arXiv subjects

Anshoo Tandon

Publications and source records attributed to Anshoo Tandon.

At least 19 recordsLinked to original sources

arXiv2026

Refined Differentially Private Linear Regression via Extension of a Free Lunch Result

As data-privacy regulations tighten and statistical models are increasingly deployed on sensitive human-sourced data, privacy-preserving linear regression has become a critical necessity. For the add-remove DP model, Kulesza et al. (2024) and Fitzsimons et al. (2024) have independently shown that the size of the dataset -- an important statistic for linear regression -- can be privately estimated for "free", via a simplex transformation of bounded variables and private sum queries on the transformed variables. In this work, we extend this free lunch result via carefully crafted multidimensional simplex transformations to variables and functions that are bounded in the interval [0,1]. We show that these transformations can be applied to refine the estimates of sufficient statistics needed for private simple linear regression based on ordinary least squares. We provide both analytical and numerical results to demonstrate the superiority of our approach. Our proposed transformations have general applicability and can be readily adapted for differentially private polynomial regression.

cs.IT↗

arXiv2026

On the Optimal Number of Grids for Differentially Private Non-Interactive $K$-Means Clustering

Differentially private $K$-means clustering enables releasing cluster centers derived from a dataset while protecting the privacy of the individuals. Non-interactive clustering techniques based on privatized histograms are attractive because the released data synopsis can be reused for other downstream tasks without additional privacy loss. The choice of the number of grids for discretizing the data points is crucial, as it directly controls the quantization bias and the amount of noise injected to preserve privacy. The widely adopted strategy selects a grid size that is independent of the number of clusters and also relies on empirical tuning. In this work, we revisit this choice and propose a refined grid-size selection rule derived by minimizing an upper bound on the expected deviation in the K-means objective function, leading to a more principled discretization strategy for non-interactive private clustering. Compared to prior work, our grid resolution differs both in its dependence on the number of clusters and in the scaling with dataset size and privacy budget. Extensive numerical results elucidate that the proposed strategy results in accurate clustering compared to the state-of-the-art techniques, even under tight privacy budgets.

cs.CR↗

arXiv2026

Bounding User Contributions for User-Level Differentially Private Mean Estimation

We revisit the problem of releasing the sample mean of bounded samples in a dataset, privately, under user-level $\varepsilon$-differential privacy (DP). We aim to derive the optimal method of preprocessing data samples, within a canonical class of processing strategies, in terms of the error in estimation. Typical error analyses of such \emph{bounding} (or \emph{clipping}) strategies in the literature assume that the data samples are independent and identically distributed (i.i.d.), and sometimes also that all users contribute the same number of samples (data homogeneity) -- assumptions that do not accurately model real-world data distributions. Our main result in this work is a precise characterization of the preprocessing strategy that gives rise to the smallest \emph{worst-case} error over all datasets -- a \emph{distribution-independent} error metric -- while allowing for data heterogeneity. We also show via experimental studies that even for i.i.d. real-valued samples, our clipping strategy performs much better, in terms of \emph{average-case} error, than the widely used bounding strategy of Amin et al. (2019).

cs.IT↗

arXiv2025

SKALD: Scalable K-Anonymisation for Large Datasets

Data privacy and anonymisation are critical concerns in today's data-driven society, particularly when handling personal and sensitive user data. Regulatory frameworks worldwide recommend privacy-preserving protocols such as k-anonymisation to de-identify releases of tabular data. Available hardware resources provide an upper bound on the maximum size of dataset that can be processed at a time. Large datasets with sizes exceeding this upper bound must be broken up into smaller data chunks for processing. In these cases, standard k-anonymisation tools such as ARX can only operate on a per-chunk basis. This paper proposes SKALD, a novel algorithm for performing k-anonymisation on large datasets with limited RAM. Our SKALD algorithm offers multi-fold performance improvement over standard k-anonymisation methods by extracting and combining sufficient statistics from each chunk during processing to ensure successful k-anonymisation while providing better utility.

