Related papers: Optimizing alphabet reduction pairs of arrays
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
Canonical Correlation Analysis (CCA) is a multivariate technique that takes two datasets and forms the most highly correlated possible pairs of linear combinations between them. Each subsequent pair of linear combinations is orthogonal to…
In a seminal paper of Charikar et al.~on the smallest grammar problem, the authors derive upper and lower bounds on the approximation ratios for several grammar-based compressors. Here we improve the lower bound for the famous {\sf RePair}…
Current sparse neural information retrieval (IR) methods, and to a lesser extent more traditional models such as BM25, do not take into account the document collection and the complex interplay between different term weights when…
We introduce new avoidability problems for words by considering equivalence relations, k-abelian equivalences, which lie properly in between equality and commutative equality, i.e. abelian equality. For two k-abelian equivalent words the…
Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious…
Machine learning algorithms are commonly specified in linear algebra (LA). LA expressions can be rewritten into more efficient forms, by taking advantage of input properties such as sparsity, as well as program properties such as common…
Given a channel with length-$n$ inputs and outputs over the alphabet $\{0,1,\ldots,q-1\}$, and of which a fraction $\varrho \in (0,1-1/q)$ of symbols can be arbitrarily corrupted by an adversary, a fundamental problem is that of…
ASP(Q) extends Answer Set Programming (ASP) with Quantifiers over answer sets. In this paper we focus on the class of ASP(Q) programs with two quantifiers and weak constraints, denoted as 2-ASP(Q)^w. 2-ASP(Q)^w is a practically relevant…
A word on $q$ symbols is a sequence of letters from a fixed alphabet of size $q$. For an integer $k\ge 1$, we say that a word $w$ is $k$-universal if, given an arbitrary word of length $k$, one can obtain it by removing entries from $w$. It…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
Understanding the benefits of quantum computing for solving combinatorial optimization problems (COPs) remains an open research question. In this work, we extend and analyze algorithms that solve COPs by recursively shrinking them. The…
The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to…
For analysing text algorithms, for computing superstrings, or for testing random number generators, one needs to compute all overlaps between any pairs of words in a given set. The positions of overlaps of a word onto itself, or of two…
In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the…
This thesis concerns sequential-access data compression, i.e., by algorithms that read the input one or more times from beginning to end. In one chapter we consider adaptive prefix coding, for which we must read the input character by…
Modern sparse arrays are maximally economic in that they retain just as many sensors required to provide a specific aperture while maintaining a hole-free difference coarray. As a result, these are susceptible to the failure of even a…
For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design,…