Related papers: Exact local Whittle estimation of fractional integ…
When a population exhibits heterogeneity, we often model it via a finite mixture: decompose it into several different but homogeneous subpopulations. Contemporary practice favors learning the mixtures by maximizing the likelihood for…
Walley's Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the…
In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
When training automated systems, it has been shown to be beneficial to adapt the representation of data by learning a problem-specific metric. This metric is global. We extend this idea and, for the widely used family of k nearest neighbors…
We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…
To achieve a maximal locality in a trivial field theory, we maximize the ultraviolet cutoff of the theory by fine tuning the infrared values of the parameters. This optimization procedure is applied to the scalar theory in $D+1$ dimensions…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
Local fixpoint iteration describes a technique that restricts fixpoint iteration in function spaces to needed arguments only. It has been studied well for first-order functions in abstract interpretation and also in model checking. Here we…
Conformal methods create prediction bands that control average coverage under no assumptions besides i.i.d. data. Besides average coverage, one might also desire to control conditional coverage, that is, coverage for every new testing…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
According to the concept of typicality, an ensemble average can be accurately approximated by an expectation value with respect to a single pure state drawn at random from a high-dimensional Hilbert space. This random-vector approximation,…
We study the problem of {\em list-decodable mean estimation} for bounded covariance distributions. Specifically, we are given a set $T$ of points in $\mathbb{R}^d$ with the promise that an unknown $\alpha$-fraction of points in $T$, where…
In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the…
Walley's Imprecise Dirichlet Model (IDM) for categorical i.i.d. data extends the classical Dirichlet model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…