cs.IT↗

arXiv2025

$(\ell,δ)$-Diversity: Linkage-Robustness via a Composition Theorem

In this paper, we consider the problem of degradation of anonymity upon linkages of anonymized datasets. We work in the setting where an adversary links together $t\geq 2$ anonymized datasets in which a user of interest participates, based on the user's known quasi-identifiers, which motivates the use of $\ell$-diversity as the notion of dataset anonymity. We first argue that in the worst case, such linkage attacks can reveal the exact sensitive attribute of the user, even when each dataset respects $\ell$-diversity, for moderately large values of $\ell$. This issue motivates our definition of (approximate) $(\ell,δ)$-diversity -- a parallel of (approximate) $(ε,δ)$-differential privacy (DP) -- which simply requires that a dataset respect $\ell$-diversity, with high probability. We then present a mechanism for achieving $(\ell,δ)$-diversity, in the setting of independent and identically distributed samples. Next, we establish bounds on the degradation of $(\ell,δ)$-diversity, via a simple ``composition theorem,'' similar in spirit to those in the DP literature, thereby showing that approximate diversity, unlike standard diversity, is roughly preserved upon linkage. Finally, we describe simple algorithms for maximizing utility, measured in terms of the number of anonymized ``equivalence classes,'' and derive explicit lower bounds on the utility, for special sample distributions.

cs.IT↗

arXiv2025

On Improving the Composition Privacy Loss in Differential Privacy for Fixed Estimation Error

This paper considers the private release of statistics of disjoint subsets of a dataset, in the setting of data heterogeneity, where users could contribute more than one sample, with different users contributing potentially different numbers of samples. In particular, we focus on the $ε$-differentially private release of sample means and variances of sample values in disjoint subsets of a dataset, under the assumption that the numbers of contributions of each user in each subset is publicly known. Our main contribution is an iterative algorithm, based on suppressing user contributions, which seeks to reduce the overall privacy loss degradation under a canonical Laplace mechanism, while not increasing the worst estimation error among the subsets. Important components of this analysis are our exact, analytical characterizations of the sensitivities and the worst-case bias errors of estimators of the sample mean and variance, which are obtained by clipping or suppressing user contributions. We test the performance of our algorithm on real-world and synthetic datasets and demonstrate clear improvements in the privacy loss degradation, for fixed worst-case estimation error.

cs.CR↗

arXiv2024

Building a Privacy Web with SPIDEr -- Secure Pipeline for Information De-Identification with End-to-End Encryption

Data de-identification makes it possible to glean insights from data while preserving user privacy. The use of Trusted Execution Environments (TEEs) allow for the execution of de-identification applications on the cloud without the need for a user to trust the third-party application provider. In this paper, we present \textit{SPIDEr - Secure Pipeline for Information De-Identification with End-to-End Encryption}, our implementation of an end-to-end encrypted data de-identification pipeline. SPIDEr supports classical anonymisation techniques such as suppression, pseudonymisation, generalisation, and aggregation, as well as techniques that offer a formal privacy guarantee such as k-anonymisation and differential privacy. To enable scalability and improve performance on constrained TEE hardware, we enable batch processing of data for differential privacy computations. We present our design of the control flows for end-to-end secure execution of de-identification operations within a TEE. As part of the control flow for running SPIDEr within the TEE, we perform attestation, a process that verifies that the software binaries were properly instantiated on a known, trusted platform.

cs.CR↗

arXiv2024

Enhancing MOTION2NX for Efficient, Scalable and Secure Image Inference using Convolutional Neural Networks

This work contributes towards the development of an efficient and scalable open-source Secure Multi-Party Computation (SMPC) protocol on machines with moderate computational resources. We use the ABY2.0 SMPC protocol implemented on the C++ based MOTION2NX framework for secure convolutional neural network (CNN) inference application with semi-honest security. Our list of contributions are as follows. Firstly, we enhance MOTION2NX by providing a tensorized version of several primitive functions including the Hadamard product, indicator function and argmax function. Secondly, we adapt an existing Helper node algorithm, working in tandem with the ABY2.0 protocol, for efficient convolution computation to reduce execution time and RAM usage. Thirdly, we also present a novel splitting algorithm that divides the computations at each CNN layer into multiple configurable chunks. This novel splitting algorithm, providing significant reduction in RAM usage, is of independent interest and is applicable to general SMPC protocols.

cs.CR↗

arXiv2024

Optimal Tree-Based Mechanisms for Differentially Private Approximate CDFs

This paper considers the $\varepsilon$-differentially private (DP) release of an approximate cumulative distribution function (CDF) of the samples in a dataset. We assume that the true (approximate) CDF is obtained after lumping the data samples into a fixed number $K$ of bins. In this work, we extend the well-known binary tree mechanism to the class of \emph{level-uniform tree-based} mechanisms and identify $\varepsilon$-DP mechanisms that have a small $\ell_2$-error. We identify optimal or close-to-optimal tree structures when either of the parameters, which are the branching factors or the privacy budgets at each tree level, are given, and when the algorithm designer is free to choose both sets of parameters. Interestingly, when we allow the branching factors to take on real values, under certain mild restrictions, the optimal level-uniform tree-based mechanism is obtained by choosing equal branching factors \emph{independent} of $K$, and equal privacy budgets at all levels. Furthermore, for selected $K$ values, we explicitly identify the optimal \emph{integer} branching factors and tree height, assuming equal privacy budgets at all levels. Finally, we describe general strategies for improving the private CDF estimates further, by combining multiple noisy estimates and by post-processing the estimates for consistency.

