arXiv research

New matrix reveals cluster info in sparse directed graphs.

New findings support a new community recovery threshold for Stochastic Block Model with many communities.

Spectral method detects communities in sparse hypergraphs, achieving detection threshold.

A new graph neural network (NBA-GNN) avoids revisiting nodes to improve accuracy.

This paper presents VEC-NBT, a variation on the unsupervised graph clustering technique VEC, which improves upon the performance of the original algorithm significantly for sparse graphs. VEC employs a novel application of the state-of-the-art word2vec model to embed a graph in Euclidean space via random walks on the n…

New findings on community recovery in SBM with many communities.

Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, non-symmetric and higher dimensional operator, related to the n…

Unified spectral clustering for sparse networks with heterogeneous degrees.

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a…

Motivated by community detection, we characterise the spectrum of the non-backtracking matrix $B$ in the Degree-Corrected Stochastic Block Model. Specifically, we consider a random graph on $n$ vertices partitioned into two equal-sized clusters. The vertices have i.i.d. weights $\{ φ_u \}_{u=1}^n$ with second moment $Φ…

A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local "richness" of the cyclic structure. In this paper, we introduce renewal non-backtrac…

New method detects communities in complex hypergraphs, matching theoretical limits.

There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight when the network is sparse and displays clustering or transitivity, which is repr…

HollowFlow speeds up likelihood evaluation for large-scale models.

We consider the problem of clustering partially labeled data from a minimal number of randomly chosen pairwise comparisons between the items. We introduce an efficient local algorithm based on a power iteration of the non-backtracking operator and study its performance on a simple model. For the case of two clusters, w…

This paper analyzes DeepWalk and node2vec for community detection in large networks.

New formula refutes random CSPs with fewer constraints.

Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these methods assume that the number of communities is known, which is often not the case in practice. We study a simple and very fast method for estimating the number of communities based on th…

We say that a subset $S\subseteq F_N$ is \emph{spectrally rigid} if whenever $T_1, T_2\in cv_N$ are points of the (unprojectivized) Outer space such that $||g||_{T_1}=||g||_{T_2}$ for every $g\in S$ then $T_1=T_2$ in $\cvn$. It is well-known that $F_N$ itself is spectrally rigid; it also follows from the result of Smil…

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we …

The paper develops methods to price and hedge options in path-dependent stock models.

Extend classical theory of affine processes to path-dependent setting

Simpler method derived for path geometries on surfaces, characterizing projective path geometries.

New Bethe-Hessian method improves community detection in sparse networks.

Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thr…

Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…

We consider the problem of path inference: given a path prefix, i.e., a partially observed sequence of nodes in a graph, we want to predict which nodes are in the missing suffix. In particular, we focus on natural paths occurring as a by-product of the interaction of an agent with a network---a driver on the transporta…

Proposes a novel path generation and evaluation method for video games.

Introduces q-paths for generalizing geometric annealing paths in machine learning.

This paper improves tail dependence analysis by introducing a path-based approach.

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume t…

One-shot path planning for multiple agents using neural networks.

Foundation for robust finance using rough path theory.

Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.

The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.

Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.

A positive path in the linear symplectic group $\Sp(2n)$ is a smooth path which is everywhere tangent to the positive cone. These paths are generated by negative definite (time-dependent) quadratic Hamiltonian functions on Euclidean space. A special case are autonomous positive paths, which are generated by time-indepe…

A new method predicts future paths using a Monte-Carlo approach.

The study proves unique path lifting properties and their implications on quotient spaces and covering maps.

The paper calculates sensitivities for financial derivatives using path weighting methods.

Develops a numerical scheme for solving path-dependent FBSDEs and PDEs.

Study of motion constraints and path-following on 3D space.

Global invariant for path structures and differential equations defined on torus.

This paper describes and evaluates the use of Generative Adversarial Networks (GANs) for path planning in support of smart mobility applications such as indoor and outdoor navigation applications, individualized wayfinding for people with disabilities (e.g., vision impairments, physical disabilities, etc.), path planni…

End-to-end KBQA system learns from multiple reasoning paths without labeled paths.

We extend path analysis by showing that, for a singly-connected path diagram, the partial covariance of two random variables factorizes over the nodes and edges in the path between the variables. This result allows us to determine the contribution of each node and edge to the partial covariance. It also allows us to sh…

In a rigorous construction of the path integral for supersymmetric quantum mechanics on a Riemann manifold, based on Bär and Pfäffle's use of piecewise geodesic paths, the kernel of the time evolution operator is the heat kernel for the Laplacian on forms. The path integral is approximated by the integral of a form on …

New algorithmic view of ℓ2 regularization using ODEs and path-following methods.