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Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
A minimum path cover (MPC) of a directed acyclic graph (DAG) $G = (V,E)$ is a minimum-size set of paths that together cover all the vertices of the DAG. Computing an MPC is a basic polynomial problem, dating back to Dilworth's and…
In this paper, we tackle structure learning of Directed Acyclic Graphs (DAGs), with the idea of exploiting available prior knowledge of the domain at hand to guide the search of the best structure. In particular, we assume to know the…
This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP…
Due to their high computational efficiency on a continuous space, gradient optimization methods have shown great potential in the neural architecture search (NAS) domain. The mapping of network representation from the discrete space to a…
Recent advancements in equivariant deep models have shown promise in accurately predicting atomic potentials and force fields in molecular dynamics simulations. Using spherical harmonics (SH) and tensor products (TP), these equivariant…
Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous…
The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model…
The efficient parallel execution of complex computations requires balancing the workload across processors while minimizing the communication between them. This inherent trade-off is often captured by graph partitioning or DAG scheduling…
In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG…
Large-scale graph processing has drawn great attention in recent years. Most of the modern-day datacenter workloads can be represented in the form of Graph Processing such as MapReduce etc. Consequently, a lot of designs for Domain-Specific…
This paper considers the scheduling of parallel real-time tasks with arbitrary-deadlines. Each job of a parallel task is described as a directed acyclic graph (DAG). In contrast to prior work in this area, where decomposition-based…
Probabilistic graphical models are graphical representations of probability distributions. Graphical models have applications in many fields including biology, social sciences, linguistic, neuroscience. In this paper, we propose directed…
We study the problem of reducing test-time acquisition costs in classification systems. Our goal is to learn decision rules that adaptively select sensors for each example as necessary to make a confident prediction. We model our system as…
Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…
Graph algorithms and techniques are increasingly being used in scientific and commercial applications to express relations and explore large data sets. Although conventional or commodity computer architectures, like CPU or GPU, can compute…
Multi-head attention powers Transformer networks, the primary deep learning architecture behind the success of large language models (LLMs). Yet, the theoretical advantages of multi-head versus single-head attention, beyond mere parallel…
Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model…
Recent works (White et al., 2020a; Yan et al., 2020) demonstrate the importance of architecture encodings in Neural Architecture Search (NAS). These encodings encode either structure or computation information of the neural architectures.…
Learning graphical structures based on Directed Acyclic Graphs (DAGs) is a challenging problem, partly owing to the large search space of possible graphs. A recent line of work formulates the structure learning problem as a continuous…