cs.IT↗

arXiv2024

Mean Estimation with User-Level Privacy for Spatio-Temporal IoT Datasets

This paper considers the problem of the private release of sample means of speed values from traffic datasets. Our key contribution is the development of user-level differentially private algorithms that incorporate carefully chosen parameter values to ensure low estimation errors on real-world datasets, while ensuring privacy. We test our algorithms on ITMS (Intelligent Traffic Management System) data from an Indian city, where the speeds of different buses are drawn in a potentially non-i.i.d. manner from an unknown distribution, and where the number of speed samples contributed by different buses is potentially different. We then apply our algorithms to large synthetic datasets, generated based on the ITMS data. Here, we provide theoretical justification for the observed performance trends, and also provide recommendations for the choices of algorithm subroutines that result in low estimation errors. Finally, we characterize the best performance of pseudo-user creation-based algorithms on worst-case datasets via a minimax approach; this then gives rise to a novel procedure for the creation of pseudo-users, which optimizes the worst-case total estimation error. The algorithms discussed in the paper are readily applicable to general spatio-temporal IoT datasets for releasing a differentially private mean of a desired value.

cs.CR↗

arXiv2023

Empowering SMPC: Bridging the Gap Between Scalability, Memory Efficiency and Privacy in Neural Network Inference

This paper aims to develop an efficient open-source Secure Multi-Party Computation (SMPC) repository, that addresses the issue of practical and scalable implementation of SMPC protocol on machines with moderate computational resources, while aiming to reduce the execution time. We implement the ABY2.0 protocol for SMPC, providing developers with effective tools for building applications on the ABY 2.0 protocol. This article addresses the limitations of the C++ based MOTION2NX framework for secure neural network inference, including memory constraints and operation compatibility issues. Our enhancements include optimizing the memory usage, reducing execution time using a third-party Helper node, and enhancing efficiency while still preserving data privacy. These optimizations enable MNIST dataset inference in just 32 seconds with only 0.2 GB of RAM for a 5-layer neural network. In contrast, the previous baseline implementation required 8.03 GB of RAM and 200 seconds of execution time.

cs.CR↗

arXiv2021

Active-LATHE: An Active Learning Algorithm for Boosting the Error Exponent for Learning Homogeneous Ising Trees

The Chow-Liu algorithm (IEEE Trans.~Inform.~Theory, 1968) has been a mainstay for the learning of tree-structured graphical models from i.i.d.\ sampled data vectors. Its theoretical properties have been well-studied and are well-understood. In this paper, we focus on the class of trees that are arguably even more fundamental, namely {\em homogeneous} trees in which each pair of nodes that forms an edge has the same correlation $ρ$. We ask whether we are able to further reduce the error probability of learning the structure of the homogeneous tree model when {\em active learning} or {\em active sampling of nodes or variables} is allowed. Our figure of merit is the {\em error exponent}, which quantifies the exponential rate of decay of the error probability with an increasing number of data samples. At first sight, an improvement in the error exponent seems impossible, as all the edges are statistically identical. We design and analyze an algorithm Active Learning Algorithm for Trees with Homogeneous Edge (Active-LATHE), which surprisingly boosts the error exponent by at least 40\% when $ρ$ is at least $0.8$. For all other values of $ρ$, we also observe commensurate, but more modest, improvements in the error exponent. Our analysis hinges on judiciously exploiting the minute but detectable statistical variation of the samples to allocate more data to parts of the graph in which we are less confident of being correct.

