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With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over…

In the decremental single-source shortest paths problem, the goal is to maintain distances from a fixed source $s$ to every vertex $v$ in an $m$-edge graph undergoing edge deletions. In this paper, we conclude a long line of research on…

In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

Let $g: \{-1,1\}^k \to \{-1,1\}$ be any Boolean function and $q_1,\dots,q_k$ be any degree-2 polynomials over $\{-1,1\}^n.$ We give a \emph{deterministic} algorithm which, given as input explicit descriptions of $g,q_1,\dots,q_k$ and an…

In this paper, we study differentially private (DP) algorithms for computing the geometric median (GM) of a dataset: Given $n$ points, $x_1,\dots,x_n$ in $\mathbb{R}^d$, the goal is to find a point $\theta$ that minimizes the sum of the…

Virtual representations of physical critical infrastructures, such as water or energy plants, are used for simulations and digital twins to ensure resilience and continuity of their services. These models usually require 3D point clouds…

We compute approximate solutions to inverse problems for determining parameters in differential equation models with stochastic data on output quantities. The formulation of the problem and modeling framework define a solution as a…

We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…

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…

We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the…

Bipartite networks manifest as a stream of edges that represent transactions, e.g., purchases by retail customers. Many machine learning applications employ neighborhood-based measures to characterize the similarity among the nodes, such as…

Airborne magnetic data are commonly used to produce preliminary geological maps. Machine learning has the potential to partly fulfill this task rapidly and objectively, as geological mapping is comparable to a semantic segmentation problem.…

This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to…

We consider the independent set problem in the semi-streaming model. For any input graph $G=(V, E)$ with $n$ vertices, an independent set is a set of vertices with no edges between any two elements. In the semi-streaming model, $G$ is…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

In the past decades, the growing amount of network data has lead to many novel statistical models. In this paper we consider so called geometric networks. Typical examples are road networks or other infrastructure networks. But also the…

We give efficient deterministic one-pass streaming algorithms for finding an ellipsoidal approximation of a symmetric convex polytope. The algorithms are near-optimal in that their approximation factors differ from that of the optimal…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

Big data problems frequently require processing datasets in a streaming fashion, either because all data are available at once but collectively are larger than available memory or because the data intrinsically arrive one data point at a…