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Aaronson and Drucker (2011) asked whether there exists a quantum finite automaton that can distinguish fair coin tosses from biased ones by spending significantly more time in accepting states, on average, given an infinite sequence of…
Conformal prediction is a valuable tool for quantifying predictive uncertainty of machine learning models. However, its applicability relies on the assumption of data exchangeability, a condition which is often not met in real-world…
A result of existence of a nonnegative and a nontrivial solution is proved via critical point theorems for non smooth functionals. The equation considered presents a convex part and a nonlinearity which changes sign.
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Interactive constraint systems often suffer from infeasibility (no solution) due to conflicting user constraints. A common approach to recover infeasibility is to eliminate the constraints that cause the conflicts in the system. This…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
We generalize the problem of coin flipping to more than two outcomes and parties. We term this problem dice rolling, and study both its weak and strong variants. We prove by construction that in quantum settings (i) weak N-sided dice…
We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
We study in this paper a generalized coupon collector problem, which consists in analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We…
We are given $n$ balls and an unknown coloring of them with two colors. Our goal is to find a ball that belongs to the larger color class, or show that the color classes have the same size. We can ask sets of $k$ balls as queries, and the…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
We present three very simple variants of the classic Heads or Tails game using chips, each of which contributes to our understanding of the Bitcoin protocol. The first variant addresses the issue of temporary Bitcoin forks, which occur when…
Many real life problems can be reduced to the solution of a complex exponentials approximation problem which is usually ill posed. Recently a new transform for solving this problem, formulated as a specific moments problem in the plane, has…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
Many problems can be solved in two ways: either by adapting an existing solution, or by exchanging it for a new one. To investigate under what conditions people consider new solutions, we traced their information acquisition processes in a…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…