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We investigate sublinear-time algorithms that take partially erased graphs represented by adjacency lists as input. Our algorithms make degree and neighbor queries to the input graph and work with a specified fraction of adversarial…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Graph model is emerging as a very effective tool for learning the complex structures and relationships hidden in data. Generally, the critical purpose of graph-oriented learning algorithms is to construct an informative graph for image…
Bilevel optimization is an important formulation for many machine learning problems. Current bilevel optimization algorithms assume that the gradient of the upper-level function is Lipschitz. However, recent studies reveal that certain…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
Work on approximate linear algebra has led to efficient distributed and streaming algorithms for problems such as approximate matrix multiplication, low rank approximation, and regression, primarily for the Euclidean norm $\ell_2$. We study…
Hierarchical reinforcement learning (HRL) improves the efficiency of long-horizon reinforcement-learning tasks with sparse rewards by decomposing the task into a hierarchy of subgoals. The main challenge of HRL is efficient discovery of the…
In this paper, we propose a novel framework, the Sampling-guided Heterogeneous Graph Neural Network (SHT-GNN), to effectively tackle the challenge of missing data imputation in longitudinal studies. Unlike traditional methods, which often…
Exact subgraph matching is a fundamental graph operator that supports many graph analytics tasks, yet it remains computationally challenging due to its NP-completeness. Recent learning-based approaches accelerate query processing via…
Motivated by extracting and summarizing relevant information in short sentence settings, such as satisfaction questionnaires, hotel reviews, and X/Twitter, we study the problem of clustering words in a hierarchical fashion. In particular,…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…
The $\ell_p$-norm regression problem is a classic problem in optimization with wide ranging applications in machine learning and theoretical computer science. The goal is to compute $x^{\star} =\arg\min_{Ax=b}\|x\|_p^p$, where $x^{\star}\in…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph.…
In this paper, we study a nonlocal variational problem which consists of minimizing in $L^2$ the sum of a quadratic data fidelity and a regularization term corresponding to the $L^p$-norm of the nonlocal gradient. In particular, we study…
Bayesian network classifiers (BNCs) possess a number of properties desirable for a modern classifier: They are easily interpretable, highly scalable, and offer adaptable complexity. However, traditional methods for learning BNCs have…
We study the convergence rate of the proximal-gradient homotopy algorithm applied to norm-regularized linear least squares problems, for a general class of norms. The homotopy algorithm reduces the regularization parameter in a series of…