Related papers: The DLR Hierarchy of Approximate Inference

This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…

In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…

Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of…

The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Let $\F$ be a family of $r$ integral forms of degree $k\geq 2$ and $\LL=(l_1,\ldots,l_m)$ be a family of pairwise linearly independent linear forms in $n$ variables $\x=(x_1,...,x_n)$. We study the number of solutions $\x\in[1,N]^n$ to the…

In this paper, we prove that the Max-Morse Matching Problem is approximable, thus resolving an open problem posed by Joswig and Pfetsch. We describe two different approximation algorithms for the Max-Morse Matching Problem. For…

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…

The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…

Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…

We study the problem of best approximations of a vector $\alpha\in{\mathbb R}^n$ by rational vectors of a lattice $\Lambda\subset {\mathbb R}^n$ whose common denominator is bounded. To this end we introduce successive minima for a periodic…

We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…

This paper presents a general framework for exploiting the representational capacity of neural networks to approximate complex, nonlinear reward functions in the context of solving the inverse reinforcement learning (IRL) problem. We show…

This paper provides a rigorous derivation for what is known in the literature as the Lie bracket approximation of control-affine systems in a more general and sequential framework for higher-orders. In fact, by using chronological calculus,…

Distributionally robust reinforcement learning (DRRL) focuses on designing policies that achieve good performance under model uncertainties. The goal is to maximize the worst-case long-term discounted reward, where the data for RL comes…

We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Several questions of approximation theory are discussed: 1) can one approximate stably in $L^\infty$ norm $f^\prime$ given approximation $f_\delta, \parallel f_\delta - f \parallel_{L^\infty} < \delta$, of an unknown smooth function $f(x)$,…

We study the problem of approximate near neighbor (ANN) search and show the following results: - An improved framework for solving the ANN problem using locality-sensitive hashing, reducing the number of evaluations of locality-sensitive…