Related papers: A framework for space-efficient string kernels
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…
We consider supervised learning problems within the positive-definite kernel framework, such as kernel ridge regression, kernel logistic regression or the support vector machine. With kernels leading to infinite-dimensional feature spaces,…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
Given a string of characters, the Burrows-Wheeler Transform rearranges the characters in it so as to produce another string of the same length which is more amenable to compression techniques such as move to front, run-length encoding, and…
The pre-image problem has to be solved during inference by most structured output predictors. For string kernels, this problem corresponds to finding the string associated to a given input. An algorithm capable of solving or finding good…
We introduce scalable deep kernels, which combine the structural properties of deep learning architectures with the non-parametric flexibility of kernel methods. Specifically, we transform the inputs of a spectral mixture base kernel with a…
The segment tree is an extremely versatile data structure. In this paper, a new heap based implementation of segment trees is proposed. In such an implementation of segment tree, the structural information associated with the tree nodes can…
In recent years, quantum computers have emerged as promising candidates for implementing kernels. Quantum Embedding Kernels embed data points into quantum states and calculate their inner product in a high-dimensional Hilbert Space by…
In this paper, we introduce zip-tries, which are simple, dynamic, memory-efficient data structures for strings. Zip-tries support search and update operations for $k$-length strings in $\mathcal{O}(k+\log n)$ time in the standard RAM model…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms…
Given \(k\) strings each of length at most $n$, computing the shortest common supersequence of them is a well-known NP-hard problem (when \(k\) is unbounded). On the other hand, when \(k=2\), such a shortest common supersequence can be…
The k-spectrum of a string is the set of all distinct substrings of length k occurring in the string. K-spectra have many applications in bioinformatics including pseudoalignment and genome assembly. The Spectral Burrows-Wheeler Transform…
The random access problem for compressed strings is to build a data structure that efficiently supports accessing the character in position $i$ of a string given in compressed form. Given a grammar of size $n$ compressing a string of size…
Given a string $S$ of $n$ integers in $[0,\sigma)$, a range minimum query RMQ$(i, j)$ asks for the index of the smallest integer in $S[i \dots j]$. It is well known that the problem can be solved with a succinct data structure of size $2n +…
Real-world data often comes in compressed form. Analyzing compressed data directly (without decompressing it) can save space and time by orders of magnitude. In this work, we focus on fundamental sequence comparison problems and try to…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…
In this paper, we present a new data structure called the packed compact trie (packed c-trie) which stores a set $S$ of $k$ strings of total length $n$ in $n \log\sigma + O(k \log n)$ bits of space and supports fast pattern matching queries…