Related papers: Metric Statistics: Exploration and Inference for R…
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs. Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has…
We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…
Collections of measures on compact metric spaces form a model category ("data complexes"), whose morphisms are marginalization integrals. The fibrant objects in this category represent collections of measures in which there is a measure on…
Information is an inherent component of stochastic processes and to measure the distance between different stochastic processes it is not sufficient to consider the distance between their laws. Instead, the information which accumulates…
Ordinal user-provided ratings across multiple items are frequently encountered in both scientific and commercial applications. Whilst recommender systems are known to do well on these type of data from a predictive point of view, their…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of…
Estimating the density of a distribution from samples is a fundamental problem in statistics. In many practical settings, the Wasserstein distance is an appropriate error metric for density estimation. For example, when estimating…
Multiple people tracking is a key problem for many applications such as surveillance, animation or car navigation, and a key input for tasks such as activity recognition. In crowded environments occlusions and false detections are common,…
Various statistical analysis methods are studied for years to extract accurate trends of network traffic and predict the future load mainly to allocate required resources. Besides, many stochastic modeling techniques are offered to…
We study the estimation and concentration on its expectation of the probability to observe data further than a specified distance from a given iid sample in a metric space. The problem extends the classical problem of estimation of the…
We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory inference, where a developing population of cells traces out a…
The relevance and importance of contextualizing data analytics is described. Qualitative characteristics might form the context of quantitative analysis. Topics that are at issue include: contrast, baselining, secondary data sources,…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
Climate statistics is of course a very broad field, along with the many connections and impacts for yet other areas, with a history as long as mankind has been recording temperatures, describing drastic weather events, etc. The important…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
Heterogeneous datasets emerge in various machine learning and optimization applications that feature different input sources, types or formats. Most models or methods do not natively tackle heterogeneity. Hence, such datasets are often…
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight…
Optimal transport (OT) distances are increasingly used as loss functions for statistical inference, notably in the learning of generative models or supervised learning. Yet, the behavior of minimum Wasserstein estimators is poorly…