Related papers: Average Bias and Polynomial Sources

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

The existing upper and lower bounds between entropy and error are mostly derived through an inequality means without linking to joint distributions. In fact, from either theoretical or application viewpoint, there exists a need to achieve a…

This paper presents a novel theoretical study of the general problem of multiple source adaptation using the notion of Renyi divergence. Our results build on our previous work [12], but significantly broaden the scope of that work in…

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…

The source count dipole from wide-area radio continuum surveys allows us to test the cosmological standard model. Many radio sources have multiple components, which can cause an overdispersion of the source counts distribution. We account…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…

In this paper, we show that the halfspace depth random variable for samples from a univariate distribution with a notion of center is distributed as a uniform distribution on the interval [0,1/2]. The simplicial depth random variable has a…

We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized…

We show how generalized Gibbs-Shannon entropies can provide new insights on the statistical properties of texts. The universal distribution of word frequencies (Zipf's law) implies that the generalized entropies, computed at the word level,…

We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…

Rating aggregation plays a crucial role in various fields, such as product recommendations, hotel rankings, and teaching evaluations. However, traditional averaging methods can be affected by participation bias, where some raters do not…

Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…

Diffusion on a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We…

We investigate the problem of semi-parametric maximum likelihood under constraints on summary statistics. Such a procedure results in a discrete probability distribution that maximises the likelihood among all such distributions under the…

For a particular experimental design, there is interest in finding which polynomial models can be identified in the usual regression set up. The algebraic methods based on Groebner bases provide a systematic way of doing this. The algebraic…

We investigate the mean number of real zeros over an interval $[a,b]$ of a random trigonometric polynomial of the form $\sum_{k=1}^n a_k \cos(kt)+b_k \sin(kt)$ where the coefficients are i.i.d. random variables. Under mild assumptions on…

We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…

Gathering the most information by picking the least amount of data is a common task in experimental design or when exploring an unknown environment in reinforcement learning and robotics. A widely used measure for quantifying the…