Related papers: Structure of Classifier Boundaries: Case Study for…

Humans are accustomed to environments that contain both regularities and exceptions. For example, at most gas stations, one pays prior to pumping, but the occasional rural station does not accept payment in advance. Likewise, deep neural…

Nanopore sensors detect the substructure of individual molecules from modulations in an ion current as molecules pass through them. In this work, we present the classification of features in the substructure as a case study to illustrate…

We introduce Smart Bayes, a new classification framework that bridges generative and discriminative modeling by integrating likelihood-ratio-based generative features into a logistic-regression-style discriminative classifier. From the…

Automated medical image segmentation inherently involves a certain degree of uncertainty. One key factor contributing to this uncertainty is the ambiguity that can arise in determining the boundaries of a target region of interest,…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

The ability to discriminate between large and small quantities is a core aspect of basic numerical competence in both humans and animals. In this work, we examine the extent to which the state-of-the-art neural networks designed for vision…

Bayesian Neural Networks (BNNs) offer a mathematically grounded framework to quantify the uncertainty of model predictions but come with a prohibitive computation cost for both training and inference. In this work, we show a novel network…

Minimizing an adversarial surrogate risk is a common technique for learning robust classifiers. Prior work showed that convex surrogate losses are not statistically consistent in the adversarial context -- or in other words, a minimizing…

Classification is an important task in many fields including biomedical research and machine learning. Traditionally, a classification rule is constructed based a bunch of labeled data. Recently, due to technological innovation and…

The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the…

One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard.…

Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation…

Quantifying biomechanical properties of the human vasculature could deepen our understanding of cardiovascular diseases. Standard nonlinear regression in constitutive modeling requires considerable high-quality data and an explicit form of…

Most feature detectors such as edge detectors or circle finders are statistical, in the sense that they decide at each point in an image about the presence of a feature, this paper describes the use of Bayesian feature detectors.

Real-life statistical samples are often plagued by selection bias, which complicates drawing conclusions about the general population. When learning causal relationships between the variables is of interest, the sample may be assumed to be…

The Nearest subspace classifier (NSS) finds an estimation of the underlying subspace within each class and assigns data points to the class that corresponds to its nearest subspace. This paper mainly studies how well NSS can be generalized…

The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision…

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable…

Adversarial training based on the maximum classifier discrepancy between two classifier structures has achieved great success in unsupervised domain adaptation tasks for image classification. The approach adopts the structure of two…

We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…