相关论文: AMS Without 4-Wise Independence on Product Domains
We consider the singular value statistics of products of independent random matrices. In particular we compute the corresponding averages of products of characteristic polynomials. To this aim we apply the projection formula recently…
We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function of smoothly perturbed random variables, as well as on the de…
A strong direct product theorem states that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then the overall success probability will be exponentially small in…
In Bayesian statistics, many problems can be expressed as the evaluation of the expectation of a quantity of interest with respect to the posterior distribution. Standard Monte Carlo method is often not applicable because the encountered…
This work gives an overview of analytic tools for the design, analysis, and modelling of communication systems which can be described by linear vector channels such as y = Hx+z where the number of components in each vector is large. Tools…
The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components $n$. Mean-field approximations provide an effective reduction in complexity of the…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…
Sketching algorithms have recently proven to be a powerful approach both for designing low-space streaming algorithms as well as fast polynomial time approximation schemes (PTAS). In this work, we develop new techniques to extend the…
The AMAS group at the Paul Scherrer Institute developed an object oriented library for high performance simulation of high intensity ion beam transport with space charge. Such particle-in-cell (PIC) simulations require a method to generate…
We prove anti-concentration bounds for the inner product of two independent random vectors, and use these bounds to prove lower bounds in communication complexity. We show that if $A,B$ are subsets of the cube $\{\pm 1\}^n$ with $|A| \cdot…
We study the problem of allocating indivisible resources under the connectivity constraints of a graph $G$. This model, initially introduced by Bouveret et al. (published in IJCAI, 2017), effectively encompasses a diverse array of scenarios…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the…
In this paper we show how to apply classical probabilistic tools for partial sums $\sum_{j=0}^{n-1}\varphi\circ\tau^j$ generated by a skew product $\tau$, built over a sufficiently well mixing base map and a random expanding dynamical…
We design new approximation algorithms for the Multiway Cut problem, improving the previously known factor of 1.32388 [Buchbinder et al., 2013]. We proceed in three steps. First, we analyze the rounding scheme of Buchbinder et al., 2013 and…
In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…
Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for non-smooth functions with kinks. For example, such kinks can arise in the uncertainty…
In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…