arXiv subjects

Anqi Dong

Publications and source records attributed to Anqi Dong.

28 records · Page 2Linked to original sources

arXiv2024

Heterogeneous Entity Representation for Medicinal Synergy Prediction

Medicinal synergy prediction is a powerful tool in drug discovery and development that harnesses the principles of combination therapy to enhance therapeutic outcomes by improving efficacy, reducing toxicity, and preventing drug resistance. While a myriad of computational methods has emerged for predicting synergistic drug combinations, a large portion of them may overlook the intricate, yet critical relationships between various entities in drug interaction networks, such as drugs, cell lines, and diseases. These relationships are complex and multidimensional, requiring sophisticated modeling to capture nuanced interplay that can significantly influence therapeutic efficacy. We introduce a salient deep hypergraph learning method, namely, Heterogeneous Entity Representation for MEdicinal Synergy prediction (HERMES), to predict anti-cancer drug synergy. HERMES integrates heterogeneous data sources, encompassing drug, cell line, and disease information, to provide a comprehensive understanding of the interactions involved. By leveraging advanced hypergraph neural networks with gated residual mechanisms, HERMES can effectively learn complex relationships/interactions within the data. Our results show HERMES demonstrates state-of-the-art performance, particularly in forecasting new drug combinations, significantly surpassing previous methods. This advancement underscores the potential of HERMES to facilitate more effective and precise drug combination predictions, thereby enhancing the development of novel therapeutic strategies.

cs.CE↗

arXiv2024

Data-driven Analysis of T-Product-based Dynamical Systems

A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors without first unfolding or flattening the data, which can result in a loss of crucial higher-order structural information. In this article, we introduce a novel framework for the data-driven analysis of T-product-based dynamical systems (TPDSs), where the system evolution is governed by the T-product between a third-order dynamic tensor and a third-order state tensor. In particular, we examine the data informativity of TPDSs concerning system identification, stability, controllability, and stabilizability and illustrate significant computational improvements over traditional approaches by leveraging the unique properties of the T-product. The effectiveness of our framework is demonstrated through numerical examples.

eess.SY↗

arXiv2024

Controllability and Observability of Temporal Hypergraphs

Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs. However, analyzing and controlling temporal hypergraphs poses significant challenges due to their inherent time-varying and nonlinear nature, while most existing methods predominantly target static hypergraphs. In this article, we generalize the notions of controllability and observability to temporal hypergraphs by leveraging tensor and nonlinear systems theory. Specifically, we establish tensor-based rank conditions to determine the weak controllability and observability of temporal hypergraphs. The proposed framework is further demonstrated with synthetic and real-world examples.

eess.SY↗

arXiv2024

Network Learning with Directional Sign Patterns

Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or encoding political of friendship differences in social networks. However, it is often the case that only an aggregate consequence of such edge weights that characterize relations may be directly observable, as in protein expression of in gene regulatory networks. Thus, learning edge weights poses a significant challenge that is further exacerbated for intricate and large-scale networks. In this article, we address a model problem to determine the strength of sign-indefinite relations that explain marginal distributions that constitute our data. To this end, we develop a paradigm akin to that of the Schrödinger bridge problem and an efficient Sinkhorn type algorithm (more properly, Schrödinger-Fortet-Sinkhorn algorithm) that allows fast convergence to parameters that minimize a relative entropy/likelihood criterion between the sought signed adjacency matrix and a prior. The formalism that we present represents a novel generalization of the earlier Schrödinger formalism in that marginal computations may incorporate weights that model directionality in underlying relations, and further, that it can be extended to high-order networks -- the Schrödinger-Fortet-Sinkhorn algorithm that we derive is applicable all the same and allows geometric convergence to a sought sign-indefinite adjacency matrix or tensor, for high-order networks. We demonstrate our framework with synthetic and real-world examples.

math.OC↗

arXiv2024

On Complexity of Stability Analysis in Higher-order Ecological Networks through Tensor Decompositions

Complex ecological networks are often characterized by intricate interactions that extend beyond pairwise relationships. Understanding the stability of higher-order ecological networks is salient for species coexistence, biodiversity, and community persistence. In this article, we present complexity analyses for determining the linear stability of higher-order ecological networks through tensor decompositions. We are interested in the higher-order generalized Lotka-Volterra model, which captures high-order interactions using tensors of varying orders. To efficiently compute Jacobian matrices and thus determine stability in large ecological networks, we exploit various tensor decompositions, including higher-order singular value decomposition, Canonical Polyadic decomposition, and tensor train decomposition, accompanied by in-depth computational and memory complexity analyses. We demonstrate the effectiveness of our framework with numerical examples.

