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The set of local modes and density ridge lines are important summary characteristics of the data-generating distribution. In this work, we focus on estimating local modes and density ridges from point cloud data in a product space combining…
The interaction between turbulent axisymmetric wakes plays an important role in many industrial applications, notably in the modelling of wind farms. While the non-equilibrium high Reynolds number scalings present in the wake of…
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…
We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional…
Wavelets have been shown to be effective bases for many classes of natural signals and images. Standard wavelet bases have the entire vector space $\mathbb R^n$ as their natural domain. It is fairly straightforward to adapt these to…
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on…
In this paper, we characterize the noise of stochastic gradients and analyze the noise-induced dynamics during training deep neural networks by gradient-based optimizers. Specifically, we firstly show that the stochastic gradient noise…
Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…
A stochastic subgrid-scale parameterization based on the Ruelle's response theory and proposed in Wouters and Lucarini [2012] is tested in the context of a low-order coupled ocean-atmosphere model for which a part of the atmospheric modes…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
We develop a stochastic foundation for bandwidth estimation of networks with random service, where bandwidth availability is expressed in terms of bounding functions with a defined violation probability. Exploiting properties of a…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
Typical properties of computing circuits composed of noisy logical gates are studied using the statistical physics methodology. A growth model that gives rise to typical random Boolean functions is mapped onto a layered Ising spin system,…
In this paper, we explore the asymptotically optimal tuning parameter choice in ridge regression for estimating nuisance functions of a statistical functional that has recently gained prominence in conditional independence testing and…
Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this…
Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph…