arXiv subjects

Satchit Sivakumar

Publications and source records attributed to Satchit Sivakumar.

9 recordsLinked to original sources

arXiv2026

Improved Accuracy for Private Continual Cardinality Estimation in Fully Dynamic Streams via Matrix Factorization

We study differentially-private statistics in the fully dynamic continual observation model, where many updates can arrive at each time step and updates to a stream can involve both insertions and deletions of an item. Earlier work (e.g., Jain et al., NeurIPS 2023 for counting distinct elements; Raskhodnikova & Steiner, PODS 2025 for triangle counting with edge updates) reduced the respective cardinality estimation problem to continual counting on the difference stream associated with the true function values on the input stream. In such reductions, a change in the original stream can cause many changes in the difference stream, this poses a challenge for applying private continual counting algorithms to obtain optimal error bounds. We improve the accuracy of several such reductions by studying the associated $\ell_p$-sensitivity vectors of the resulting difference streams and isolating their properties. We demonstrate that our framework gives improved bounds for counting distinct elements, estimating degree histograms, and estimating triangle counts (under a slightly relaxed privacy model), thus offering a general approach to private continual cardinality estimation in streaming settings. Our improved accuracy stems from tight analysis of known factorization mechanisms for the counting matrix in this setting; the key technical challenge is arguing that one can use state-of-the-art factorizations for sensitivity vector sets with the properties we isolate. Empirically and analytically, we demonstrate that our improved error bounds offer a substantial improvement in accuracy for cardinality estimation problems over a large range of parameters.

cs.CR↗

arXiv2025

Interactive Proofs For Distribution Testing With Conditional Oracles

We revisit the framework of interactive proofs for distribution testing, first introduced by Chiesa and Gur (ITCS 2018), which has recently experienced a surge in interest, accompanied by notable progress (e.g., Herman and Rothblum, STOC 2022, FOCS 2023; Herman, RANDOM~2024). In this model, a data-poor verifier determines whether a probability distribution has a property of interest by interacting with an all-powerful, data-rich but untrusted prover bent on convincing them that it has the property. While prior work gave sample-, time-, and communication-efficient protocols for testing and estimating a range of distribution properties, they all suffer from an inherent issue: for most interesting properties of distributions over a domain of size $N$, the verifier must draw at least $\Omega(\sqrt{N})$ samples of its own. While sublinear in $N$, this is still prohibitive for large domains encountered in practice. In this work, we circumvent this limitation by augmenting the verifier with the ability to perform an exponentially smaller number of more powerful (but reasonable) \emph{pairwise conditional} queries, effectively enabling them to perform ``local comparison checks'' of the prover's claims. We systematically investigate the landscape of interactive proofs in this new setting, giving polylogarithmic query and sample protocols for (tolerantly) testing all \emph{label-invariant} properties, thus demonstrating exponential savings without compromising on communication, for this large and fundamental class of testing tasks.

cs.CC↗

arXiv2025

Enforcing Demographic Coherence: A Harms Aware Framework for Reasoning about Private Data Release

The technical literature about data privacy largely consists of two complementary approaches: formal definitions of conditions sufficient for privacy preservation and attacks that demonstrate privacy breaches. Differential privacy is an accepted standard in the former sphere. However, differential privacy's powerful adversarial model and worst-case guarantees may make it too stringent in some situations, especially when achieving it comes at a significant cost to data utility. Meanwhile, privacy attacks aim to expose real and worrying privacy risks associated with existing data release processes but often face criticism for being unrealistic. Moreover, the literature on attacks generally does not identify what properties are necessary to defend against them. We address the gap between these approaches by introducing demographic coherence, a condition inspired by privacy attacks that we argue is necessary for data privacy. This condition captures privacy violations arising from inferences about individuals that are incoherent with respect to the demographic patterns in the data. Our framework focuses on confidence rated predictors, which can in turn be distilled from almost any data-informed process. Thus, we capture privacy threats that exist even when no attack is explicitly being carried out. Our framework not only provides a condition with respect to which data release algorithms can be analysed but suggests natural experimental evaluation methodologies that could be used to build practical intuition and make tangible assessment of risks. Finally, we argue that demographic coherence is weaker than differential privacy: we prove that every differentially private data release is also demographically coherent, and that there are demographically coherent algorithms which are not differentially private.

cs.CR↗

arXiv2024

Instance-Optimal Private Density Estimation in the Wasserstein Distance

Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating population densities in a geographic region, a small Wasserstein distance means that the estimate is able to capture roughly where the population mass is. In this work we study differentially private density estimation in the Wasserstein distance. We design and analyze instance-optimal algorithms for this problem that can adapt to easy instances. For distributions $P$ over $\mathbb{R}$, we consider a strong notion of instance-optimality: an algorithm that uniformly achieves the instance-optimal estimation rate is competitive with an algorithm that is told that the distribution is either $P$ or $Q_P$ for some distribution $Q_P$ whose probability density function (pdf) is within a factor of 2 of the pdf of $P$. For distributions over $\mathbb{R}^2$, we use a different notion of instance optimality. We say that an algorithm is instance-optimal if it is competitive with an algorithm that is given a constant-factor multiplicative approximation of the density of the distribution. We characterize the instance-optimal estimation rates in both these settings and show that they are uniformly achievable (up to polylogarithmic factors). Our approach for $\mathbb{R}^2$ extends to arbitrary metric spaces as it goes via hierarchically separated trees. As a special case our results lead to instance-optimal private learning in TV distance for discrete distributions.

cs.LG↗

arXiv2023

Counting Distinct Elements in the Turnstile Model with Differential Privacy under Continual Observation

