相关论文: Updating Probabilities
We calculate survival probability of a special state which couples randomly to a regular or chaotic environment. The environment is modelled by a suitably chosen random matrix ensemble. The exact results exhibit non--perturbative features…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…
This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction,…
Based on a weak convergence argument, we provide a necessary and sufficient condition that guarantees that a nonnegative local martingale is indeed a martingale. Typically, conditions of this sort are expressed in terms of integrability…
The present paper investigates the update of an empirical probability distribution with the results of a new set of observations. The optimal update is obtained by minimizing either the Hellinger distance or the quadratic Bregman…
This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate…
A national voting population, when segmented into groups like, for example, different states, can yield a counter-intuitive scenario where the winner may not necessarily get the most number of total votes. A recent example is the 2016…
In typical machine learning systems, an estimate of the probability of the prediction is used to assess the system's confidence in the prediction. This confidence measure is usually uncalibrated; i.e.\ the system's confidence in the…
Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de-…
A central question in causal inference with observational studies is the sensitivity of conclusions to unmeasured confounding. The classical Cornfield condition allows us to assess whether an unmeasured binary confounder can explain away…
We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate…
The Naive-Bayes classifier is widely used due to its simplicity, speed and accuracy. However this approach fails when, for at least one attribute value in a test sample, there are no corresponding training samples with that attribute value.…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Standard conformal prediction offers a marginal guarantee on coverage, but for prediction sets to be truly useful, they should ideally ensure coverage conditional on each test point. Unfortunately, it is impossible to achieve exact,…
We present a simple equality that distinguishes non-contextual deterministic hidden-variable theories (NCHV) from standard quantum mechanics using a single three-level system. The protocol is inspired by the Monty Hall puzzle: a coherent…
The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics…
Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of…
There is a growing use of neural network classifiers as unbinned, high-dimensional (and variable-dimensional) reweighting functions. To date, the focus has been on marginal reweighting, where a subset of features are used for reweighting…
In this paper, we have obtained conditions on parameters that result in dispersive ordering and star ordering among two unequal sets of random variables from Proportional hazard rate and Proportional reversed hazard rate family of…
We study the problem of conditional predictive inference on multiple outcomes missing at random (MAR) -- or equivalently, under covariate shift. While the weighted conformal prediction offers a tool for inference under covariate shift with…