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Source author record

Shahab Asoodeh

Explore this author’s publications, collaborators and research topics. This catalog record has not been claimed by its author.

ResearcherUnclaimed source record
Information Theorymath.ITMachine LearningCryptography and Securitymath.STStatistics TheoryArtificial IntelligenceComputer Visioncs.CY

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16works
9topics
4close collaborators

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16 publications

preprint2026arXiv

Breaking the Finite-Sample Barrier in Entropy Coupling

Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \emph{minimum list entropy coupling} H(P∥Q1,…,Qm)H(P\|Q_1,\dots,Q_m), the minimum conditional entropy H(X∣Y1,…,Ym)H(X|Y_1,\dots,Y_m) over all joint distributions with prescribed discrete marginals X∼PX\sim P and Yi∼QiY_i\sim Q_i. Unlike classical formulations based on independent observations, our model allows Y1,…,YmY_1,\dots,Y_m to be arbitrarily dependent while keeping each marginal fixed. This enlarged coupling space reveals a sharp dichotomy: independent observations reduce residual uncertainty exponentially, whereas dependent observations can eliminate it exactly after finitely many samples. We characterize this zero-entropy regime through necessary and sufficient conditions and give concrete structural criteria under which it occurs. In particular, under mild support assumptions, zero entropy is achieved with O(log⁡(1/Pmin⁡))O(\log(1/P_{\min})) observations, where Pmin⁡P_{\min} is the minimum nonzero mass of PP. We also develop a greedy algorithm with monotone approximation guarantees for computing H(P∥Q1,…,Qm)H(P\|Q_1,\dots,Q_m). Finally, we show that the same framework formalizes finite-sample limits in distribution-matching representation learning and randomness extraction, where zero entropy corresponds to exact recovery and exact extraction.

Open access
preprint2026arXiv

PVRF: All-in-one Adverse Weather Removal via Prior-modulated and Velocity-constrained Rectified Flow

Adverse weather removal (AWR) in real-world images remains challenging due to heterogeneous and unseen degradations, while distortion-driven training often yields overly smooth results. We propose PVRF, a unified framework that integrates zero-shot soft weather perceptions with velocity-constrained rectified-flow refinement. PVRF introduces an AWR-specific question answering module (AWR-QA) that uses frozen vision--language models (VLMs) to estimate soft probabilities of weather types and low-level attribute scores. These perceptions condition restoration networks via attribute-modulated normalization (AMN) and weather-weighted adapters (WWA), producing an anchor estimate for refinement. We then learn a terminal-consistent residual rectified flow with perception-adaptive source perturbation and a terminal-consistent velocity parameterization to stabilize learning near the terminal regime. Extensive experiments show that PVRF improves both fidelity and perceptual quality over state-of-the-art baselines, with strong cross-dataset generalization on single and combined degradations. Code will be released at https://github.com/dongw22/PVRF.

Open access
preprint2022arXiv

Beyond Adult and COMPAS: Fairness in Multi-Class Prediction

We consider the problem of producing fair probabilistic classifiers for multi-class classification tasks. We formulate this problem in terms of "projecting" a pre-trained (and potentially unfair) classifier onto the set of models that satisfy target group-fairness requirements. The new, projected model is given by post-processing the outputs of the pre-trained classifier by a multiplicative factor. We provide a parallelizable iterative algorithm for computing the projected classifier and derive both sample complexity and convergence guarantees. Comprehensive numerical comparisons with state-of-the-art benchmarks demonstrate that our approach maintains competitive performance in terms of accuracy-fairness trade-off curves, while achieving favorable runtime on large datasets. We also evaluate our method at scale on an open dataset with multiple classes, multiple intersectional protected groups, and over 1M samples.

Open access
preprint2022arXiv

Cactus Mechanisms: Optimal Differential Privacy Mechanisms in the Large-Composition Regime

Most differential privacy mechanisms are applied (i.e., composed) numerous times on sensitive data. We study the design of optimal differential privacy mechanisms in the limit of a large number of compositions. As a consequence of the law of large numbers, in this regime the best privacy mechanism is the one that minimizes the Kullback-Leibler divergence between the conditional output distributions of the mechanism given two different inputs. We formulate an optimization problem to minimize this divergence subject to a cost constraint on the noise. We first prove that additive mechanisms are optimal. Since the optimization problem is infinite dimensional, it cannot be solved directly; nevertheless, we quantize the problem to derive near-optimal additive mechanisms that we call "cactus mechanisms" due to their shape. We show that our quantization approach can be arbitrarily close to an optimal mechanism. Surprisingly, for quadratic cost, the Gaussian mechanism is strictly sub-optimal compared to this cactus mechanism. Finally, we provide numerical results which indicate that cactus mechanism outperforms the Gaussian mechanism for a finite number of compositions.