eess.SY↗

arXiv2023

Data Assimilation for Sign-indefinite Priors: A generalization of Sinkhorn's algorithm

The purpose of this work is to develop a framework to calibrate signed datasets so as to be consistent with specified marginals by suitably extending the Schrödinger-Fortet-Sinkhorn paradigm. Specifically, we seek to revise sign-indefinite multi-dimensional arrays in a way that the updated values agree with specified marginals. Our approach follows the rationale in Schrödinger's problem, aimed at updating a "prior" probability measure to agree with marginal distributions. The celebrated Sinkhorn's algorithm (established earlier by R.\ Fortet) that solves Schrödinger's problem found early applications in calibrating contingency tables in statistics and, more recently, multi-marginal problems in machine learning and optimal transport. Herein, we postulate a sign-indefinite prior in the form of a multi-dimensional array, and propose an optimization problem to suitably update this prior to ensure consistency with given marginals. The resulting algorithm generalizes the Sinkhorn algorithm in that it amounts to iterative scaling of the entries of the array along different coordinate directions. The scaling is multiplicative but also, in contrast to Sinkhorn, inverse-multiplicative depending on the sign of the entries. Our algorithm reduces to the classical Sinkhorn algorithm when the entries of the prior are positive.

stat.ML↗

arXiv2023

Promotion/Inhibition Effects in Networks: A Model with Negative Probabilities

Biological networks often encapsulate promotion/inhibition as signed edge-weights of a graph. Nodes may correspond to genes assigned expression levels (mass) of respective proteins. The promotion/inhibition nature of co-expression between nodes is encoded in the sign of the corresponding entry of a sign-indefinite adjacency matrix, though the strength of such co-expression (i.e., the precise value of edge weights) cannot typically be directly measured. Herein we address the inverse problem to determine network edge-weights based on a sign-indefinite adjacency and expression levels at the nodes. While our motivation originates in gene networks, the framework applies to networks where promotion/inhibition dictates a stationary mass distribution at the nodes. In order to identify suitable edge-weights we adopt a framework of ``negative probabilities,'' advocated by P.\ Dirac and R.\ Feynman, and we set up a likelihood formalism to obtain values for the sought edge-weights. The proposed optimization problem can be solved via a generalization of the well-known Sinkhorn algorithm; in our setting the Sinkhorn-type ``diagonal scalings'' are multiplicative or inverse-multiplicative, depending on the sign of the respective entries in the adjacency matrix, with value computed as the positive root of a quadratic polynomial.

q-bio.MN↗

arXiv2023

Optimal transport through a toll

We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We provide a precise formulation which, in addition, is amenable to generalization in higher dimensions. We work out in detail the case of transport in one dimension by proving existence and uniqueness of solution. Under suitable regularity assumptions we give an explicit construction of the transport plan. Generalization of flux constraints to higher dimensions and possible extensions of the theory are discussed.

eess.SY↗

arXiv2023

Monge-Kantorovich Optimal Transport Through Constrictions and Flow-rate Constraints

We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified points, limit the flow rate across. We quantify flow-rate constraints via a bound on a sought probability density of the times that mass-elements cross toll stations and cast the transportation scheduling in a Kantorovich-type of formalism. Recent work by our team focused on the existence of Monge maps for similarly constrained transport minimizing average kinetic energy. The present formulation in this paper, besides being substantially more general, is cast as a (generalized) multi-marginal transport problem - a problem of considerable interest in modern-day machine learning literature and motivated extensive computational analyses. An enabling feature of our formalism is the representation of an average quadratic cost on the speed of transport as a convex constraint that involves crossing times.

eess.SY↗

arXiv2020

Lasso formulation of the shortest path problem

The shortest path problem is formulated as an $l_1$-regularized regression problem, known as lasso. Based on this formulation, a connection is established between Dijkstra's shortest path algorithm and the least angle regression (LARS) for the lasso problem. Specifically, the solution path of the lasso problem, obtained by varying the regularization parameter from infinity to zero (the regularization path), corresponds to shortest path trees that appear in the bi-directional Dijkstra algorithm. Although Dijkstra's algorithm and the LARS formulation provide exact solutions, they become impractical when the size of the graph is exceedingly large. To overcome this issue, the alternating direction method of multipliers (ADMM) is proposed to solve the lasso formulation. The resulting algorithm produces good and fast approximations of the shortest path by sacrificing exactness that may not be absolutely essential in many applications. Numerical experiments are provided to illustrate the performance of the proposed approach.

math.OC↗