Related papers: Analytical confidence intervals for the number of …
Complex data objects arise in many areas of modern science including evolutionary biology, nueroscience, dynamics of gene expression and medical imaging. Object oriented data analysis (OODA) is the statistical analysis of datasets of…
In recent years, multi-objective optimization (MOO) emerges as a foundational problem underpinning many multi-agent multi-task learning applications. However, existing algorithms in MOO literature remain limited to centralized learning…
We study fine-grained error bounds for differentially private algorithms for counting under continual observation. Our main insight is that the matrix mechanism when using lower-triangular matrices can be used in the continual observation…
We study the general problem of computing frequency-based functions, i.e., the sum of any given function of data stream frequencies. Special cases include fundamental data stream problems such as computing the number of distinct elements…
A set of intervals is independent when the intervals are pairwise disjoint. In the interval selection problem we are given a set $\mathbb{I}$ of intervals and we want to find an independent subset of intervals of largest cardinality. Let…
Factor analysis (FA) and principal component analysis (PCA) are popular statistical methods for summarizing and explaining the variability in multivariate datasets. By default, FA and PCA assume the number of components or factors to be…
Since its inception in 1982, Oja's algorithm has become an established method for streaming principle component analysis (PCA). We study the problem of streaming PCA, where the data-points are sampled from an irreducible, aperiodic, and…
For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log…
Given a data stream $\mathcal{A} = \langle a_1, a_2, \ldots, a_m \rangle$ of $m$ elements where each $a_i \in [n]$, the Distinct Elements problem is to estimate the number of distinct elements in $\mathcal{A}$.Distinct Elements has been a…
Multi-stream sequential change detection involves simultaneously monitoring many streams of data and trying to detect when their distributions change, if at all. Here, we theoretically study multiple testing issues that arise from detecting…
Floating-point arithmetic (FPA) is a mechanical representation of real arithmetic (RA), where each operation is replaced with a rounded counterpart. Various numerical properties can be verified by using SMT solvers that support the logic of…
Meshfree simulation methods are emerging as compelling alternatives to conventional mesh-based approaches, particularly in the fields of Computational Fluid Dynamics (CFD) and continuum mechanics. In this publication, we provide a…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
Privately counting distinct elements in a stream is a fundamental data analysis problem with many applications in machine learning. In the turnstile model, Jain et al. [NeurIPS2023] initiated the study of this problem parameterized by the…
We study the problem of distributed distinct element estimation, where $\alpha$ servers each receive a subset of a universe $[n]$ and aim to compute a $(1+\varepsilon)$-approximation to the number of distinct elements using minimal…
Membership inference attacks (MIA) can reveal whether a particular data point was part of the training dataset, potentially exposing sensitive information about individuals. This article provides theoretical guarantees by exploring the…
As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to…
Although the scientific digital library is growing at a rapid pace, scholars/students often find reading Science, Technology, Engineering, and Mathematics (STEM) literature daunting, especially for the math-content/formula. In this paper,…
Unsatisfying accuracy of learning methods is mostly caused by omitting the influence of important parameters such as membership assignments, type of data objects, and distance or similarity functions. The proposed method, called Bounded…
The streaming max-min diversification problem concerns the selection of a limited and diverse sample of items out of a data stream of known finite length. The objective to be maximized is the minimum distance among any pair of selected…