Related papers: Group-$k$ Consistent Measurement Set Maximization …
The maximum clique problem, a well-known graph-based combinatorial optimization problem, has been addressed through various algorithmic approaches, though systematic analyses of the problem instances remain sparse. This study employs the…
Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we…
In the context of cluster analysis and graph partitioning, many external evaluation measures have been proposed in the literature to compare two partitions of the same set. This makes the task of selecting the most appropriate measure for a…
In this work we solve the problem of robustly learning a high-dimensional Gaussian mixture model with $k$ components from $\epsilon$-corrupted samples up to accuracy $\widetilde{O}(\epsilon)$ in total variation distance for any constant $k$…
The problem of synchronization over a group $\mathcal{G}$ aims to estimate a collection of group elements $G^*_1, \dots, G^*_n \in \mathcal{G}$ based on noisy observations of a subset of all pairwise ratios of the form $G^*_i {G^*_j}^{-1}$.…
We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Existing approaches remain largely constrained by traditional distance metrics, limiting their effectiveness in handling random data. In this work, we introduce the first k-means variant in the literature that operates within a…
Orthogonal group synchronization aims to recover orthogonal group elements from their noisy pairwise measurements. It has found numerous applications including computer vision, imaging science, and community detection. Due to the orthogonal…
Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means…
Existence of symmetric objects, whose observation at different viewpoints can be identical, can deteriorate the performance of simultaneous localization and mapping(SLAM). This work proposes a system for robustly optimizing the pose of…
We give the first outlier-robust efficient algorithm for clustering a mixture of $k$ statistically separated d-dimensional Gaussians (k-GMMs). Concretely, our algorithm takes input an $\epsilon$-corrupted sample from a $k$-GMM and whp in…
We experimentally demonstrate a two-particle collective measurement proposed as the optimal solution to a quantum state estimation game. Our results suggest that, in practice, the collective measurement strategy is at least as good as the…
SLAM technology plays a crucial role in indoor mapping and localization. A common challenge in indoor environments is the "double-sided mapping issue", where closely positioned walls, doors, and other surfaces are mistakenly identified as a…
Data required to calibrate uncertain GCM parameterizations are often only available in limited regions or time periods, for example, observational data from field campaigns, or data generated in local high-resolution simulations. This…
Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…
This paper presents a novel approach to visual simultaneous localization and mapping (SLAM) using multiple RGB-D cameras. The proposed method, Multicam-SLAM, significantly enhances the robustness and accuracy of SLAM systems by capturing…
The Gamma Variance Model (GVM) is a statistical model that incorporates uncertainties in the assignment of systematic errors (informally called errors-on-errors). The model is of particular use in analyses that combine the results of…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
Mobile robots require basic information to navigate through an environment: they need to know where they are (localization) and they need to know where they are going. For the latter, robots need a map of the environment. Using sensors of a…