Related papers: A New Distance Measure for Non-Identical Data with…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson $\chi^2$-distance. The results are based on proper non-uniform estimates for…
Displacement estimation is a critical step of virtually all Ultrasound Elastography (USE) techniques. Two main features make this task unique compared to the general optical flow problem: the high-frequency nature of ultrasound…
This paper introduces a new framework to quantify distance between finite sets with uncertainty present, where probability distributions determine the locations of individual elements. Combining this with a Bayesian change point detection…
Super-resolution results are usually measured by full-reference image quality metrics or human rating scores. However, these evaluation methods are general image quality measurement, and do not account for the nature of the super-resolution…
We developed a new joint probabilistic segmentation and image distribution matching generative adversarial network (PSIGAN) for unsupervised domain adaptation (UDA) and multi-organ segmentation from magnetic resonance (MRI) images. Our UDA…
Why rely on dense neural networks and then blindly sparsify them when prior knowledge about the problem structure is already available? Many inverse problems admit algorithm-unrolled networks that naturally encode physics and sparsity. In…
We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between…
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…
We explore the utility of information contained within a dropout based Bayesian neural network (BNN) for the task of detecting out of distribution (OOD) data. We first show how previous attempts to leverage the randomized embeddings induced…
Testing the equality of two conditional distributions is crucial in various modern applications, including transfer learning and causal inference. Despite its importance, this fundamental problem has received surprisingly little attention…
The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
Data collection is a fundamental problem in the scenario of big data, where the size of sampling sets plays a very important role, especially in the characterization of data structure. This paper considers the information collection process…
To reduce the communication cost of differential privacy mechanisms, we introduce a novel construction, called Poisson private representation (PPR), designed to compress and simulate any local randomizer while ensuring local differential…
Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…
One of the key issues in quantum information theory related problems concerns with that of distinguishability of quantum states. In this context, Bures distance serves as one of the foremost choices among various distance measures. It also…
In this paper, distributed Bayesian detection problems with unknown prior probabilities of hypotheses are considered. The sensors obtain observations which are conditionally dependent across sensors and their probability density functions…
Applications in data science, shape analysis and object classification frequently require comparison of probability distributions defined on different ambient spaces. To accomplish this, one requires a notion of distance on a given class of…