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Motivated by problems from neuroimaging in which existing approaches make use of "mass univariate" analysis which neglects spatial structure entirely, but the full joint modelling of all quantities of interest is computationally infeasible,…
Gaussian process modeling is a standard tool for building emulators for computer experiments, which are usually used to study deterministic functions, for example, a solution to a given system of partial differential equations. This work…
Motivated by small bandwidth asymptotics for kernel-based semiparametric estimators in econometrics, this paper establishes Gaussian approximation results for high-dimensional fixed-order $U$-statistics whose kernels depend on the sample…
Although exchangeable processes from Bayesian nonparametrics have been used as a generating mechanism for random partition models, we deviate from this paradigm to explicitly incorporate clustering information in the formulation of our…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
We study sequential probability assignment in the Gaussian setting, where the goal is to predict, or equivalently compress, a sequence of real-valued observations almost as well as the best Gaussian distribution with mean constrained to a…
Linear fractional Galton-Watson branching processes in i.i.d.~random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals.…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
Gaussian mixture models are widely used to model data generated from multiple latent sources. Despite its popularity, most theoretical research assumes that the labels are either independent and identically distributed, or follows a Markov…
It is classical, following Furstenberg's theorem on positive Lyapunov exponent for products of random SL$(2, \mathbb R)$ matrices, that the one dimensional random Schr\"odinger operator has Anderson localization at arbitrary disorder. This…
We study analytically the effect of a weak random chemical potential of zero average in an Einstein-Maxwell background. For uncorrelated disorder this perturbation is relevant however we show that it can become marginal or even irrelevant…
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions…
Motivated by mapping from a stochastic system with spatially random rates, we consider disordered non-conserving free-fermion systems using a scaling procedure for the equations of motion. This approach demonstrates disorder-induced…
In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling.…
We numerically study the effect of adding quenched disorder in the form of randomly placed pinning sites on jamming transitions in systems that jam at a well defined point J in the clean limit. Quenched disorder decreases the jamming…
A bipartite spin-1/2 system having the probabilities $\frac{1+3x}{4}$ of being in the Einstein-Podolsky-Rosen entangled state $|\Psi^-$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\downarrow>_B$$-|$$\downarrow>_A|$$\uparrow>_B)$ and…
Cognitive diagnosis models have been popularly used in fields such as education, psychology, and social sciences. While parametric likelihood estimation is a prevailing method for fitting cognitive diagnosis models, nonparametric…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from…
Dynamical scaling and ageing in disordered systems far from equilibrium is reviewed. Particular attention is devoted to the question to what extent a recently introduced generalization of dynamical scaling to local scale-invariance can…