Related papers: Normal approximation for functions of hidden Marko…
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…
A stochastic conjugate gradient method for approximation of a function is proposed. The proposed method avoids computing and storing the covariance matrix in the normal equations for the least squares solution. In addition, the method…
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…
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…
We develop a general approach to Stein's method for approximating a random process in the path space $D([0,T]\to R^d)$ by a real continuous Gaussian process. We then use the approach in the context of processes that have a representation as…
MCMC methods (Monte Carlo Markov Chain) are a class of methods used to perform simulations per a probability distribution $P$. These methods are often used when we have difficulties to directly sample per a given probability distribution…
We consider the problem of minimizing the average of a large number of smooth but possibly non-convex functions. In the context of most machine learning applications, each loss function is non-negative and thus can be expressed as the…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
To preserve client privacy in the data mining process, a variety of techniques based on random perturbation of data records have been proposed recently. In this paper, we present a generalized matrix-theoretic model of random perturbation,…
The dynamics of non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…
Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
Stein's method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation the functional equation is a first order differential equation. Malliavin calculus is an…
There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…
A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations…
In a recent paper by the authors, a new approach--called the "embedding method"--was introduced, which allows to make use of exchangeable pairs for normal and multivariate normal approximation with Stein's method in cases where the…