Related papers: Sliced Distribution Matching based on Cumulative D…
There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…
We consider the problem of uniformity testing of Lipschitz continuous distributions with bounded support. The alternative hypothesis is a composite set of Lipschitz continuous distributions that are at least $\varepsilon$ away in $\ell_1$…
Flexible variational distributions improve variational inference but are harder to optimize. In this work we present a control variate that is applicable for any reparameterizable distribution with known mean and covariance matrix, e.g.…
This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…
Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When…
The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…
Curve matching is a prediction technique that relies on predictive mean matching, which matches donors that are most similar to a target based on the predictive distance. Even though this approach leads to high prediction accuracy, the…
It is well-known that the scale-free networks are ubiquitous in nature and society and have been one of the hotspot topic in complex networks. Recently, scholars presented a large quantity of scale-free networks by calculating cumulative…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
Some properties of chaotic dynamical systems can be probed through features of recurrences, also called analogs. In practice, analogs are nearest neighbours of the state of a system, taken from a large database called the catalog. Analogs…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
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…
In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
We revisit extending the Kolmogorov-Smirnov distance between probability distributions to the multidimensional setting and make new arguments about the proper way to approach this generalization. Our proposed formulation maximizes the…