Related papers: Fundamental Limits of Coded Polynomial Aggregation
In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining…
We study the fundamental tradeoffs between statistical accuracy and computational tractability in the analysis of high dimensional heterogeneous data. As examples, we study sparse Gaussian mixture model, mixture of sparse linear…
Distributed computing enables large-scale computation tasks to be processed over multiple workers in parallel. However, the randomness of communication and computation delays across workers causes the straggler effect, which may degrade the…
This paper studies kernel PCA in a decentralized setting, where data are distributively observed with full features in local nodes and a fusion center is prohibited. Compared with linear PCA, the use of kernel brings challenges to the…
Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we…
Coded computation can be used to speed up distributed learning in the presence of straggling workers. Partial recovery of the gradient vector can further reduce the computation time at each iteration; however, this can result in biased…
Matching pursuit, especially its orthogonal version (OMP) and variations, is a greedy algorithm widely used in signal processing, compressed sensing, and sparse modeling. Inspired by constrained sparse signal recovery, this paper proposes a…
We study a practical algorithm for sparse principal component analysis (PCA) of incomplete and noisy data. Our algorithm is based on the semidefinite program (SDP) relaxation of the non-convex $l_1$-regularized PCA problem. We provide…
Coded distributed batch computation distributes a computation task, such as matrix multiplication, $N$-linear computation, or multivariate polynomial evaluation, across $S$ servers through a coding scheme, such that the response from any…
Coded distributed computing was recently introduced to mitigate the effect of stragglers on distributed computing. This paper combines ideas of approximate computing with coded computing to further accelerate computation. We propose…
The problem of $T$-colluding private information retrieval (PIR) enables the user to retrieve one out of $M$ files from a distributed storage system with $N$ servers without revealing anything about the index of the desired file to any…
We prove a \emph{query complexity} lower bound on rank-one principal component analysis (PCA). We consider an oracle model where, given a symmetric matrix $M \in \mathbb{R}^{d \times d}$, an algorithm is allowed to make $T$ \emph{exact}…
In this work, we present a simplification and a corresponding hardware architecture for hard-decision recursive projection-aggregation (RPA) decoding of Reed-Muller (RM) codes. In particular, we transform the recursive structure of RPA…
In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…
Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to…
Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…
We consider the problem of computing the convolution of two long vectors using parallel processing units in the presence of "stragglers". Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation…
In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the "complete defective set" given the outcomes of different group tests. In contrast, the main…
The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ…