Related papers: Conditionality principle under unconstrained rando…
We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…
A general principle is advanced allowing the classification of nonunique solutions to nonlinear evolution equations, corresponding to different spatio-temporal patterns. This is done by defining the probability distribution of patterns,…
In Machine Learning, an accepted definition of fairness of a decision taken by a classifier is that it should not depend on protected features, such as gender. Unfortunately, when constraints exist between features, such dependencies can be…
In a probability-based reasoning system, Bayes' theorem and its variations are often used to revise the system's beliefs. However, if the explicit conditions and the implicit conditions of probability assignments `me properly distinguished,…
To construct interpretable explanations that are consistent with the original ML model, counterfactual examples---showing how the model's output changes with small perturbations to the input---have been proposed. This paper extends the work…
We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint…
Kolmogorov's axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
We initiate the study of fairness for ordinal regression. We adapt two fairness notions previously considered in fair ranking and propose a strategy for training a predictor that is approximately fair according to either notion. Our…
We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…
We introduce a criterion, resilience, which allows properties of a dataset (such as its mean or best low rank approximation) to be robustly computed, even in the presence of a large fraction of arbitrary additional data. Resilience is a…
A random forest prediction can be computed by the scalar product of the labels of the training examples and a set of weights that are determined by the leafs of the forest into which the test object falls; each prediction can hence be…
U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\theta(P_{X})$ of…
Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators…
Randomization tests allow simple and unambiguous tests of null hypotheses, by comparing observed data to a null ensemble in which experimentally-controlled variables are randomly resampled. In behavioral and neuroscience experiments,…
Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that…
This paper has been withdrawn. This paper focuses on the admissibility condition for fractional-order singular system with order $\alpha \in (0,1)$. The definitions of regularity, impulse-free and admissibility are given first, then a…
Properties expressed as the provability of a first-order sentence can be disproved by just finding a model of the negation of the sentence. This fact, however, is meaningful in restricted cases only, depending on the shape of the sentence…
The causal effect of an intervention (treatment/exposure) on an outcome can be estimated by: i) specifying knowledge about the data-generating process; ii) assessing under what assumptions a target quantity, such as for example a causal…