe a number of sometimes subtle implementation issues and offer practical solutions that, together, make an industrial-scale system for differentially private data analysis possible. Plume is currently deployed at Google and is routinely used to process datasets with trillions of records.

Cecilia Ferrando, Jennifer Gillenwater, Alex Kulesza

Differential privacy is widely adopted to provide provable privacy guarantees in data analysis. We consider the problem of combining public and private data (and, more generally, data with heterogeneous privacy needs) for estimating aggregate statistics. We introduce a mixed estimator of the mean optimized to minimize the variance. We argue that our mechanism is preferable to techniques that preserve the privacy of individuals by subsampling data proportionally to the privacy needs of users. Similarly, we present a mixed median estimator based on the exponential mechanism. We compare our mechanisms to the methods proposed in Jorgensen et al. [2015]. Our experiments provide empirical evidence that our mechanisms often outperform the baseline methods.

Daniel Levy, Ziteng Sun, Kareem Amin et al.

We propose and analyze algorithms to solve a range of learning tasks under user-level differential privacy constraints. Rather than guaranteeing only the privacy of individual samples, user-level DP protects a user's entire contribution ($m \ge 1$ samples), providing more stringent but more realistic protection against information leaks. We show that for high-dimensional mean estimation, empirical risk minimization with smooth losses, stochastic convex optimization, and learning hypothesis classes with finite metric entropy, the privacy cost decreases as $O(1/\sqrt{m})$ as users provide more samples. In contrast, when increasing the number of users $n$, the privacy cost decreases at a faster $O(1/n)$ rate. We complement these results with lower bounds showing the minimax optimality of our algorithms for mean estimation and stochastic convex optimization. Our algorithms rely on novel techniques for private mean estimation in arbitrary dimension with error scaling as the concentration radius $τ$ of the distribution rather than the entire range.

Jennifer Gillenwater, Matthew Joseph, Alex Kulesza

Quantiles are often used for summarizing and understanding data. If that data is sensitive, it may be necessary to compute quantiles in a way that is differentially private, providing theoretical guarantees that the result does not reveal private information. However, when multiple quantiles are needed, existing differentially private algorithms fare poorly: they either compute quantiles individually, splitting the privacy budget, or summarize the entire distribution, wasting effort. In either case the result is reduced accuracy. In this work we propose an instance of the exponential mechanism that simultaneously estimates exactly $m$ quantiles from $n$ data points while guaranteeing differential privacy. The utility function is carefully structured to allow for an efficient implementation that returns estimates of all $m$ quantiles in time $O(mn\log(n) + m^2n)$. Experiments show that our method significantly outperforms the current state of the art on both real and synthetic data while remaining efficient enough to be practical.

Nematollah Kayhan Batmanghelich, Gerald Quon, Alex Kulesza et al.

We propose a novel diverse feature selection method based on determinantal point processes (DPPs). Our model enables one to flexibly define diversity based on the covariance of features (similar to orthogonal matching pursuit) or alternatively based on side information. We introduce our approach in the context of Bayesian sparse regression, employing a DPP as a variational approximation to the true spike and slab posterior distribution. We subsequently show how this variational DPP approximation generalizes and extends mean-field approximation, and can be learned efficiently by exploiting the fast sampling properties of DPPs. Our motivating application comes from bioinformatics, where we aim to identify a diverse set of genes whose expression profiles predict a tumor type where the diversity is defined with respect to a gene-gene interaction network. We also explore an application in spatial statistics. In both cases, we demonstrate that the proposed method yields significantly more diverse feature sets than classic sparse methods, without compromising accuracy.

Jennifer Gillenwater, Alex Kulesza, Emily Fox et al.

A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by maximizing the log-likelihood of the available data. However, log-likelihood is non-convex in the entries of the kernel matrix, and this learning problem is conjectured to be NP-hard. Thus, previous work has instead focused on more restricted convex learning settings: learning only a single weight for each row of the kernel matrix, or learning weights for a linear combination of DPPs with fixed kernel matrices. In this work we propose a novel algorithm for learning the full kernel matrix. By changing the kernel parameterization from matrix entries to eigenvalues and eigenvectors, and then lower-bounding the likelihood in the manner of expectation-maximization algorithms, we obtain an effective optimization procedure. We test our method on a real-world product recommendation task, and achieve relative gains of up to 16.5% in test log-likelihood compared to the naive approach of maximizing likelihood by projected gradient ascent on the entries of the kernel matrix.

Ko-Jen Hsiao, Alex Kulesza, Alfred Hero

Socially-based recommendation systems have recently attracted significant interest, and a number of studies have shown that social information can dramatically improve a system's predictions of user interests. Meanwhile, there are now many potential applications that involve aspects of both recommendation and information retrieval, and the task of collaborative retrieval---a combination of these two traditional problems---has recently been introduced. Successful collaborative retrieval requires overcoming severe data sparsity, making additional sources of information, such as social graphs, particularly valuable. In this paper we propose a new model for collaborative retrieval, and show that our algorithm outperforms current state-of-the-art approaches by incorporating information from social networks. We also provide empirical analyses of the ways in which cultural interests propagate along a social graph using a real-world music dataset.

Raja Hafiz Affandi, Alex Kulesza, Emily B. Fox

A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For example, we might use a DPP to display a set of news headlines that are relevant to a user's interests while covering a variety of topics. Suppose, however, that we are asked to sequentially select multiple diverse sets of items, for example, displaying new headlines day-by-day. We might want these sets to be diverse not just individually but also through time, offering headlines today that are unlike the ones shown yesterday. In this paper, we construct a Markov DPP (M-DPP) that models a sequence of random sets {Yt}. The proposed M-DPP defines a stationary process that maintains DPP margins. Crucially, the induced union process Zt = Yt u Yt-1 is also marginally DPP-distributed. Jointly, these properties imply that the sequence of random sets are encouraged to be diverse both at a given time step as well as across time steps. We describe an exact, efficient sampling procedure, and a method for incrementally learning a quality measure over items in the base set Y based on external preferences. We apply the M-DPP to the task of sequentially displaying diverse and relevant news articles to a user with topic preferences.

Alex Kulesza, Ben Taskar

Determinantal point processes (DPPs) are elegant probabilistic models of repulsion that arise in quantum physics and random matrix theory. In contrast to traditional structured models like Markov random fields, which become intractable and hard to approximate in the presence of negative correlations, DPPs offer efficient and exact algorithms for sampling, marginalization, conditioning, and other inference tasks. We provide a gentle introduction to DPPs, focusing on the intuitions, algorithms, and extensions that are most relevant to the machine learning community, and show how DPPs can be applied to real-world applications like finding diverse sets of high-quality search results, building informative summaries by selecting diverse sentences from documents, modeling non-overlapping human poses in images or video, and automatically building timelines of important news stories.

Alex Kulesza, Ben Taskar

Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs offer tractable algorithms for exact inference, including computing marginal probabilities and sampling; however, an important open question has been how to learn a DPP from labeled training data. In this paper we propose a natural feature-based parameterization of conditional DPPs, and show how it leads to a convex and efficient learning formulation. We analyze the relationship between our model and binary Markov random fields with repulsive potentials, which are qualitatively similar but computationally intractable. Finally, we apply our approach to the task of extractive summarization, where the goal is to choose a small subset of sentences conveying the most important information from a set of documents. In this task there is a fundamental tradeoff between sentences that are highly relevant to the collection as a whole, and sentences that are diverse and not repetitive. Our parameterization allows us to naturally balance these two characteristics. We evaluate our system on data from the DUC 2003/04 multi-document summarization task, achieving state-of-the-art results.