Related papers: A Tight Lower Bound for Comparison-Based Quantile …
Estimating frequency moments of data streams is a very well studied problem and tight bounds are known on the amount of space that is necessary and sufficient when the stream is adversarially ordered. Recently, motivated by various…
Let $X$ be a set of items of size $n$ that contains some defective items, denoted by $I$, where $I \subseteq X$. In group testing, a {\it test} refers to a subset of items $Q \subset X$. The outcome of a test is $1$ if $Q$ contains at least…
We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to…
This paper studies the \emph{$\varepsilon$-approximate range emptiness} problem, where the task is to represent a set $S$ of $n$ points from $\{0,\ldots,U-1\}$ and answer emptiness queries of the form "$[a ; b]\cap S \neq \emptyset$ ?" with…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
It is well known that it is impossible to construct useful confidence intervals (CIs) about the mean or median of a response $Y$ conditional on features $X = x$ without making strong assumptions about the joint distribution of $X$ and $Y$.…
The recent development of general quantum resource theories has given a sound basis for the quantification of useful quantum effects. Nevertheless, the evaluation of a resource measure can be highly non-trivial, involving an optimisation…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
We present a system based on sequential decision making for the online summarization of massive document streams, such as those found on the web. Given an event of interest (e.g. "Boston marathon bombing"), our system is able to filter the…
We show an improved lower bound for the Fp estimation problem in a data stream setting for p>2. A data stream is a sequence of items from the domain [n] with possible repetitions. The frequency vector x is an n-dimensional non-negative…
Quantum measurements are not deterministic. For this reason quantum measurements are repeated for a number of shots on identically prepared systems. The uncertainty in each measurement depends on the number of shots and the expected outcome…
We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…
We study the use of sampling for efficiently mining the top-K frequent itemsets of cardinality at most w. To this purpose, we define an approximation to the top-K frequent itemsets to be a family of itemsets which includes (resp., excludes)…
In the minimal scenario of quantum correlations, two parties can choose from two observables with two possible outcomes each. Probabilities are specified by four marginals and four correlations. The resulting four-dimensional convex body of…
Why do larger language models generalize better? To investigate this question, we develop generalization bounds on the pretraining objective of large language models (LLMs) in the compute-optimal regime, as described by the Chinchilla…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
We address the problem of whether parties who cannot communicate but share nonsignaling quantum correlations between the outcomes of sharp measurements can distinguish, just from the value of a correlation observable, whether their outcomes…
One of the most useful and correct methodological approaches in bibliometrics is ranking. In the context of highly skewed bibliometric distributions and severe distortions caused by outliers, it is often the preferable way of analysis.…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
Quantile regression presents a complete picture of the effects on the location, scale, and shape of the dependent variable at all points, not just the mean. We focus on two challenges for citation count analysis by quantile regression:…