Related papers: Bias Reduction for Sum Estimation
As the use of machine learning in high impact domains becomes widespread, the importance of evaluating safety has increased. An important aspect of this is evaluating how robust a model is to changes in setting or population, which…
Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods…
We consider two multi-armed bandit problems with $n$ arms: (i) given an $\epsilon > 0$, identify an arm with mean that is within $\epsilon$ of the largest mean and (ii) given a threshold $\mu_0$ and integer $k$, identify $k$ arms with means…
Let $P=(x_1,\ldots,x_n)$ be a population consisting of $n\ge 2$ real numbers whose sum is zero, and let $k <n$ be a positive integer. We sample $k$ elements from $P$ without replacement and denote by $X_P$ the sum of the elements in our…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
Let $Y=X_1+\cdots+X_N$ be a sum of a random number of exchangeable random variables, where the random variable $N$ is independent of the $X_j$, and the $X_j$ are from the generalized multinomial model introduced by Tallis (1962). This…
Estimating the support size of a distribution is a well-studied problem in statistics. Motivated by the fact that this problem is highly non-robust (as small perturbations in the distributions can drastically affect the support size) and…
Let X be a real or complex Hilbert space of finite but large dimension d, let S(X) denote the unit sphere of X, and let u denote the normalized uniform measure on S(X). For a finite subset B of S(X), we may test whether it is approximately…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
Boson sampling is one of the main quantum computation models to demonstrate the quantum computational advantage. However, this aim may be hard to realize considering two main kinds of noises, which are photon distinguishability and photon…
Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely-quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
Statistical query (SQ) algorithms are algorithms that have access to an {\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $\phi:X \rightarrow [-1,1]$, the oracle returns an estimate…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…