arXiv research

We show that deleting an edge of a 3-cycle in an intrinsically knotted graph gives an intrinsically linked graph.

Graph pruning improves neural network performance by addressing squashing and smoothing issues.

New graph shows edge deletion/contraction doesn't always result in intrinsically linked graphs.

We propose an approach for approximating the partition function which is based on two steps: (1) computing the partition function of a simplified model which is obtained by deleting model edges, and (2) rectifying the result by applying an edge-by-edge correction. The approach leads to an intuitive framework in which o…

Paper determines Assouad-Nagata dimension for all minor-closed metrics.

A well-known problem in data science and machine learning is {\em linear regression}, which is recently extended to dynamic graphs. Existing exact algorithms for updating the solution of dynamic graph regression require at least a linear time (in terms of $n$: the size of the graph). However, this time complexity might…

XGES improves GES by favoring early edge deletion, outperforming GES in finite data settings.

Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which deliberately add carefully created unnoticeable perturbation to the graph structure. …

We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesti…

Data ownership and data protection are increasingly important topics with ethical and legal implications, e.g., with the right to erasure established in the European General Data Protection Regulation (GDPR). In this light, we investigate network embeddings, i.e., the representation of network nodes as low-dimensional …

A graph is 2-apex if it is planar after the deletion of at most two vertices. Such graphs are not intrinsically knotted, IK. We investigate the converse, does not IK imply 2-apex? We determine the simplest possible counterexample, a graph on nine vertices and 21 edges that is neither IK nor 2-apex. In the process, we s…

We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums. In 1997 Murakami and Ohtsuki [MO] first constructed such an extension, building on Drinfel'd's theory of associators. We construct a step …

We extend the edge version of the classical Menger's Theorem for undirected graphs to $n$-dimensional simplicial complexes with chains over the field $\mathbb{F}_2$. The classical Menger's Theorem states that two different vertices in an undirected graph can be connected by $k$ pairwise edge-disjoint paths if, and only…

Many real datasets contain values missing not at random (MNAR). In this scenario, investigators often perform list-wise deletion, or delete samples with any missing values, before applying causal discovery algorithms. List-wise deletion is a sound and general strategy when paired with algorithms such as FCI and RFCI, b…

New approach protects privacy of deleted records in machine learning.

Paper tackles adaptive deletion of data points from trained models.

This research tackles data deletion in linear regression with noisy SGD, finding perfect deleted points.

We propose the Insertion-Deletion Transformer, a novel transformer-based neural architecture and training method for sequence generation. The model consists of two phases that are executed iteratively, 1) an insertion phase and 2) a deletion phase. The insertion phase parameterizes a distribution of insertions on the c…

New causal models for growing networks avoid node deletion constraints.

Efficient algorithms for deleting data from machine learning models without significantly affecting performance.

Paper proposes a fast method for approximate data deletion in generative models.

New method for efficiently deleting data from ML models.

While many statistical models and methods are now available for network analysis, resampling network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but is not directly applicable to networks since splitting network nodes into groups requires delet…

A plane graph $H$ is a {\em plane minor} of a plane graph $G$ if there is a sequence of vertex and edge deletions, and edge contractions performed on the plane, that takes $G$ to $H$. Motivated by knot theory problems, it has been asked if the plane minor relation is a well-quasi-order. We settle this in the affirmativ…

Proposes TNPM for better node popularity in directed and bipartite networks.

Graphs can be fooled by small edge changes, but this work protects them.

Study on deleting user data in linear regression models to maintain limited memory.

A finite simple graph $Γ$ determines a quotient $P_Γ$ of the pure braid group, called a graphic arrangement group. We analyze homomorphisms of these groups defined by deletion of sets of vertices, using methods developed in prior joint work with R. Randell. We show that, for a $K_4$-free graph $Γ$, a product of deletio…

Approximates cycles in planar and bounded-genus graphs.

The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.

The paper develops algorithms to find a robust summary of data under deletion, achieving good approximation guarantees.

New examples show deletion type admissible pairs can be rigid under rational saturation.

A graph is apex if it can be made planar by deleting a vertex, that is, $\exists v$ such that $G-v$ is planar. We define the related notions of edge apex, $\exists e$ such that $G-e$ is planar, and contraction apex, $\exists e$ such that $G/e$ is planar, as well as the analogues with a universal quantifier: $\forall v$…

ID-ExpO fine-tunes neural networks for more faithful explanations.

The paper compares two methods for handling missing data in causal discovery.

We observe the effects of the three different events that cause spread changes in the order book, namely trades, deletions and placement of limit orders. By looking at the frequencies of the relative amounts of price changing events, we discover that deletions of orders open the bid-ask spread of a stock more often tha…

Intense recent discussions have focused on how to provide individuals with control over when their data can and cannot be used --- the EU's Right To Be Forgotten regulation is an example of this effort. In this paper we initiate a framework studying what to do when it is no longer permissible to deploy models derivativ…

Networks evolve continuously over time with the addition, deletion, and changing of links and nodes. Such temporal networks (or edge streams) consist of a sequence of timestamped edges and are seemingly ubiquitous. Despite the importance of accurately modeling the temporal information, most embedding methods ignore it …

DaRE forests enable efficient data deletion from random forests.

FedCD improves non-IID federated learning performance.

Develops structured noise for more accurate graph classifier robustness certificates.

The paper tackles robust submodular maximization under matroid constraints, providing approximation algorithms for summary extraction.

Linear filtration helps delete training data from models.

We use a variation on the commutator collection process to characterize those pure braids which become trivial when any one strand is deleted, or, more generally, those pure braids which become trivial when all the strands in any one of a list of sets of strands is deleted.

RS-Del provides robustness for sequence classifiers against edit distance attacks.

Graph neural networks (GNNs) which apply the deep neural networks to graph data have achieved significant performance for the task of semi-supervised node classification. However, only few work has addressed the adversarial robustness of GNNs. In this paper, we first present a novel gradient-based attack method that fa…

Gordon and Litherland showed that all compact, unoriented, possibly non-orientable surfaces in $S^3$ bounded by a link are realted by attaching/deleting tubes and half twisted bands. In this note we give an elementary proof for this result.

The configuration space $F_2 (M)$ of ordered pairs of distinct points in a manifold $M$, also known as the deleted square of $M$, is not a homotopy invariant of $M$: Longoni and Salvatore produced examples of homotopy equivalent lens spaces $M$ and $N$ of dimension three for which $F_2 (M)$ and $F_2 (N)$ are not homoto…