cs.LG↗

arXiv2021

SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples

We consider learning Ising tree models when the observations from the nodes are corrupted by independent but non-identically distributed noise with unknown statistics. Katiyar et al. (2020) showed that although the exact tree structure cannot be recovered, one can recover a partial tree structure; that is, a structure belonging to the equivalence class containing the true tree. This paper presents a systematic improvement of Katiyar et al. (2020). First, we present a novel impossibility result by deriving a bound on the necessary number of samples for partial recovery. Second, we derive a significantly improved sample complexity result in which the dependence on the minimum correlation $ρ_{\min}$ is $ρ_{\min}^{-8}$ instead of $ρ_{\min}^{-24}$. Finally, we propose Symmetrized Geometric Averaging (SGA), a more statistically robust algorithm for partial tree recovery. We provide error exponent analyses and extensive numerical results on a variety of trees to show that the sample complexity of SGA is significantly better than the algorithm of Katiyar et al. (2020). SGA can be readily extended to Gaussian models and is shown via numerical experiments to be similarly superior.

stat.ML↗

arXiv2020

Exact Asymptotics for Learning Tree-Structured Graphical Models with Side Information: Noiseless and Noisy Samples

Given side information that an Ising tree-structured graphical model is homogeneous and has no external field, we derive the exact asymptotics of learning its structure from independently drawn samples. Our results, which leverage the use of probabilistic tools from the theory of strong large deviations, refine the large deviation (error exponents) results of Tan, Anandkumar, Tong, and Willsky [IEEE Trans. on Inform. Th., 57(3):1714--1735, 2011] and strictly improve those of Bresler and Karzand [Ann. Statist., 2020]. In addition, we extend our results to the scenario in which the samples are observed in random noise. In this case, we show that they strictly improve on the recent results of Nikolakakis, Kalogerias, and Sarwate [Proc. AISTATS, 1771--1782, 2019]. Our theoretical results demonstrate keen agreement with experimental results for sample sizes as small as that in the hundreds.

stat.ML↗

arXiv2019

On the Bee-Identification Error Exponent with Absentee Bees

The "bee-identification problem" was formally defined by Tandon, Tan and Varshney [IEEE Trans. Commun. (2019) [Online early access]], and the error exponent was studied. This work extends the results for the "absentee bees" scenario, where a small fraction of the bees are absent in the beehive image used for identification. For this setting, we present an exact characterization of the bee-identification error exponent, and show that independent barcode decoding is optimal, i.e., joint decoding of the bee barcodes does not result in a better error exponent relative to independent decoding of each noisy barcode. This is in contrast to the result without absentee bees, where joint barcode decoding results in a significantly higher error exponent than independent barcode decoding. We also define and characterize the "capacity" for the bee-identification problem with absentee bees, and prove the strong converse for the same.

cs.IT↗

arXiv2019

Error Exponent Bounds for the Bee-Identification Problem

Consider the problem of identifying a massive number of bees, uniquely labeled with barcodes, using noisy measurements. We formally introduce this `bee-identification problem', define its error exponent, and derive efficiently computable upper and lower bounds for this exponent. We show that joint decoding of barcodes provides a significantly better exponent compared to separate decoding followed by permutation inference. For low rates, we prove that the lower bound on the bee-identification exponent obtained using typical random codes (TRC) is strictly better than the corresponding bound obtained using a random code ensemble (RCE). Further, as the rate approaches zero, we prove that the upper bound on the bee-identification exponent meets the lower bound obtained using TRC with joint barcode decoding.

cs.IT↗

arXiv2019

Multicasting Energy and Information Simultaneously

Communication systems for multicasting information and energy simultaneously to more than one user are investigated. In the system under study, a transmitter sends the same message and signal to multiple receivers over distinct and independent channels. The fundamental communication limit under a received energy constraint, called the multicast capacity-energy function, is studied and a single-letter expression is derived. This is based on coding theorems for compound channels. The problem of receiver segmentation, where receivers are divided into related groups, is also considered.

cs.IT↗

arXiv2019

Generalized Sphere-Packing Bound for Subblock-Constrained Codes

We apply the generalized sphere-packing bound to two classes of subblock-constrained codes. A la Fazeli et al. (2015), we made use of automorphism to significantly reduce the number of variables in the associated linear programming problem. In particular, we study binary constant subblock-composition codes (CSCCs), characterized by the property that the number of ones in each subblock is constant, and binary subblock energy-constrained codes (SECCs), characterized by the property that the number of ones in each subblock exceeds a certain threshold. For CSCCs, we show that the optimization problem is equivalent to finding the minimum of $N$ variables, where $N$ is independent of the number of subblocks. We then provide closed-form solutions for the generalized sphere-packing bounds for single- and double-error correcting CSCCs. For SECCs, we provide closed-form solutions for the generalized sphere-packing bounds for single errors in certain special cases. We also obtain improved bounds on the optimal asymptotic rate for CSCCs and SECCs, and provide numerical examples to highlight the improvement.

cs.IT↗