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Recently, due to the popularity of deep neural networks and other methods whose training typically relies on the optimization of an objective function, and due to concerns for data privacy, there is a lot of interest in differentially…
In the task of differentially private (DP) continual counting, we receive a stream of increments and our goal is to output an approximate running total of these increments, without revealing too much about any specific increment. Despite…
Datasets containing sensitive information are often sequentially analyzed by many algorithms. This raises a fundamental question in differential privacy regarding how the overall privacy bound degrades under composition. To address this…
Boosting is one of the most successful ideas in machine learning. The most well-accepted explanations for the low generalization error of boosting algorithms such as AdaBoost stem from margin theory. The study of margins in the context of…
Consider a database of $n$ people, each represented by a bit-string of length $d$ corresponding to the setting of $d$ binary attributes. A $k$-way marginal query is specified by a subset $S$ of $k$ attributes, and a $|S|$-dimensional binary…
In 2009, Roeglin and Teng showed that the smoothed number of Pareto optimal solutions of linear multi-criteria optimization problems is polynomially bounded in the number $n$ of variables and the maximum density $\phi$ of the semi-random…
Root separation bounds play an important role as a complexity measure in understanding the behaviour of various algorithms in computational algebra, e.g., root isolation algorithms. A classic result in the univariate setting is the…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
Differential privacy is a rigorous privacy condition achieved by randomizing query answers. This paper develops efficient algorithms for answering multiple queries under differential privacy with low error. We pursue this goal by advancing…
Prior work on differential privacy analysis of randomized SGD algorithms relies on composition theorems, where the implicit (unrealistic) assumption is that the internal state of the iterative algorithm is revealed to the adversary. As a…
We propose an algorithm for counting the number of cycles under local differential privacy for degeneracy-bounded input graphs. Numerous studies have focused on counting the number of triangles under the privacy notion, demonstrating that…
We study memory-efficient matrix factorization for differentially private counting under continual observation. While recent work by Henzinger and Upadhyay 2024 introduced a factorization method with reduced error based on group algebra,…
We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…
In this work, we present an $\Omega\left(\min\{\log \Delta, \sqrt{\log n}\}\right)$ lower bound for Maximal Matching (MM) in $\Delta$-ary trees against randomized algorithms. By a folklore reduction, the same lower bound applies to Maximal…
In this paper, we address the challenge of differential privacy in the context of graph cuts, specifically focusing on the multiway cut and the minimum $k$-cut. We introduce edge-differentially private algorithms that achieve nearly optimal…
The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem.…
For every $p\leq n$ positive integer we obtain the lower bound $(3-\frac{1}{p+1})n^2-\big(2\binom{2p}{p+1}-\binom{2p-2}{p-1}+2\big)n$ for the rank of the $n\times n$ matrix multiplication. This bound improves the previous one…
In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In…
A Private Repetition algorithm takes as input a differentially private algorithm with constant success probability and boosts it to one that succeeds with high probability. These algorithms are closely related to private metaselection…