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Reconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to…
In statistical machine learning, kernel methods allow to consider infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done by solving an optimization problem…
We introduce data structures for solving robust regression through stochastic gradient descent (SGD) by sampling gradients with probability proportional to their norm, i.e., importance sampling. Although SGD is widely used for large scale…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
Sampling from the conditional (or posterior) probability distribution of the latent states of a Hidden Markov Model, given the realization of the observed process, is a non-trivial problem in the context of Markov Chain Monte Carlo. To do…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based…
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…
Since its discovery over the last decade, Compressed Sensing (CS) has been successfully applied to Magnetic Reso- nance Imaging (MRI). It has been shown to be a powerful way to reduce scanning time without sacrificing image quality. MR…
This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…
Importance sampling with data-driven proposal distributions is widely used in practice. A common workflow first generates an auxiliary sample of size $N$ from an approximation of the target distribution, constructs a density estimate $\hat…
For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system…
In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in…
More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains one of the most effective methods for marginal likelihood estimation. It relies on a sequence of distributions interpolating between a tractable…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
We develop a new method to sample from posterior distributions in hierarchical models without using Markov chain Monte Carlo. This method, which is a variant of importance sampling ideas, is generally applicable to high-dimensional models…
The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…
We apply the stochastic approximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil (1994). We study the properties of these estimators and compare…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…