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This study developed a novel formulation of conditional expectations within the framework of a jump-diffusion mean-field stochastic differential equation. We introduce an integrated approach that combines unconditioned expectations with…
Expectations of marginals conditional on the total risk of a portfolio are crucial in risk-sharing and allocation. However, computing these conditional expectations may be challenging, especially in critical cases where the marginal risks…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
Structured prediction provides a general framework to deal with supervised problems where the outputs have semantically rich structure. While classical approaches consider finite, albeit potentially huge, output spaces, in this paper we…
Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…
In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…
This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine…
A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is…
In this short note, we try to provide the reader with a brief pedagogical account of some similarities and differences between stochastic and deterministic processes. A short presentation of some basic notions related to the mathematical…
Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are…
The ubiquity of machine learning based predictive models in modern society naturally leads people to ask how trustworthy those models are? In predictive modeling, it is quite common to induce a trade-off between accuracy and…
The standard odds ratio of logistic regression is foundational but limited to individual explanatory variables. This work derives a multivariable odds ratio that applies to all the explanatory variables in all their combinations.
We treat projective dependency trees as latent variables in our probabilistic model and induce them in such a way as to be beneficial for a downstream task, without relying on any direct tree supervision. Our approach relies on Gumbel…
We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…
An experiment or theory is classically explainable if it can be reproduced by some noncontextual ontological model. In this work, we adapt the notion of ontological models and generalized noncontextuality so it applies to the framework of…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
Gaussian processes (GPs) offer a principled probabilistic model over functions, but exact inference is restricted to the linear-Gaussian regime. We establish an explicit equivalence between GPs and a class of linear diffusion models,…
Conformal prediction is a general distribution-free approach for constructing prediction sets combined with any machine learning algorithm that achieve valid marginal or conditional coverage in finite samples. Ordinal classification is…