Related papers: Bucket Renormalization for Approximate Inference
Simulation-based inference has been popular for amortized Bayesian computation. It is typical to have more than one posterior approximation, from different inference algorithms, different architectures, or simply the randomness of…
Approximate vanishing ideal is a concept from computer algebra that studies the algebraic varieties behind perturbed data points. To capture the nonlinear structure of perturbed points, the introduction of approximation to exact vanishing…
We propose a safe approximation to joint chance-constrained programming where the constraint functions are additively dependent on a normally-distributed random vector. The approximation is analytical, meaning that it requires neither…
In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs)…
Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…
We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods…
In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in the aggregate models a desired property of the ideal solution…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
We demonstrate how path integrals often used in problems of theoretical physics can be adapted to provide a machinery for performing Bayesian inference in function spaces. Such inference comes about naturally in the study of inverse…
This paper provides a unifying view of a wide range of problems of interest in machine learning by framing them as the minimization of functionals defined on the space of probability measures. In particular, we show that generative…
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…
Exact computation of the partition function is known to be intractable, necessitating approximate inference techniques. Existing methods for approximate inference are slow to converge for many benchmarks. The control of accuracy-complexity…
This paper presents a sequential randomized lowrank matrix factorization approach for incrementally predicting values of an unknown function at test points using the Gaussian Processes framework. It is well-known that in the Gaussian…
Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
Bayesian neural networks (BNNs) are a principled approach to modeling predictive uncertainties in deep learning, which are important in safety-critical applications. Since exact Bayesian inference over the weights in a BNN is intractable,…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…