Open access
preprint2022arXiv

The Saddle-Point Accountant for Differential Privacy

We introduce a new differential privacy (DP) accountant called the saddle-point accountant (SPA). SPA approximates privacy guarantees for the composition of DP mechanisms in an accurate and fast manner. Our approach is inspired by the saddle-point method -- a ubiquitous numerical technique in statistics. We prove rigorous performance guarantees by deriving upper and lower bounds for the approximation error offered by SPA. The crux of SPA is a combination of large-deviation methods with central limit theorems, which we derive via exponentially tilting the privacy loss random variables corresponding to the DP mechanisms. One key advantage of SPA is that it runs in constant time for the nn-fold composition of a privacy mechanism. Numerical experiments demonstrate that SPA achieves comparable accuracy to state-of-the-art accounting methods with a faster runtime.

Open access
preprint2021arXiv

Three Variants of Differential Privacy: Lossless Conversion and Applications

We consider three different variants of differential privacy (DP), namely approximate DP, Rényi DP (RDP), and hypothesis test DP. In the first part, we develop a machinery for optimally relating approximate DP to RDP based on the joint range of two ff-divergences that underlie the approximate DP and RDP. In particular, this enables us to derive the optimal approximate DP parameters of a mechanism that satisfies a given level of RDP. As an application, we apply our result to the moments accountant framework for characterizing privacy guarantees of noisy stochastic gradient descent (SGD). When compared to the state-of-the-art, our bounds may lead to about 100 more stochastic gradient descent iterations for training deep learning models for the same privacy budget. In the second part, we establish a relationship between RDP and hypothesis test DP which allows us to translate the RDP constraint into a tradeoff between type I and type II error probabilities of a certain binary hypothesis test. We then demonstrate that for noisy SGD our result leads to tighter privacy guarantees compared to the recently proposed ff-DP framework for some range of parameters.

Open access
preprint2020arXiv

A Better Bound Gives a Hundred Rounds: Enhanced Privacy Guarantees via ff-Divergences

We derive the optimal differential privacy (DP) parameters of a mechanism that satisfies a given level of Rényi differential privacy (RDP). Our result is based on the joint range of two ff-divergences that underlie the approximate and the Rényi variations of differential privacy. We apply our result to the moments accountant framework for characterizing privacy guarantees of stochastic gradient descent. When compared to the state-of-the-art, our bounds may lead to about 100 more stochastic gradient descent iterations for training deep learning models for the same privacy budget.

Open access
preprint2020arXiv

Differentially Private Mechanisms for Count Queries

In this paper, we consider the problem of responding to a count query (or any other integer-valued queries) evaluated on a dataset containing sensitive attributes. To protect the privacy of individuals in the dataset, a standard practice is to add continuous noise to the true count. We design a differentially-private mechanism which adds integer-valued noise allowing the released output to remain integer. As a trade-off between utility and privacy, we derive privacy parameters $\eps$ and δδ in terms of the the probability of releasing an erroneous count under the assumption that the true count is no smaller than half the support size of the noise. We then numerically demonstrate that our mechanism provides higher privacy guarantee compared to the discrete Gaussian mechanism that is recently proposed in the literature.

Open access
preprint2020arXiv

Privacy Amplification of Iterative Algorithms via Contraction Coefficients

We investigate the framework of privacy amplification by iteration, recently proposed by Feldman et al., from an information-theoretic lens. We demonstrate that differential privacy guarantees of iterative mappings can be determined by a direct application of contraction coefficients derived from strong data processing inequalities for ff-divergences. In particular, by generalizing the Dobrushin's contraction coefficient for total variation distance to an ff-divergence known as EγE_γ-divergence, we derive tighter bounds on the differential privacy parameters of the projected noisy stochastic gradient descent algorithm with hidden intermediate updates.

Open access
preprint2016arXiv

Almost Perfect Privacy for Additive Gaussian Privacy Filters

We study the maximal mutual information about a random variable YY (representing non-private information) displayed through an additive Gaussian channel when guaranteeing that only εε bits of information is leaked about a random variable XX (representing private information) that is correlated with YY. Denoting this quantity by gε(X,Y)g_ε(X,Y), we show that for perfect privacy, i.e., ε=0ε=0, one has g0(X,Y)=0g_0(X,Y)=0 for any pair of absolutely continuous random variables (X,Y)(X,Y) and then derive a second-order approximation for gε(X,Y)g_ε(X,Y) for small εε. This approximation is shown to be related to the strong data processing inequality for mutual information under suitable conditions on the joint distribution PXYP_{XY}. Next, motivated by an operational interpretation of data privacy, we formulate the privacy-utility tradeoff in the same setup using estimation-theoretic quantities and obtain explicit bounds for this tradeoff when εε is sufficiently small using the approximation formula derived for gε(X,Y)g_ε(X,Y).

