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The Levenshtein distance is an important tool for the comparison of symbolic sequences, with many appearances in genome research, linguistics and other areas. For efficient applications, an approximation by a distance of smaller…
Fr\'echet Inception Distance (FID) is widely used to evaluate image generators, yet lower FID does not always correspond to better sample quality. We show that this mismatch depends in part on the geometry of the reference dataset. In a…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…
The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…
Many generative models have to combat $\textit{missing modes}$. The conventional wisdom to this end is by reducing through training a statistical distance (such as $f$-divergence) between the generated distribution and provided data…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…
Evaluating generative models for synthetic medical imaging is crucial yet challenging, especially given the high standards of fidelity, anatomical accuracy, and safety required for clinical applications. Standard evaluation of generated…
Channel modelling is essential to designing modern wireless communication systems. The increasing complexity of channel modelling and the cost of collecting high-quality wireless channel data have become major challenges. In this paper, we…
Generative models are now widely used by graphic designers and artists. Prior works have shown that these models remember and often replicate content from their training data during generation. Hence as their proliferation increases, it has…
Causal discovery, the task of automatically constructing a causal model from data, is of major significance across the sciences. Evaluating the performance of causal discovery algorithms should ideally involve comparing the inferred models…
Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high…
Generative models aim to learn the distribution of observed data by generating new instances. With the advent of neural networks, deep generative models, including variational autoencoders (VAEs), generative adversarial networks (GANs), and…
Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as…
In this paper, we address the question of comparison between populations of trees. We study an statistical test based on the distance between empirical mean trees, as an analog of the two sample z statistic for comparing two means. Despite…
Minimum distance estimation (MDE) gained recent attention as a formulation of (implicit) generative modeling. It considers minimizing, over model parameters, a statistical distance between the empirical data distribution and the model. This…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…