Related papers: Distribution Testing Meets Sum Estimation
The Subset Sum problem is a classical NP-complete problem with a long-standing $O^*(2^{n/2})$ deterministic bound due to Horowitz and Sahni. We present results at two distinct levels of generality. First (instance-sensitive bound), we…
This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and…
We consider the problem of estimating the support size of a discrete distribution whose minimum non-zero mass is at least $ \frac{1}{k}$. Under the independent sampling model, we show that the sample complexity, i.e., the minimal sample…
We consider predictions of the random number and the magnitude of each iid component in a random sum based on its distributional structure, where only a total value of the sum is available and where iid random components are non-negative.…
The Ewens sampling formula is a distribution related to the random partition of a positive integer. In this study, we investigate the issue of non-existence solutions in parameter estimation under the distribution. As a result, the first…
We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference, especially in…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
In observational studies, accurately characterizing variance is critical for sample size determination, yet unaccounted-for variability from propensity score estimation and the resulting weights limit the accuracy of standard variance…
We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in $\R^d$. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension…
We study the asymptotic behavior of random variables of the form \begin{equation*} E_{\alpha}^i\left(x_1,\ldots,x_n\right)=\sum_{\left(b,d\right)\in \mathit{PH}_i\left(x_1,\ldots,x_n\right)} \left(d-b\right)^{\alpha} \end{equation*} where…
Distributed signal-processing algorithms in (wireless) sensor networks often aim to decentralize processing tasks to reduce communication cost and computational complexity or avoid reliance on a single device (i.e., fusion center) for…
This paper studies the asymptotic properties of weighted sums of the form $Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or singular…
The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…
Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectations and variances. We consider the sum $W=\sum_{i\in J}X_i$ and use Stein's method to establish general upper error…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
Given a non-negative random variable $W$ and $\theta>0$, let the generalized Dickman transformation map the distribution of $W$ to that of $$ W^*=_d U^{1/\theta}(W+1), $$ where $U \sim {\cal U}[0,1]$, a uniformly distributed variable on the…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…