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Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented…

In this paper, we consider an inverse problem in graph learning domain -- ``given the graph representations smoothed by Graph Convolutional Network (GCN), how can we reconstruct the input graph signal?" We propose Graph Deconvolutional…

Graph neural networks (GNNs) are shown to be successful in modeling applications with graph structures. However, training an accurate GNN model requires a large collection of labeled data and expressive features, which might be inaccessible…

Graph sampling addresses the problem of selecting a node subset in a graph to collect samples, so that a K-bandlimited signal can be reconstructed in high fidelity. Assuming an independent and identically distributed (i.i.d.) noise model,…

In this thesis, we address the problem of identifying and quantifying variants (alternative splicing and genomic polymorphism) in RNA-seq data when no reference genome is available, without assembling the full transcripts. Based on the…

Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…

$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…

We consider an \emph{approximate} version of the trace reconstruction problem, where the goal is to recover an unknown string $s\in\{0,1\}^n$ from $m$ traces (each trace is generated independently by passing $s$ through a probabilistic…

The problem of reconstructing a string from its error-prone copies, the trace reconstruction problem, was introduced by Vladimir Levenshtein two decades ago. While there has been considerable theoretical work on trace reconstruction,…

The population recovery problem asks one to recover an unknown distribution over $n$-bit strings given access to independent noisy samples of strings drawn from the distribution. Recently, Ban et al. [BCF+19] studied the problem where the…

The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of $n$ nodes. In this paper we consider the situation where the joint input to the nodes is an…

The high-throughput short-reads RNA-seq protocols often produce paired-end reads, with the middle portion of the fragments being unsequenced. We explore if the full-length fragments can be computationally reconstructed from the sequenced…

For every integer $g$, isomorphism of graphs of Euler genus at most $g$ can be decided in linear time. This improves previously known algorithms whose time complexity is $n^{O(g)}$ (shown in early 1980's), and in fact, this is the first…

This work concerns sampling of smooth signals on arbitrary graphs. We first study a structured sampling strategy for such smooth graph signals that consists of a random selection of few pre-defined groups of nodes. The number of groups to…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique,…

In the trace reconstruction problem, the goal is to reconstruct an unknown string $x$ of length $n$ from multiple traces obtained by passing $x$ through the deletion channel. In the relaxed problem of $approximate$ trace reconstruction, the…

Temporal graphs are graphs where the topology and/or other properties of the graph change with time. They have been used to model applications with temporal information in various domains. Problems on static graphs become more challenging…

Pedigrees, or family trees, are graphs of family relationships that are used to study inheritance. A fundamental problem in computational biology is to find, for a pedigree with $n$ individuals genotyped at every site, a set of…

Motivation: Data volumes generated by next-generation sequencing technolo- gies is now a major concern, both for storage and transmission. This triggered the need for more efficient methods than general purpose compression tools, such as…