Open access
preprint2016arXiv

Information Extraction Under Privacy Constraints

A privacy-constrained information extraction problem is considered where for a pair of correlated discrete random variables (X,Y)(X,Y) governed by a given joint distribution, an agent observes YY and wants to convey to a potentially public user as much information about YY as possible without compromising the amount of information revealed about XX. To this end, the so-called {\em rate-privacy function} is introduced to quantify the maximal amount of information (measured in terms of mutual information) that can be extracted from YY under a privacy constraint between XX and the extracted information, where privacy is measured using either mutual information or maximal correlation. Properties of the rate-privacy function are analyzed and information-theoretic and estimation-theoretic interpretations of it are presented for both the mutual information and maximal correlation privacy measures. It is also shown that the rate-privacy function admits a closed-form expression for a large family of joint distributions of (X,Y)(X,Y). Finally, the rate-privacy function under the mutual information privacy measure is considered for the case where (X,Y)(X,Y) has a joint probability density function by studying the problem where the extracted information is a uniform quantization of YY corrupted by additive Gaussian noise. The asymptotic behavior of the rate-privacy function is studied as the quantization resolution grows without bound and it is observed that not all of the properties of the rate-privacy function carry over from the discrete to the continuous case.

Open access
preprint2016arXiv

Privacy-Aware MMSE Estimation

We investigate the problem of the predictability of random variable YY under a privacy constraint dictated by random variable XX, correlated with YY, where both predictability and privacy are assessed in terms of the minimum mean-squared error (MMSE). Given that XX and YY are connected via a binary-input symmetric-output (BISO) channel, we derive the \emph{optimal} random mapping PZ∣YP_{Z|Y} such that the MMSE of YY given ZZ is minimized while the MMSE of XX given ZZ is greater than (1−ε)var(X)(1-ε)\mathsf{var}(X) for a given ε≥0ε\geq 0. We also consider the case where (X,Y)(X,Y) are continuous and PZ∣YP_{Z|Y} is restricted to be an additive noise channel.

Open access
preprint2015arXiv

Lossless Secure Source Coding: Yamamoto's Setting

Given a private source of information, XnX^n and a public correlated source, YnY^n, we study the problem of encoding the two-dimensional source (Xn,Yn)(X^n, Y^n) into an index JJ such that a remote party, knowing JJ and some external side information ZnZ^n, can losslessly recover YnY^n while any eavesdropper knowing JJ and possibly a correlated side information EnE^n can retrieve very little information about XnX^n. We give general converse results for the amount of information about XnX^n that might be leaked in such systems and and also achievability results that are optimal in some special cases.

Open access
preprint2015arXiv

Notes on Information-Theoretic Privacy

We investigate the tradeoff between privacy and utility in a situation where both privacy and utility are measured in terms of mutual information. For the binary case, we fully characterize this tradeoff in case of perfect privacy and also give an upper-bound for the case where some privacy leakage is allowed. We then introduce a new quantity which quantifies the amount of private information contained in the observable data and then connect it to the optimal tradeoff between privacy and utility.

Open access
preprint2015arXiv

On Maximal Correlation, Mutual Information and Data Privacy

The rate-privacy function is defined in \cite{Asoodeh} as a tradeoff between privacy and utility in a distributed private data system in which both privacy and utility are measured using mutual information. Here, we use maximal correlation in lieu of mutual information in the privacy constraint. We first obtain some general properties and bounds for maximal correlation and then modify the rate-privacy function to account for the privacy-constrained estimation problem. We find a bound for the utility in this problem when the maximal correlation privacy is set to some threshold ε>0ε>0 and construct an explicit privacy scheme which achieves this bound.

Open access
preprint2010arXiv

It takes half the energy of a photon to send one bit reliably on the Poisson channel with feedback

We consider the transmission of a single bit over the continuous-time Poisson channel with noiseless feedback. We show that to send the bit reliably requires, on the average, half the energy of a photon. In the absence of peak-power constraints this holds irrespective of the intensity of the dark current. We also solve for the energy required to send log2Mlog_{2} M bits.

Open access

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