Related papers: A Note on Nonlocal Prior Method
Prior distributions for high-dimensional linear regression require specifying a joint distribution for the unobserved regression coefficients, which is inherently difficult. We instead propose a new class of shrinkage priors for linear…
This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…
Zero-shot text classification typically relies on prompt engineering, but the inherent prompt brittleness of large language models undermines its reliability. Minor changes in prompt can cause significant discrepancies in model performance.…
Non-local self similarity (NSS) is a powerful prior of natural images for image denoising. Most of existing denoising methods employ similar patches, which is a patch-level NSS prior. In this paper, we take one step forward by introducing a…
The construction of objective priors is, at best, challenging for multidimensional parameter spaces. A common practice is to assume independence and set up the joint prior as the product of marginal distributions obtained via "standard"…
Nonlocal models have recently had a major impact in nonlinear continuum mechanics and are used to describe physical systems/processes which cannot be accurately described by classical, calculus based "local" approaches. In part, this is due…
Deep Bayesian neural networks (BNNs) are a powerful tool, though computationally demanding, to perform parameter estimation while jointly estimating uncertainty around predictions. BNNs are typically implemented using arbitrary…
In this paper, we propose a novel approach for outlier detection, called local projections, which is based on concepts of Local Outlier Factor (LOF) (Breunig et al., 2000) and RobPCA (Hubert et al., 2005). By using aspects of both methods,…
The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This…
We present a new methodology for handling AI errors by introducing weakly supervised AI error correctors with a priori performance guarantees. These AI correctors are auxiliary maps whose role is to moderate the decisions of some previously…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
With increasing scale in model and dataset size, the training of deep neural networks becomes a massive computational burden. One approach to speed up the training process is Selective Backprop. For this approach, we perform a forward pass…
Most of the current boundary detection systems rely exclusively on low-level features, such as color and texture. However, perception studies suggest that humans employ object-level reasoning when judging if a particular pixel is a…
This paper presents a pre-processing and a distance which improve the performance of machine learning algorithms working on independent and identically distributed stochastic processes. We introduce a novel non-parametric approach to…
Neural networks are not learning optimal decision boundaries. We show that decision boundaries are situated in areas of low training data density. They are impacted by few training samples which can easily lead to overfitting. We provide a…
Gradient-based meta-learning techniques aim to distill useful prior knowledge from a set of training tasks such that new tasks can be learned more efficiently with gradient descent. While these methods have achieved successes in various…
Large-scale modern data often involves estimation and testing for high-dimensional unknown parameters. It is desirable to identify the sparse signals, ``the needles in the haystack'', with accuracy and false discovery control. However, the…
Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…