Privacy is a central challenge for systems that learn from sensitive data sets, especially when a system's outputs must be continuously updated to reflect changing data. We consider the achievable error for differentially private continual release of a basic statistic - the number of distinct items - in a stream where items may be both inserted and deleted (the turnstile model). With only insertions, existing algorithms have additive error just polylogarithmic in the length of the stream $T$. We uncover a much richer landscape in the turnstile model, even without considering memory restrictions. We show that every differentially private mechanism that handles insertions and deletions has worst-case additive error at least $T^{1/4}$ even under a relatively weak, event-level privacy definition. Then, we identify a parameter of the input stream, its maximum flippancy, that is low for natural data streams and for which we give tight parameterized error guarantees. Specifically, the maximum flippancy is the largest number of times that the contribution of a single item to the distinct elements count changes over the course of the stream. We present an item-level differentially private mechanism that, for all turnstile streams with maximum flippancy $w$, continually outputs the number of distinct elements with an $O(\sqrt{w} \cdot poly\log T)$ additive error, without requiring prior knowledge of $w$. We prove that this is the best achievable error bound that depends only on $w$, for a large range of values of $w$. When $w$ is small, the error of our mechanism is similar to the polylogarithmic in $T$ error in the insertion-only setting, bypassing the hardness in the turnstile model.

cs.DS↗

arXiv2023

Stability is Stable: Connections between Replicability, Privacy, and Adaptive Generalization

The notion of replicable algorithms was introduced in Impagliazzo et al. [STOC '22] to describe randomized algorithms that are stable under the resampling of their inputs. More precisely, a replicable algorithm gives the same output with high probability when its randomness is fixed and it is run on a new i.i.d. sample drawn from the same distribution. Using replicable algorithms for data analysis can facilitate the verification of published results by ensuring that the results of an analysis will be the same with high probability, even when that analysis is performed on a new data set. In this work, we establish new connections and separations between replicability and standard notions of algorithmic stability. In particular, we give sample-efficient algorithmic reductions between perfect generalization, approximate differential privacy, and replicability for a broad class of statistical problems. Conversely, we show any such equivalence must break down computationally: there exist statistical problems that are easy under differential privacy, but that cannot be solved replicably without breaking public-key cryptography. Furthermore, these results are tight: our reductions are statistically optimal, and we show that any computational separation between DP and replicability must imply the existence of one-way functions. Our statistical reductions give a new algorithmic framework for translating between notions of stability, which we instantiate to answer several open questions in replicability and privacy. This includes giving sample-efficient replicable algorithms for various PAC learning, distribution estimation, and distribution testing problems, algorithmic amplification of $\delta$ in approximate DP, conversions from item-level to user-level privacy, and the existence of private agnostic-to-realizable learning reductions under structured distributions.

cs.LG↗

arXiv2022

Differentially Private Sampling from Distributions

We initiate an investigation of private sampling from distributions. Given a dataset with $n$ independent observations from an unknown distribution $P$, a sampling algorithm must output a single observation from a distribution that is close in total variation distance to $P$ while satisfying differential privacy. Sampling abstracts the goal of generating small amounts of realistic-looking data. We provide tight upper and lower bounds for the dataset size needed for this task for three natural families of distributions: arbitrary distributions on $\{1,\ldots ,k\}$, arbitrary product distributions on $\{0,1\}^d$, and product distributions on $\{0,1\}^d$ with bias in each coordinate bounded away from 0 and 1. We demonstrate that, in some parameter regimes, private sampling requires asymptotically fewer observations than learning a description of $P$ nonprivately; in other regimes, however, private sampling proves to be as difficult as private learning. Notably, for some classes of distributions, the overhead in the number of observations needed for private learning compared to non-private learning is completely captured by the number of observations needed for private sampling.

cs.LG↗

arXiv2021

The Price of Differential Privacy under Continual Observation

We study the accuracy of differentially private mechanisms in the continual release model. A continual release mechanism receives a sensitive dataset as a stream of $T$ inputs and produces, after receiving each input, an accurate output on the obtained inputs. In contrast, a batch algorithm receives the data as one batch and produces a single output. We provide the first strong lower bounds on the error of continual release mechanisms. In particular, for two fundamental problems that are widely studied and used in the batch model, we show that the worst case error of every continual release algorithm is $\tilde \Omega(T^{1/3})$ times larger than that of the best batch algorithm. Previous work shows only a polylogarithimic (in $T$) gap between the worst case error achievable in these two models; further, for many problems, including the summation of binary attributes, the polylogarithmic gap is tight (Dwork et al., 2010; Chan et al., 2010). Our results show that problems closely related to summation -- specifically, those that require selecting the largest of a set of sums -- are fundamentally harder in the continual release model than in the batch model. Our lower bounds assume only that privacy holds for streams fixed in advance (the "nonadaptive" setting). However, we provide matching upper bounds that hold in a model where privacy is required even for adaptively selected streams. This model may be of independent interest.

cs.DS↗

arXiv2021

Multiclass versus Binary Differentially Private PAC Learning

We show a generic reduction from multiclass differentially private PAC learning to binary private PAC learning. We apply this transformation to a recently proposed binary private PAC learner to obtain a private multiclass learner with sample complexity that has a polynomial dependence on the multiclass Littlestone dimension and a poly-logarithmic dependence on the number of classes. This yields an exponential improvement in the dependence on both parameters over learners from previous work. Our proof extends the notion of $\Psi$-dimension defined in work of Ben-David et al. [JCSS '95] to the online setting and explores its general properties.

cs.LG↗