Related papers: A note on averaging prediction accuracy, Green's f…

Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…

We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both…

Confidence interval of mean is often used when quoting statistics. The same rigor is often missing when quoting percentiles and tolerance or percentile intervals. This article derives the expression for confidence in percentiles of a sample…

In this paper, we study the generalized Clifford-Fourier transform introduced in [6] using the Laplace transform technique. We give explicit expressions in the even dimensional case, we obtain polynomial bounds for the kernel functions and…

This letter gives approximations to an integral appearing in the formula for downlink coverage probability of a typical user in Poisson point process (PPP) based stochastic geometry frameworks of the form $\int_0^\infty \exp\{ - (Ax + B…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

With multiple outcomes in empirical research, a common strategy is to define a composite outcome as a weighted average of the original outcomes. However, the choices of weights are often subjective and can be controversial. We propose an…

This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a…

Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been…

We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…

We characterize a Hawkes point process with kernel proportional to the probability density function of Mittag-Leffler random variables. This kernel decays as a power law with exponent $\beta +1 \in (1,2]$. Several analytical results can be…

E.T. Jaynes, originator of the maximum entropy interpretation of statistical mechanics, emphasized that there is an inevitable trade-off between the conflicting requirements of robustness and accuracy for any inferencing algorithm. This is…

It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e. in symmetric spaces, may be presented in form of an averaging over the Lie group of isometries with some nontrivial…

This paper establishes the functional average as an important estimand for causal inference. The significance of the estimand lies in its robustness against traditional issues of confounding. We prove that this robustness holds even when…

By considering a least squares approximation of a given square integrable function f:[0,1]^n --> R by a shifted L-statistic function (a shifted linear combination of order statistics), we define an index which measures the global influence…

We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement-errors. We prove consistency of the…

A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We…

While regression models capture the relationship between predictors and the response variable, they often lack intuitive accompanying methods to understand the influence of predictors on the outcome. To address this, we introduce an…

Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules,…

Variable selection, also known as feature selection in machine learning, plays an important role in modeling high dimensional data and is key to data-driven scientific discoveries. We consider here the problem of detecting influential…