Related papers: Closure properties of classes of multiple testing …
We consider a class of simple one parameter families of interval maps, and we study how metric (resp. topological) entropy changes as the parameter varies. We show that in many cases the entropy displays a semi-regular behaviour, i.e. it is…
Top-down and bottom-up theorem proving approaches each have specific advantages and disadvantages. Bottom-up provers profit from strong redundancy control but suffer from the lack of goal-orientation, whereas top-down provers are…
Acquisition of data is a difficult task in many applications of machine learning, and it is only natural that one hopes and expects the population risk to decrease (better performance) monotonically with increasing data points. It turns…
Many experiments are concerned with the comparison of counts between treatment groups. Examples include the number of successful signups in conversion rate experiments, or the number of errors produced by software versions in canary…
The estimation of functional networks through functional covariance and graphical models have recently attracted increasing attention in settings with high dimensional functional data, where the number of functional variables p is…
We present a unifying approach to multiple testing procedures for sequential (or streaming) data by giving sufficient conditions for a sequential multiple testing procedure to control the familywise error rate (FWER), extending to the…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…
Dose groups are compared with a control assuming an order restriction usually by the Williams trend test. Here, as an alternative, two variants of the closed testing procedure are considered, one where global Williams tests are used in the…
This note presents a method that provides optimal monotone conditional error functions for a large class of adaptive two stage designs. The presented method builds on a previously developed general theory for optimal adaptive two stage…
We obtain a characterization of two classes of dynamics with nonuniformly hyperbolic behavior in terms of an admissibility property. Namely, we consider exponential dichotomies with respect to a sequence of norms and nonuniformly hyperbolic…
A key challenge in building theoretical foundations for deep learning is the complex optimization dynamics of neural networks, resulting from the high-dimensional interactions between the large number of network parameters. Such non-trivial…
The dynamics of motor protein molecules that have two subunits is investigated using simple discrete stochastic models. Exact steady-state analytical expressions are obtained for velocities and dispersions for any number of intermediate…
In this paper, we studied two identically-trained neural networks (i.e. networks with the same architecture, trained on the same dataset using the same algorithm, but with different initialization) and found that their outputs discrepancy…
In contemporary problems involving genetic or neuroimaging data, thousands of hypotheses need to be tested. Due to their high power, and finite sample guarantees on type-I error under weak assumptions, Monte Carlo permutation tests are…
Compositionality supports the manipulation of large systems by working on their components. For model-based testing, this means that large systems can be tested by modelling and testing their components: passing tests for all components…
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is…
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one…
The objective of the paper is to study accuracy of multi-class classification in high-dimensional setting, where the number of classes is also large ("large $L$, large $p$, small $n$" model). While this problem arises in many practical…
Complex large-scale studies, such as those related to microarray data and fMRI studies, often involve testing multiple hierarchically ordered hypotheses. However, most existing false discovery rate (FDR) controlling procedures do not…