Related papers: A smooth ROC curve estimator based on log-concave …
The assumption of log-concavity is a flexible and appealing nonparametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator (MLE) of a probability mass function (pmf). We show…
Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…
The estimation of a log-concave density on $\mathbb{R}$ is a canonical problem in the area of shape-constrained nonparametric inference. We present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
Shape-constrained density estimation is an important topic in mathematical statistics. We focus on densities on $\mathbb{R}^d$ that are log-concave, and we study geometric properties of the maximum likelihood estimator (MLE) for weighted…
To evaluate a classification algorithm, it is common practice to plot the ROC curve using test data. However, the inherent randomness in the test data can undermine our confidence in the conclusions drawn from the ROC curve, necessitating…
The assumption that the sampling distribution of the crude odds ratio (ORcrude) is a log-normal distribution with parameters mu and sigma leads to the incorrect conclusion that the expectation of the log of ORcrude is equal to the parameter…
In medical diagnostics, leveraging multiple biomarkers can significantly improve classification accuracy compared to using a single biomarker. While existing methods based on exponential tilting or density ratio models have shown promise,…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
The log-concave maximum likelihood estimator of a density on the real line based on a sample of size $n$ is known to attain the minimax optimal rate of convergence of $O(n^{-4/5})$ with respect to, e.g., squared Hellinger distance. In this…
We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…
Free-response observer performance studies are of great importance for accuracy evaluation and comparison in tasks related to the detection and localization of multiple targets or signals. The free-response receiver operating characteristic…
Score estimation has recently emerged as a key modern statistical challenge, due to its pivotal role in generative modelling via diffusion models. Moreover, it is an essential ingredient in a new approach to linear regression via convex…
In this work we give new density estimators by averaging classical density estimators such as the histogram, the frequency polygon and the kernel density estimators obtained over different bootstrap samples of the original data. We prove…
We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear…
We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a…
We propose a fast stochastic Hamilton Monte Carlo (HMC) method, for sampling from a smooth and strongly log-concave distribution. At the core of our proposed method is a variance reduction technique inspired by the recent advance in…
The receiver operating characteristic (ROC) curve is a powerful statistical tool and has been widely applied in medical research. In the ROC curve estimation, a commonly used assumption is that larger the biomarker value, greater severity…
The receiver operating characteristic (ROC) curve is the most popular tool used to evaluate the discriminatory capability of diagnostic tests/biomarkers measured on a continuous scale when distinguishing between two alternative disease…