相关论文: Stochastic Distance in Property Testing

In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…

Stochastic network calculus is a theory for stochastic service guarantee analysis of computer communication networks. In the current stochastic network calculus literature, its traffic and server models are typically based on the cumulative…

Optimal Transport has sparked vivid interest in recent years, in particular thanks to the Wasserstein distance, which provides a geometrically sensible and intuitive way of comparing probability measures. For computational reasons, the…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

Among various distance functions for graphs, graph and subgraph edit distances (GED and SED respectively) are two of the most popular and expressive measures. Unfortunately, exact computations for both are NP-hard. To overcome this…

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

The graph edit distance (GED) is a well-established distance measure widely used in many applications. However, existing methods for the GED computation suffer from several drawbacks including oversized search space, huge memory…

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…

In this thesis, we present fast deterministic algorithm to find small cuts in distributed networks. Finding small min-cuts for a network is essential for ensuring the quality of service and reliability. Throughout this thesis, we use the…

A $k$-modal probability distribution over the discrete domain $\{1,...,n\}$ is one whose histogram has at most $k$ "peaks" and "valleys." Such distributions are natural generalizations of monotone ($k=0$) and unimodal ($k=1$) probability…

We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…

Graph-based methods are known to be successful in many machine learning and pattern classification tasks. These methods consider semi-structured data as graphs where nodes correspond to primitives (parts, interest points, segments, etc.)…

Let k be a natural number. Let G be a graph and let N_1,...,N_k be k independent sets in G. The graph G is k-probe distance hereditary if G can be embedded into a DH-graph by adding edges between vertices that are contained in the same…

Graph similarity search is a common and fundamental operation in graph databases. One of the most popular graph similarity measures is the Graph Edit Distance (GED) mainly because of its broad applicability and high interpretability.…

The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…

Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…

We study property testing in the context of distributed computing, under the classical CONGEST model. It is known that testing whether a graph is triangle-free can be done in a constant number of rounds, where the constant depends on how…

Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…

Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…