Related papers: Energy distance and kernel mean embeddings for two…

The kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. In this paper we propose a method to boost the power…

Kernel conditional mean embeddings (CMEs) offer a powerful framework for representing conditional distribution, but they often face scalability and expressiveness challenges. In this work, we propose a new method that effectively combines…

The focus of this study is to evaluate the effectiveness of Machine Learning (ML) methods for two-sample testing with right-censored observations. To achieve this, we develop several ML-based methods with varying architectures and implement…

We prove that kernel covariance embeddings lead to information-theoretically perfect separation of distinct continuous probability distributions. In statistical terms, we establish that testing for the \emph{equality} of two non-atomic…

The distribution-free method of conformal prediction (Vovk et al, 2005) has gained considerable attention in computer science, machine learning, and statistics. Candes et al. (2023) extended this method to right-censored survival data,…

Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating…

We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…

We develop two new classes of tests for the Weibull distribution based on Stein's method. The proposed tests are applied in the full sample case as well as in the framework of random right censoring. We investigate the finite sample…

Imbalanced data occurs in a wide range of scenarios. The skewed distribution of the target variable elicits bias in machine learning algorithms. One of the popular methods to combat imbalanced data is to artificially balance the data…

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the…

Kernel two-sample tests have been widely used for multivariate data to test equality of distributions. However, existing tests based on mapping distributions into a reproducing kernel Hilbert space mainly target specific alternatives and do…

Non-parametric maximum likelihood estimation encompasses a group of classic methods to estimate distribution-associated functions from potentially censored and truncated data, with extensive applications in survival analysis. These methods,…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…

Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…

We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…

The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification…

The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…

One straightforward metric to evaluate a survival prediction model is based on the Mean Absolute Error (MAE) -- the average of the absolute difference between the time predicted by the model and the true event time, over all subjects.…