Related papers: Pointwise defined version of conditional expectati…
In this paper, we prove the existence and uniqueness of the conditional expectation of an event $A$ given a $\sigma$-algebra $\mathcal{G}$ as a linear problem in the Lebesgue spaces $L^{p}$ associated with a probability space through the…
Many key quantities in statistics and probability theory such as the expectation, quantiles, expectiles and many risk measures are law-determined maps from a space of random variables to the reals. We call such a law-determined map, which…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
Conditional expectation \mathbb{E}(Y \mid X) often fails to capture the complexity of multimodal conditional distributions \mathcal{L}(Y \mid X). To address this, we propose using n-point conditional quantizations--functional mappings of X…
Recently established, directed dependence measures for pairs $(X,Y)$ of random variables build upon the natural idea of comparing the conditional distributions of $Y$ given $X=x$ with the marginal distribution of $Y$. They assign pairs…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing data framework, we give a novel characterisation of the observed data as a stopping-set sigma algebra. We demonstrate that…
The linear conditional expectation (LCE) provides a best linear (or rather, affine) estimate of the conditional expectation and hence plays an important r\^ole in approximate Bayesian inference, especially the Bayes linear approach. This…
We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal…
Point processes offer a versatile framework for sequential event modeling. However, the computational challenges and constrained representational power of the existing point process models have impeded their potential for wider…
Let $(X,Y)$ be a bivariate random vector. The estimation of a probability of the form $P(Y\leq y \mid X >t) $ is challenging when $t$ is large, and a fruitful approach consists in studying, if it exists, the limiting conditional…
Given an unconditional diffusion model targeting a joint model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…
Conditional distributions, as defined by the Markov category framework, are studied in the setting of matrix algebras (quantum systems). Their construction as linear unital maps are obtained via a categorical Bayesian inversion procedure.…
Let $Y$ be a nonnegative random variable with mean $\mu$ and finite positive variance $\sigma^2$, and let $Y^s$, defined on the same space as $Y$, have the $Y$ size biased distribution, that is, the distribution characterized by…
In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…