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The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…

We address discrete-time consensus on the Euclidean unit sphere. For this purpose we consider a distributed algorithm comprising the iterative projection of a conical combination of neighboring states. Neighborhoods are represented by a…

We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time.…

Counting small subgraphs, referred to as motifs, in large graphs is a fundamental task in graph analysis, extensively studied across various contexts and computational models. In the sublinear-time regime, the relaxed problem of approximate…

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone…

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being…

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of…

Causal modelling frameworks link observable correlations to causal explanations, which is a crucial aspect of science. These models represent causal relationships through directed graphs, with vertices and edges denoting systems and…

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…

Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If $f(\boldsymbol{x})$ is the loss function, and $C$ is the constraint set in a constrained minimization problem, then…

Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…

We introduce and analyze a post-processing for a family of variational space-time approximations to wave problems. The discretization in space and time is based on continuous finite element methods. The post-processing lifts the fully…

Simulation models often lack tractable likelihood functions, making likelihood-free inference methods indispensable. Approximate Bayesian computation generates likelihood-free posterior samples by comparing simulated and observed data…

Quantum approximate optimization algorithm (QAOA) aims to solve discrete optimization problems by sampling bitstrings using a parameterized quantum circuit. The circuit parameters (angles) are optimized in the way that minimizes the cost…

Quasi-probability decompositions (QPDs) have proven essential in many quantum algorithms and protocols -- one replaces a ``difficult'' quantum circuit with an ensemble of ``easier'' circuit variants whose weighted outcomes reproduce any…

This paper addresses the challenge of out-of-distribution (OOD) generalization in graph machine learning, a field rapidly advancing yet grappling with the discrepancy between source and target data distributions. Traditional graph learning…

This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient…

We revisit Approximate Graph Propagation (AGP), a unified framework which captures various graph propagation tasks, such as PageRank, feature propagation in Graph Neural Networks (GNNs), and graph-based Retrieval-Augmented Generation (RAG).…

A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, followed by a mean-based clustering to obtain the symbolic…