Related papers: Exact Distribution-Free Hypothesis Tests for the R…
We study three notions of uncertainty quantification -- calibration, confidence intervals and prediction sets -- for binary classification in the distribution-free setting, that is without making any distributional assumptions on the data.…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…
A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
In the framework of semiparametric distribution regression, we consider the problem of comparing the conditional distribution functions corresponding to two samples. In contrast to testing for exact equality, we are interested in the (null)…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
Reproducing Kernel Hilbert Space (RKHS) embedding of probability distributions has proved to be an effective approach, via MMD (maximum mean discrepancy), for nonparametric hypothesis testing problems involving distributions defined over…
Binary classification is a task that involves the classification of data into one of two distinct classes. It is widely utilized in various fields. However, conventional classifiers tend to make overconfident predictions for data that…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of…
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well…
The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…
We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…
Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
The performance and ease of use of deep learning-based binary classifiers have improved significantly in recent years. This has opened up the potential for automating critical inspection tasks, which have traditionally only been trusted to…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…