Related papers: Pandora with Inaccurate Priors
Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes,…
Algorithmic rankers have a profound impact on our increasingly data-driven society. From leisurely activities like the movies that we watch, the restaurants that we patronize; to highly consequential decisions, like making educational and…
As machine learning systems move from computer-science laboratories into the open world, their accountability becomes a high priority problem. Accountability requires deep understanding of system behavior and its failures. Current…
In this paper, we give an algorithm to infer the positions of the vertices of an unknown tetrahedron, given a sample of points which are uniformly distributed within the tetrahedron. The accuracy of the algorithm is demonstrated using some…
The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical…
Bin packing is a classic optimization problem with a wide range of applications, from load balancing to supply chain management. In this work, we study the online variant of the problem, in which a sequence of items of various sizes must be…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
We compare the classical Kolmogorov and quantum probability models. We show that the gap between these model is not so huge as it was commonly believed. The main structures of quantum theory (interference of probabilities, Born's rule,…
Reliable uncertainty estimation is crucial for robust object detection in autonomous driving. However, previous works on probabilistic object detection either learn predictive probability for bounding box regression in an un-supervised…
Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…
The Gittins index is a tool that optimally solves a variety of decision-making problems involving uncertainty, including multi-armed bandit problems, minimizing mean latency in queues, and search problems like the Pandora's box model.…
The Luders postulate is reviewed and implications for quantum algorithms are discussed. A search algorithm for an unstructured database is described.
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
This paper studies some basic problems in a multiple-object auction model using methodologies from theoretical computer science. We are especially concerned with situations where an adversary bidder knows the bidding algorithms of all the…
Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modelled as a distribution of unitary processes arising from slowly…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring…
"All models are wrong, but some are useful", wrote George E. P. Box (1979). Machine learning has focused on the usefulness of probability models for prediction in social systems, but is only now coming to grips with the ways in which these…
The ability to ensure that a classifier gives reliable confidence scores is essential to ensure informed decision-making. To this end, recent work has focused on miscalibration, i.e., the over or under confidence of model scores. Yet…
A pair of lower and upper cumulative distribution functions, also called probability box or p-box, is among the most popular models used in imprecise probability theory. They arise naturally in expert elicitation, for instance in cases…