Related papers: A priori estimates for classification problems usi…

The majority of traditional classification ru les minimizing the expected probability of error (0-1 loss) are inappropriate if the class probability distributions are ill-defined or impossible to estimate. We argue that in such cases class…

In this work, we propose a novel prior learning method for advancing generalization and uncertainty estimation in deep neural networks. The key idea is to exploit scalable and structured posteriors of neural networks as informative priors…

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including…

We show that the Rademacher complexity-based framework can establish non-vacuous generalization bounds for Convolutional Neural Networks (CNNs) in the context of classifying a small set of image classes. A key technical advancement is the…

Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class…

In this paper, we demonstrate the application of generalised rational uniform (Chebyshev) approximation in neural networks. In particular, our activation functions are one degree rational functions and the loss function is based on the…

In this paper we consider the possibility of computing rather than training the decision layer weights of a neural classifier. Such a possibility arises in two way, from making an appropriate choice of loss function and by solving a problem…

We present a new family of model selection algorithms based on the resampling heuristics. It can be used in several frameworks, do not require any knowledge about the unknown law of the data, and may be seen as a generalization of local…

We construct neural network regression models to predict key metrics of complexity for Gr\"obner bases of binomial ideals. This work illustrates why predictions with neural networks from Gr\"obner computations are not a straightforward…

We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…

We propose a new loss function for supervised and physics-informed training of neural networks and operators that incorporates a posteriori error estimate. More specifically, during the training stage, the neural network learns additional…

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…

We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…

When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…

Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary…

Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear…

Some machine learning applications require continual learning - where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward:…

To get Bayesian neural networks to perform comparably to standard neural networks it is usually necessary to artificially reduce uncertainty using a "tempered" or "cold" posterior. This is extremely concerning: if the prior is accurate,…

Prediction models based on deep neural networks are increasingly gaining attention for fast and accurate virtual screening systems. For decision makings in virtual screening, researchers find it useful to interpret an output of…