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In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
Representing distributions over permutations can be a daunting task due to the fact that the number of permutations of $n$ objects scales factorially in $n$. One recent way that has been used to reduce storage complexity has been to exploit…
With the growing interest in the machine learning community to solve real-world problems, it has become crucial to uncover the hidden reasoning behind their decisions by focusing on the fairness and auditing the predictions made by these…
Although there is growing interest in measuring integrated information in computational and cognitive systems, current methods for doing so in practice are computationally unfeasible. Existing and novel integration measures are investigated…
A different general philosophy, to be called Full Randomness (FR), for the analysis of random effects models is presented, involving a notion of reducing or preferably eliminating fixed effects, at least formally. For example, under FR…
This work investigates the potential of Federated Learning (FL) for official statistics and shows how well the performance of FL models can keep up with centralized learning methods.F L is particularly interesting for official statistics…
Normalizing flows define a probability distribution by an explicit invertible transformation $\boldsymbol{\mathbf{z}}=f(\boldsymbol{\mathbf{x}})$. In this work, we present implicit normalizing flows (ImpFlows), which generalize normalizing…
Federated learning (FL) has shown promising potential in safeguarding data privacy in healthcare collaborations. While the term "FL" was originally coined by the engineering community, the statistical field has also explored similar…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
When modeling the distribution of a multivariate continuous random vector using the so-called \emph{copula approach}, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement…
We study the problem of interpolating all values of a discrete signal f of length N when d<N values are known, especially in the case when the Fourier transform of the signal is zero outside some prescribed index set J; these comprise the…
Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this…
It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $\phi(x)$, called an…
Federated inference enhances LLM performance in edge computing through weighted averaging of distributed model predictions. However, autoregressive LLM inference requires frequent full-model forward passes across workers, severely limiting…
This paper introduces the concept of hyperpolation: a way of generalising from a limited set of data points that is a peer to the more familiar concepts of interpolation and extrapolation. Hyperpolation is the task of estimating the value…
We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal…
Factor models are widely applied to the analysis of multivariate data across disparate fields of research. However, modern scientific data are often incomplete, and estimating a factor model from partially observed data can be very…
Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to…
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
Training classifiers under fairness constraints such as group fairness, regularizes the disparities of predictions between the groups. Nevertheless, even though the constraints are satisfied during training, they might not generalize at…