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This paper considers vector network coding solutions based on rank-metric codes and subspace codes. The main result of this paper is that vector solutions can significantly reduce the required alphabet size compared to the optimal scalar…
Subspace codes are collections of subspaces of a projective space such that any two subspaces satisfy a pairwise minimum distance criterion. Recent results have shown that it is possible to construct optimal $(5,3)$ subspace codes from…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…
A new family of codes, called clustering-correcting codes, is presented in this paper. This family of codes is motivated by the special structure of data that is stored in DNA-based storage systems. The data stored in these systems has the…
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…
Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes,…
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two…
We introduce an information-theoretic framework for caching in derivation-based reasoning engines under independent premise erasure. Two decoder models are compared: a coded scheme using an arbitrary bit-string cache with a general-purpose…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
Consider a pair of correlated Gaussian sources (X1,X2). Two separate encoders observe the two components and communicate compressed versions of their observations to a common decoder. The decoder is interested in reconstructing a linear…
Coded caching is a promising technique to smooth out network traffic by storing part of the library content at the users' local caches. The seminal work on coded caching for single file retrieval by Maddah-Ali and Niesen (MAN) showed the…
Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into…
Coded caching aims to minimize the network's peak-time communication load by leveraging the information pre-stored in the local caches at the users. The original single file retrieval setting by Maddah-Ali and Niesen has been recently…
We study the problem of identifying correlations in multivariate data, under information constraints: Either on the amount of memory that can be used by the algorithm, or the amount of communication when the data is distributed across…
Many network information theory problems face the similar difficulty of single-letterization. We argue that this is due to the lack of a geometric structure on the space of probability distribution. In this paper, we develop such a…
Deep convolutional networks (convnets) show a remarkable ability to learn disentangled representations. In recent years, the generalization of deep learning to Lie groups beyond rigid motion in $\mathbb{R}^n$ has allowed to build convnets…
Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…
Although learning in high dimensions is commonly believed to suffer from the curse of dimensionality, modern machine learning methods often exhibit an astonishing power to tackle a wide range of challenging real-world learning problems…
Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries…