Related papers: Probabilistic Error Analysis for Inner Products
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
Noise perturbation is one of the most fundamental approaches for achieving $(\epsilon,\delta)$-differential privacy (DP) guarantees when releasing the result of a query or function $f(\cdot)\in\mathbb{R}^M$ evaluated on a sensitive dataset…
It is often desirable to summarise a probability measure on a space $X$ in terms of a mode, or MAP estimator, i.e.\ a point of maximum probability. Such points can be rigorously defined using masses of metric balls in the small-radius…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
We present a coupled decreasing sequence of random walks on $ \mathbb Z $ that dominates the edge process of oriented-bond percolation in two dimensions. Using the concept of "random walk in a strip ", we construct an algorithm that…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
We develop a novel stochastic valuation and premium calculation principle based on probability measure distortions that are induced by quantile processes in continuous time. Necessary and sufficient conditions are derived under which the…
Suppose that A is a set of n real numbers, each at least 1 apart. Define the ``perturbed sum and product sets'' S and P to be the sums a + b + f(a,b) and products (a+g(a,b))(b+h(a,b)), where f, g, and h satisfy certain upper bounds in terms…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
We derive two related novel bounds on single-variable marginal probability distributions in factor graphs with discrete variables. The first method propagates bounds over a subtree of the factor graph rooted in the variable, and the second…
The partial monitoring (PM) framework provides a theoretical formulation of sequential learning problems with incomplete feedback. On each round, a learning agent plays an action while the environment simultaneously chooses an outcome. The…
In this paper, we consider $m$ independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of the $m$ rectangular matrices is an $n$ by…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
Trotter product formulas are a natural and powerful approach to perform quantum simulation. However, the error analysis of product formulas is challenging, and their cost is often overestimated. It is established that Trotter error can be…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…