Related papers: Estimating odds and log odds with guaranteed accur…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
Recent research has made significant progress on the problem of bounding log partition functions for exponential family graphical models. Such bounds have associated dual parameters that are often used as heuristic estimates of the marginal…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
We consider search by mobile agents for a hidden, idle target, placed on the infinite line. Feasible solutions are agent trajectories in which all agents reach the target sooner or later. A special feature of our problem is that the agents…
Let $\eta_i, i=1,..., n$ be iid Bernoulli random variables. Given a multiset $\bv$ of $n$ numbers $v_1, ..., v_n$, the \emph{concentration probability} $\P_1(\bv)$ of $\bv$ is defined as $\P_1(\bv) := \sup_{x} \P(v_1 \eta_1+ ... v_n…
In optimization problems, the quality of a candidate solution can be characterized by the optimality gap. For most stochastic optimization problems, this gap must be statistically estimated. We show that for risk-averse problems, standard…
Estimating a large alphabet probability distribution from a limited number of samples is a fundamental problem in machine learning and statistics. A variety of estimation schemes have been proposed over the years, mostly inspired by the…
We address the problem of optimizing a Brownian motion. We consider a (random) realization $W$ of a Brownian motion with input space in $[0,1]$. Given $W$, our goal is to return an $\epsilon$-approximation of its maximum using the smallest…
A common way to discretize a probability measure is to use an empirical measure as a discrete approximation. But how far from being optimal is this approximation in the p-Wasserstein distance? In this paper, we study this question in two…
We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…
We study the complexity of optimizing highly smooth convex functions. For a positive integer $p$, we want to find an $\epsilon$-approximate minimum of a convex function $f$, given oracle access to the function and its first $p$ derivatives,…
Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $ X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are…
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the…
In robust statistics, the breakdown point of an estimator is the percentage of outliers with which an estimator still generates reliable estimation. The upper bound of breakdown point is 50%, which means it is not possible to generate…
Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…
We find a two term asymptotic expansion for the optimal expected value of a sequentially selected monotone subsequence from a random permutation of length n. A striking feature of this expansion is that tells us that the expected value of…
We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative-binomial experiment having the same p.
We propose a randomized a posteriori error estimator for reduced order approximations of parametrized (partial) differential equations. The error estimator has several important properties: the effectivity is close to unity with prescribed…
We design and analyze a posteriori error estimators for the Stokes system with singular sources in suitable $\mathbf{W}^{1,p}\times \mathrm{L}^p$ spaces. We consider classical low-order inf-sup stable and stabilized finite element…
Reliability is probability of success in a success-failure experiment. Confidence in reliability estimate improves with increasing number of samples. Assurance sets confidence level same as reliability to create one number for easier…