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Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for…

This paper studies the problem of encoding messages into sequences which can be uniquely recovered from some noisy observations about their substrings. The observed reads comprise consecutive substrings with some given minimum overlap. This…

Kernel methods are powerful tools in machine learning. They have to be computationally efficient. In this paper, we present a novel Geometric-based approach to compute efficiently the string subsequence kernel (SSK). Our main idea is that…

In this article, we review existing probabilistic models for modeling abundance of fixed-length strings (k-mers) in DNA sequencing data. These models capture dependence of the abundance on various phenomena, such as the size and repeat…

Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…

Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: encounter the expensive time overhead, fail in exploring the explicit clusters, and cannot generalize to…

Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…

Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…

k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to…

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very…

Given a graph $G$ and two independent sets $I_s$ and $I_t$ of size $k$, the independent set reconfiguration problem asks whether there exists a sequence of $k$-sized independent sets $I_s = I_0, I_1, I_2, \ldots, I_\ell = I_t$ such that…

The learning complexity of special sets of vertices in graphs is studied in the model(s) of exact learning by (extended) equivalence and membership queries. Polynomial-time learning algorithms are described for vertex covers, independent…

Hitting Set is a classic problem in combinatorial optimization. Its input consists of a set system F over a finite universe U and an integer t; the question is whether there is a set of t elements that intersects every set in F. The Hitting…

String matching algorithm plays the vital role in the Computational Biology. The functional and structural relationship of the biological sequence is determined by similarities on that sequence. For that, the researcher is supposed to aware…

We study the k-route cut problem: given an undirected edge-weighted graph G=(V,E), a collection {(s_1,t_1),(s_2,t_2),...,(s_r,t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset…

In computational genomics, many analyses rely on efficient storage and traversal of $k$-mers, motivating compact representations such as spectrum-preserving string sets (SPSS), which store strings whose $k$-mer spectrum matches that of the…

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased…

The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…

String kernels are typically used to compare genome-scale sequences whose length makes alignment impractical, yet their computation is based on data structures that are either space-inefficient, or incur large slowdowns. We show that a…