arXiv subjects

Ephraim Linder

Publications and source records attributed to Ephraim Linder.

5 recordsLinked to original sources

arXiv2026

Privately Estimating Monotone Statistics in Polynomial Time

We study efficient differentially private algorithms for estimating monotone statistics, i.e., statistics that are monotone under the addition of new observations. The starting point for our investigation is subsample-and-aggregate: a classical paradigm that partitions the dataset into blocks, estimates the statistic on each block, and then privately aggregates the estimates. While practical and generically applicable, this approach is quite data-hungry. We improve upon this framework for the class of monotone statistics -- compared to subsample-and-aggregate, our algorithms save a factor of $t$ in sample complexity and pay a factor of $e^t$ in running time, where $t>0$ is a tunable parameter. We complement our results with a query-complexity lower bound, showing that our algorithms are essentially optimal for this task. As an application, we obtain improved results for private eigenvalue estimation, private loss estimation, and privately estimating a single parameter of a high-dimensional model, e.g., in linear regression.

cs.CR↗

arXiv2025

Refereed Learning

We initiate an investigation of learning tasks in a setting where the learner is given access to two competing provers, only one of which is honest. Specifically, we consider the power of such learners in assessing purported properties of opaque models. Following prior work in complexity theory that considers the power of competing provers in various settings, we call this setting refereed learning. After formulating a general definition of refereed learning tasks, we show refereed learning protocols that obtain a level of accuracy that far exceeds what is obtainable at comparable cost without provers, or even with a single prover. We concentrate on the task of choosing the better one out of two black-box models, with respect to some ground truth. While we consider a range of parameters, perhaps our most notable result is in the high-precision range: For all $\varepsilon>0$ and ambient dimension $d$, our learner makes only one query to the ground truth function, communicates only $(1+\frac{1}{\varepsilon^2})\cdot\text{poly}(d)$ bits with the provers, and outputs a model whose loss is within a multiplicative factor of $(1+\varepsilon)$ of the best model's loss. Obtaining comparable loss with a single prover would require the learner to access the ground truth at almost all of the points in the domain. We also present lower bounds that demonstrate the optimality of our protocols in a number of respects, including prover complexity, number of samples, and need for query access.

stat.ML↗

arXiv2025

Privately Evaluating Untrusted Black-Box Functions

We provide tools for sharing sensitive data when the data curator does not know in advance what questions an (untrusted) analyst might ask about the data. The analyst can specify a program that they want the curator to run on the dataset. We model the program as a black-box function $f$. We study differentially private algorithms, called privacy wrappers, that, given black-box access to a real-valued function $f$ and a sensitive dataset $x$, output an accurate approximation to $f(x)$. The dataset $x$ is modeled as a finite subset of a possibly infinite set $U$, in which each entry represents data of one individual. A privacy wrapper calls $f$ on the dataset $x$ and on some subsets of $x$ and returns either an approximation to $f(x)$ or a nonresponse symbol $\perp$. The wrapper may also use additional information (that is, parameters) provided by the analyst, but differential privacy is required for all values of these parameters. Correct setting of these parameters will ensure better accuracy of the wrapper. The bottleneck in the running time of our wrappers is the number of calls to $f$, which we refer to as queries. Our goal is to design wrappers with high accuracy and low query complexity. We introduce a novel setting, the automated sensitivity detection setting, where the analyst supplies the black-box function $f$ and the intended (finite) range of $f$. In the previously considered setting, the claimed sensitivity bound setting, the analyst supplies additional parameters that describe the sensitivity of $f$. We design privacy wrappers for both settings and show that our wrappers are nearly optimal in terms of accuracy, locality (i.e., the depth of the local neighborhood of the dataset $x$ they explore), and query complexity. In the claimed sensitivity bound setting, we provide the first accuracy guarantees that have no dependence on the size of the universe $U$.

cs.DS↗

arXiv2024

Online versus Offline Adversaries in Property Testing

We study property testing with incomplete or noisy inputs. The models we consider allow for adversarial manipulation of the input, but differ in whether the manipulation can be done only offline, i.e., before the execution of the algorithm, or online, i.e., as the algorithm runs. The manipulations by an adversary can come in the form of erasures or corruptions. We compare the query complexity and the randomness complexity of property testing in the offline and online models. Kalemaj, Raskhodnikova, and Varma (Theory Comput `23) provide properties that can be tested with a small number of queries with offline erasures, but cannot be tested at all with online erasures. We demonstrate that the two models are incomparable in terms of query complexity: we construct properties that can be tested with a constant number of queries in the online corruption model, but require querying a significant fraction of the input in the offline erasure model. We also construct properties that exhibit a strong separation between the randomness complexity of testing in the presence of offline and online adversaries: testing these properties in the online model requires exponentially more random bits than in the offline model, even when they are tested with nearly the same number of queries in both models. Our randomness separation relies on a novel reduction from randomness-efficient testers in the adversarial online model to query-efficient testers in the standard model.

cs.DS↗

arXiv2024

Local Lipschitz Filters for Bounded-Range Functions with Applications to Arbitrary Real-Valued Functions

We study local filters for the Lipschitz property of real-valued functions $f: V \to [0,r]$, where the Lipschitz property is defined with respect to an arbitrary undirected graph $G=(V,E)$. We give nearly optimal local Lipschitz filters both with respect to $\ell_1$-distance and $\ell_0$-distance. Previous work only considered unbounded-range functions over $[n]^d$. Jha and Raskhodnikova (SICOMP `13) gave an algorithm for such functions with lookup complexity exponential in $d$, which Awasthi et al. (ACM Trans. Comput. Theory) showed was necessary in this setting. We demonstrate that important applications of local Lipschitz filters can be accomplished with filters for functions with bounded-range. For functions $f: [n]^d\to [0,r]$, we circumvent the lower bound and achieve running time $(d^r\log n)^{O(\log r)}$ for the $\ell_1$-respecting filter and $d^{O(r)}\text{polylog } n$ for the $\ell_0$-respecting filter. Our local filters provide a novel Lipschitz extension that can be implemented locally. Furthermore, we show that our algorithms have nearly optimal dependence on $r$ for the domain $\{0,1\}^d$. In addition, our lower bound resolves an open question of Awasthi et al., removing one of the conditions necessary for their lower bound for general range. We prove our lower bound via a reduction from distribution-free Lipschitz testing and a new technique for proving hardness for adaptive algorithms. We provide two applications of our local filters to arbitrary real-valued functions. In the first application, we use them in conjunction with the Laplace mechanism for differential privacy and noisy binary search to provide mechanisms for privately releasing outputs of black-box functions, even in the presence of malicious clients. In the second application, we use our local filters to obtain the first nontrivial tolerant tester for the Lipschitz property.

cs.DS↗