Related papers: Efficient Mod Approximation and Its Applications t…
Fully homomorphic encryption (FHE) enables an entity to perform arbitrary computation on encrypted data without decrypting the ciphertexts. An ongoing group-theoretical approach to construct an FHE scheme uses a certain "compression"…
The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…
Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued…
The intuitive sphere-packing argument is used to obtain analytically-tractable closed-form approximations for achievable information rates of coded modulation transmission systems, for which only analytically-intractable expressions are…
Fully Homomorphic Encryption (FHE), a novel cryptographic theory enabling computation directly on ciphertext data, offers significant security benefits but is hampered by substantial performance overhead. In recent years, a series of…
In this paper we study constrained subspace approximation problem. Given a set of $n$ points $\{a_1,\ldots,a_n\}$ in $\mathbb{R}^d$, the goal of the {\em subspace approximation} problem is to find a $k$ dimensional subspace that best…
Data privacy concerns often prevent the use of cloud-based machine learning services for sensitive personal data. While homomorphic encryption (HE) offers a potential solution by enabling computations on encrypted data, the challenge is to…
In this paper, we present a novel method for solving a class of quadratically constrained quadratic optimization problems using only additions and multiplications. This approach enables solving constrained optimization problems on private…
Submodular functions are set functions mapping every subset of some ground set of size $n$ into the real numbers and satisfying the diminishing returns property. Submodular minimization is an important field in discrete optimization theory…
Homomorphic encryption enables arbitrary computation over data while it remains encrypted. This privacy-preserving feature is attractive for machine learning, but requires significant computational time due to the large overhead of the…
One way of investigating how genes affect human traits would be with a genome-wide association study (GWAS). Genetic markers, known as single-nucleotide polymorphism (SNP), are used in GWAS. This raises privacy and security concerns as…
Fully Homomorphic Encryption (FHE) promises the ability to compute over encrypted data without revealing sensitive contents. However, enabling high-frequency updates and statistical analysis in outsourced databases remains elusive due to…
We consider an architecture of confidential cloud-based control synthesis based on Homomorphic Encryption (HE). Our study is motivated by the recent surge of data-driven control such as deep reinforcement learning, whose heavy computational…
In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a…
Homomorphic encryption (HE) enables the secure offloading of computations to the cloud by providing computation on encrypted data (ciphertexts). HE is based on noisy encryption schemes in which noise accumulates as more computations are…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding.…
In this paper, we introduce a privacy-preserving stable diffusion framework leveraging homomorphic encryption, called HE-Diffusion, which primarily focuses on protecting the denoising phase of the diffusion process. HE-Diffusion is a…
We study the problem of maximizing a monotone submodular function subject to a Multiple Knapsack constraint. The input is a set $I$ of items, each has a non-negative weight, and a set of bins of arbitrary capacities. Also, we are given a…
We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…