相关论文: High-dimensional cointegration and Kuramoto system…
We consider the problem of estimating the covariance structure of a random vector $Y\in \mathbb R^d$ from a sample $Y_1,\ldots,Y_n$. We are interested in the situation when $d$ is large compared to $n$ but the covariance matrix $\Sigma$ of…
The synchronization pattern of a fully connected competing Kuramoto model with a uniform intrinsic frequency distribution $g(\omega)$ was recently considered. This competing Kuramoto model assigns two coupling constants with opposite signs,…
We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…
UMAP is a non-parametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) Compute a…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Let $X=C+\mathrm{E}$ with a deterministic matrix $C\in\R^{M\times M}$ and $\mathrm{E}$ some centered Gaussian $M\times M$-matrix whose entries are independent with variance $\sigma^2$. In the present work, the accuracy of reduced-rank…
We generalize 2-Wasserstein dependence coefficients to measure dependence between a finite number of random vectors. This generalization includes theoretical properties, and in particular focuses on an interpretation of maximal dependence…
Large spatial datasets are becoming ubiquitous in environmental sciences with the explosion in the amount of data produced by sensors that monitor and measure the Earth system. Consequently, the geostatistical analysis of these data…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…
Modern high-dimensional point process data, especially those from neuroscience experiments, often involve observations from multiple conditions and/or experiments. Networks of interactions corresponding to these conditions are expected to…
We investigate algebraic and topological signatures of networks of coupled oscillators. Translating dynamics into a system of algebraic equations enables us to identify classes of network topologies that exhibit unexpected behaviors. Many…
Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…
Doubly intractable models are encountered in a number of fields, e.g. social networks, ecology and epidemiology. Inference for such models requires the evaluation of a likelihood function, whose normalising factor depends on the model…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
We propose a novel, lightweight, and physically inspired approach to modeling the dynamics of parallel distributed-memory programs. Inspired by the Kuramoto model, we represent MPI processes as coupled oscillators with topology-aware…
Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are…