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Many modern statistically efficient methods come with tremendous computational challenges, often leading to large-scale optimisation problems. In this work, we examine such computational issues for recently developed estimation methods in…
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…
Derivative Free Optimization is known to be an efficient and robust method to tackle the black-box optimization problem. When it comes to noisy functions, classical comparison-based algorithms are slower than gradient-based algorithms. For…
Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However,…
Recently, flat-minima optimizers, which seek to find parameters in low-loss neighborhoods, have been shown to improve a neural network's generalization performance over stochastic and adaptive gradient-based optimizers. Two methods have…
We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics is described: a deterministic low-rank approximation of the…
Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…
Mixture variational distributions in black box variational inference (BBVI) have demonstrated impressive results in challenging density estimation tasks. However, currently scaling the number of mixture components can lead to a linear…
Analysis of variance (ANOVA) reveals some disadvantages, such as non-robustness against heteroscedastic or non-normal errors and using difference to overall mean as effect sizes only. As an alternative the multiple contrast test comparing…
Deep Neural Networks have often been called the black box because of the complex, deep architecture and non-transparency presented by the inner layers. There is a lack of trust to use Artificial Intelligence in critical and high-precision…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
It is well-known that deep neural networks (DNNs) have shown remarkable success in many fields. However, when adding an imperceptible magnitude perturbation on the model input, the model performance might get rapid decrease. To address this…
One of the main challenges for feature representation in deep learning-based classification is the design of appropriate loss functions that exhibit strong discriminative power. The classical softmax loss does not explicitly encourage…
Neural networks are commonly regarded as black boxes performing incomprehensible functions. For classification problems networks provide maps from high dimensional feature space to K-dimensional image space. Images of training vector are…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…
An exciting recent development is the uptake of deep neural networks in many scientific fields, where the main objective is outcome prediction with the black-box nature. Significance testing is promising to address the black-box issue and…
This paper reviews the state-of-the-art model-based adaptive sampling approaches for single-objective black-box optimization (BBO). While BBO literature includes various promising sampling techniques, there is still a lack of comprehensive…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
The analysis of variance (ANOVA) decomposition offers a systematic method to understand the interaction effects that contribute to a specific decision output. In this paper we introduce Neural-ANOVA, an approach to decompose neural networks…
Explaining the predictions of neural black-box models is an important problem, especially when such models are used in applications where user trust is crucial. Estimating the influence of training examples on a learned neural model's…