Related papers: Constructing Sublinear Expectations on Path Space
Motivated by applications in conditional sampling, given a probability measure $\mu$ and a diffeomorphism $\phi$, we consider the problem of simultaneously approximating $\phi$ and the pushforward $\phi_{\#}\mu$ by means of the flow of a…
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…
We study pathwise $p$-th variation of continuous paths on a compact interval along a fixed partition sequence. Although the class of continuous paths with finite $p$-th variation is generally not linear, we develop a coefficient-based…
In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be…
To quantify uncertainty around point estimates of conditional objects such as conditional means or variances, parameter uncertainty has to be taken into account. Attempts to incorporate parameter uncertainty are typically based on the…
We first give a decomposition for a $T$-invariant sublinear expectation $\mathbb{E}=\sup_{P\in\Theta}\mathrm{E}_P$, and show that each component $\mathbb{E}^{(d)}=\sup_{P\in\Theta^{(d)}}\mathrm{E}_P$ of the decomposition has a finite period…
We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first discuss the notion of G-standard normal distribution. With this nonlinear distribution we can…
This paper is concerned with the connection between G-Brownian Motion and analytic functions. We introduce the complex version of sublinear expectation, and then do the stochastic analysis in this framework. Furthermore, the conformal…
One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. An extension of his approach is…
Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional…
We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…
Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce "graph-based…
Future trajectories play an important role across domains such as autonomous driving, hurricane forecasting, and epidemic modeling, where practitioners commonly generate ensemble paths by sampling probabilistic models or leveraging multiple…
Given a sequence of Borel probability measures on a Hausdorff space which satisfy a large deviation principle, we consider the corresponding sequence of measures formed by conditioning on a set $B$. If the large deviation rate function $I$…
In recent years we have been able to gather large amounts of genomic data at a fast rate, creating situations where the number of variables greatly exceeds the number of observations. In these situations, most models that can handle a…
Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…
We study subordination of free convolutions. We prove that for free random variables $X,Y$ and a Borel function $f$ the conditional expectation $E_\varphi\left[ (z-X-f(X)Yf^*(X))^{-1}| X\right]$, is a resolvent again. This result allows…
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global…
Let $\{X_n;n\ge 1\}$ be a sequence of independent random variables on a probability space $(\Omega, \mathcal{F}, P)$ and $S_n=\sum_{k=1}^n X_k$. It is well-known that the almost sure convergence, the convergence in probability and the…
We consider the problem of constructing distribution-free prediction sets with finite-sample conditional guarantees. Prior work has shown that it is impossible to provide exact conditional coverage universally in finite samples. Thus, most…