Related papers: Randomness Efficient Fast-Johnson-Lindenstrauss Tr…
In this paper we make a novel use of the Johnson-Lindenstrauss Lemma. The Lemma has an existential form saying that there exists a JL transformation $f$ of the data points into lower dimensional space such that all of them fall into…
Distributed stochastic optimization enables multi-agent collaboration in applications such as distributed learning and sensor networks, but also raises critical privacy concerns due to the involvement of sensitive data. While existing…
We study discrete distribution estimation under user-level local differential privacy (LDP). In user-level $\varepsilon$-LDP, each user has $m\ge1$ samples and the privacy of all $m$ samples must be preserved simultaneously. We resolve the…
Let $M_n$ be a class of symmetric sparse random matrices, with independent entries $M_{ij} = \delta_{ij} \xi_{ij}$ for $i \leq j$. $\delta_{ij}$ are i.i.d. Bernoulli random variables taking the value $1$ with probability $p \geq…
The recently introduced theory of compressive sensing (CS) enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be…
Random Projections have been widely used to generate embeddings for various graph learning tasks due to their computational efficiency. The majority of applications have been justified through the Johnson-Lindenstrauss Lemma. In this paper,…
Numerical linear algebra plays an important role in computer science. In this paper, we initiate the study of performing linear algebraic tasks while preserving privacy when the data is streamed online. Our main focus is the space…
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…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Designing privacy-preserving machine learning algorithms has received great attention in recent years, especially in the setting when the data contains sensitive information. Differential privacy (DP) is a widely used mechanism for data…
We investigate the privacy of {\em any} algorithm whose outputs have Gaussian distribution. This work is motivated by the prevalence of such algorithms in several useful (ML) applications, and the comparatively little research that focuses…
Although robust learning and local differential privacy are both widely studied fields of research, combining the two settings is just starting to be explored. We consider the problem of estimating a discrete distribution in total variation…
Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the…
Differential privacy schemes have been widely adopted in recent years to address issues of data privacy protection. We propose a new Gaussian scheme combining with another data protection technique, called random orthogonal matrix masking,…
An algorithm is developed to gradually relax the Differential Privacy (DP) guarantee of a randomized response. The output from each relaxation maintains the same probability distribution as a standard randomized response with the equivalent…
We study the problem of estimating a set of $d$ linear queries with respect to some unknown distribution $\mathbf{p}$ over a domain $\mathcal{J}=[J]$ based on a sensitive data set of $n$ individuals under the constraint of local…
We provide a simple proof of the Johnson-Lindenstrauss lemma for sub-Gaussian variables. We extend the analysis to identify how sparse projections can be, and what the cost of sparsity is on the target dimension.The Johnson-Lindenstrauss…
For scalable machine learning on large data sets, subsampling a representative subset is a common approach for efficient model training. This is often achieved through importance sampling, whereby informative data points are sampled more…
Distributed model predictive control (DMPC) has attracted extensive attention as it can explicitly handle system constraints and achieve optimal control in a decentralized manner. However, the deployment of DMPC strategies generally…
The famous Johnson-Lindenstrauss lemma states that for any set of n vectors, there is a linear transformation into a space of dimension O(log n) that approximately preserves all their lengths. In fact, a Haar random unitary transformation…