Related papers: Sampling to estimate arbitrary subset sums
When reporting the results of clinical studies, some researchers may choose the five-number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
Importance sampling is a central idea underlying off-policy prediction in reinforcement learning. It provides a strategy for re-weighting samples from a distribution to obtain unbiased estimates under another distribution. However,…
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at…
We study the problem of estimating the sum of $n$ elements, each with weight $w(i)$, in a structured universe. Our goal is to estimate $W = \sum_{i=1}^n w(i)$ within a $(1 \pm \epsilon)$ factor using a sublinear number of samples, assuming…
We propose a sampling scheme suitable for reducing a data set prior to selecting a hypothesis with minimum empirical risk. The sampling only considers a subset of the ultimate (unknown) hypothesis set, but can nonetheless guarantee that the…
Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and…
Importance sampling is a technique that is commonly used to speed up Monte Carlo simulation of rare events. However, little is known regarding the design of efficient importance sampling algorithms in the context of queueing networks. The…
$k$-subset sampling is ubiquitous in machine learning, enabling regularization and interpretability through sparsity. The challenge lies in rendering $k$-subset sampling amenable to end-to-end learning. This has typically involved relaxing…
Preferential sampling has attracted considerable attention in geostatistics since the pioneering work of Diggle et al. (2010). A variety of likelihood-based approaches have been developed to correct estimation bias by explicitly modelling…
Consider the fundamental problem of drawing a simple random sample of size k without replacement from [n] := {1, . . . , n}. Although a number of classical algorithms exist for this problem, we construct algorithms that are even simpler,…
Consider a collection of weighted subsets of a ground set N. Given a query subset Q of N, how fast can one (1) find the weighted sum over all subsets of Q, and (2) sample a subset of Q proportionally to the weights? We present a tree-based…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and…
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency,…
Temporal networks representing a stream of timestamped edges are seemingly ubiquitous in the real-world. However, the massive size and continuous nature of these networks make them fundamentally challenging to analyze and leverage for…
This paper introduces new techniques for sampling attributed networks to support standard Data Mining tasks. The problem is important for two reasons. First, it is commonplace to perform data mining tasks such as clustering and…
Importance Sampling methods are broadly used to approximate posterior distributions or some of their moments. In its standard approach, samples are drawn from a single proposal distribution and weighted properly. However, since the…
Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to…
We consider the following sample selection problem. We observe in an online fashion a sequence of samples, each endowed by a quality. Our goal is to either select or reject each sample, so as to maximize the aggregate quality of the…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtain robust estimates. The weight, attached to each score contribution, is evaluated by comparing the statistical data depth at the model…