Abram Magner
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View article: Sparse Coding Representation of 2-way Data
Sparse Coding Representation of 2-way Data Open
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial dictionari…
View article: Continuous Symmetry Discovery and Enforcement Using Infinitesimal Generators of Multi-parameter Group Actions
Continuous Symmetry Discovery and Enforcement Using Infinitesimal Generators of Multi-parameter Group Actions Open
Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting aff…
View article: Low Rank Multi-Dictionary Selection at Scale
Low Rank Multi-Dictionary Selection at Scale Open
The sparse dictionary coding framework represents signals as a linear combination of a few predefined dictionary atoms. It has been employed for images, time series, graph signals and recently for 2-way (or 2D) spatio-temporal data employi…
View article: A deep learning architecture for metabolic pathway prediction
A deep learning architecture for metabolic pathway prediction Open
Motivation Understanding the mechanisms and structural mappings between molecules and pathway classes are critical for design of reaction predictors for synthesizing new molecules. This article studies the problem of prediction of classes …
View article: Low Rank Multi-Dictionary Selection at Scale
Low Rank Multi-Dictionary Selection at Scale Open
The sparse dictionary coding framework represents signals as a linear combination of a few predefined dictionary atoms. It has been employed for images, time series, graph signals and recently for 2-way (or 2D) spatio-temporal data employi…
View article: Symmetry Discovery Beyond Affine Transformations
Symmetry Discovery Beyond Affine Transformations Open
Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline…
View article: Fat Shattering, Joint Measurability, and PAC Learnability of POVM Hypothesis Classes
Fat Shattering, Joint Measurability, and PAC Learnability of POVM Hypothesis Classes Open
We characterize learnability for quantum measurement classes by establishing matching necessary and sufficient conditions for their PAC learnability, along with corresponding sample complexity bounds, in the setting where the learner is gi…
View article: Promise and Limitations of Supervised Optimal Transport-Based Graph Summarization via Information Theoretic Measures
Promise and Limitations of Supervised Optimal Transport-Based Graph Summarization via Information Theoretic Measures Open
Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller compressed graphs capture relevant structural information for downstream tasks. There is a recent graph…
View article: Promise and Limitations of Supervised Optimal Transport-Based Graph Summarization via Information Theoretic Measures
Promise and Limitations of Supervised Optimal Transport-Based Graph Summarization via Information Theoretic Measures Open
Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller compressed graphs capture relevant structural information for downstream tasks. One of the recent graph…
View article: Temporal Scale Estimation for Oversampled Network Cascades: Theory, Algorithms, and Experiment
Temporal Scale Estimation for Oversampled Network Cascades: Theory, Algorithms, and Experiment Open
Spreading processes on graphs arise in a host of application domains, from the study of online social networks to viral marketing to epidemiology. Various discrete-time probabilistic models for spreading processes have been proposed. These…
View article: Struct2Graph: A graph attention network for structure based predictions of protein-protein interactions
Struct2Graph: A graph attention network for structure based predictions of protein-protein interactions Open
Background Development of new methods for analysis of protein-protein interactions (PPIs) at molecular and nanometer scales gives insights into intracellular signaling pathways and will improve understanding of protein functions, as well a…
View article: The Power of Graph Convolutional Networks to Distinguish Random Graph Models
The Power of Graph Convolutional Networks to Distinguish Random Graph Models Open
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish betw…
View article: Compression of Dynamic Graphs Generated by a Duplication Model
Compression of Dynamic Graphs Generated by a Duplication Model Open
We continue building up the information theory of non-sequential data structures such as trees, sets, and graphs. In this paper, we consider dynamic graphs generated by a full duplication model in which a new vertex selects an existing ver…
View article: The Power of Graph Convolutional Networks to Distinguish Random Graph Models: Short Version
The Power of Graph Convolutional Networks to Distinguish Random Graph Models: Short Version Open
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…
View article: Fundamental Limits of Deep Graph Convolutional Networks
Fundamental Limits of Deep Graph Convolutional Networks Open
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish betw…
View article: Toward Universal Testing of Dynamic Network Models
Toward Universal Testing of Dynamic Network Models Open
Numerous networks in the real world change over time, in the sense that nodes and edges enter and leave the networks. Various dynamic random graph models have been proposed to explain the macroscopic properties of these systems and to prov…
View article: Goodness of Fit Testing for Dynamic Networks
Goodness of Fit Testing for Dynamic Networks Open
Numerous networks in the real world change over time, in the sense that nodes and edges enter and leave the networks. Various dynamic random graph models have been proposed to explain the macroscopic properties of these systems and to prov…
View article: Asymmetry and structural information in preferential attachment graphs
Asymmetry and structural information in preferential attachment graphs Open
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erdős‐Rényi graphs are typically asymmetric, real networ…
View article: Compression of Dynamic Graphs Generated by a Duplication Model
Compression of Dynamic Graphs Generated by a Duplication Model Open
We continue building up the information theory of non-sequential data structures such as trees, sets, and graphs. In this paper, we consider dynamic graphs generated by a full duplication model in which a new vertex selects an existing ver…
View article: Entropy and Optimal Compression of Some General Plane Trees
Entropy and Optimal Compression of Some General Plane Trees Open
We continue developing the information theory of structured data. In this article, we study models generating d -ary trees ( d ≥ 2) and trees with unrestricted degree. We first compute the entropy which gives us the fundamental lower bound…
View article: Lossless Compression of Binary Trees With Correlated Vertex Names
Lossless Compression of Binary Trees With Correlated Vertex Names Open
Compression schemes for advanced data structures have become a central modern challenge. Information theory has traditionally dealt with conventional data such as text, images, or video. In contrast, most data available today is multitype …
View article: Asymmetric Rényi Problem
Asymmetric Rényi Problem Open
In 1960 Rényi, in his Michigan State University lectures, asked for the number of random queries necessary to recover a hidden bijective labelling of n distinct objects. In each query one selects a random subset of labels and asks, which o…
View article: TIMES
TIMES Open
Inferring the node arrival sequence from a snapshot of a dynamic network is an important problem, with applications ranging from identifying sources of contagion to flow of capital in financial transaction networks. Variants of this proble…
View article: On Symmetries of Non-Plane Trees in a Non-Uniform Model
On Symmetries of Non-Plane Trees in a Non-Uniform Model Open
Binary trees come in two varieties: plane trees, often simply called binary trees, and non-plane trees, in which the order of subtrees does not matter. Nonplane trees find many applications; for example in modeling epidemics, in studying p…
View article: A Study of the Boltzmann Sequence-Structure Channel
A Study of the Boltzmann Sequence-Structure Channel Open
We rigorously study a channel that maps sequences from a finite alphabet to self-avoiding walks in the two-dimensional grid, inspired by a model of protein folding from statistical physics and studied empirically by biophysicists. This cha…
View article: Asymmetry and structural information in preferential attachment graphs
Asymmetry and structural information in preferential attachment graphs Open
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erdős-Rényi graphs are typically asymmetric, real networ…
View article: Preferential Attachment Graphs are All But Asymmetric
Preferential Attachment Graphs are All But Asymmetric Open
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erdős-Renyi graphs are typically asymmetric, real networ…
View article: Combining Density and Overlap (CoDO): A New Method for Assessing the Significance of Overlap Among Subgraphs
Combining Density and Overlap (CoDO): A New Method for Assessing the Significance of Overlap Among Subgraphs Open
Algorithms for detecting clusters (including overlapping clusters) in graphs have received significant attention in the research community. A closely related important aspect of the problem -- quantification of statistical significance of …