Related papers: Tighter risk certificates for neural networks

We propose Trusted Neural Network (TNN) models, which are deep neural network models that satisfy safety constraints critical to the application domain. We investigate different mechanisms for incorporating rule-based knowledge in the form…

While deep learning models and techniques have achieved great empirical success, our understanding of the source of success in many aspects remains very limited. In an attempt to bridge the gap, we investigate the decision boundary of a…

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect,…

We introduce a data-driven approach to analyze the performance of continuous optimization algorithms using generalization guarantees from statistical learning theory. We study classical and learned optimizers to solve families of parametric…

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…

Despite achieving excellent performance on benchmarks, deep neural networks often underperform in real-world deployment due to sensitivity to minor, often imperceptible shifts in input data, known as distributional shifts. These shifts are…

In this paper, we present new high-probability PAC-Bayes bounds for different types of losses. Firstly, for losses with a bounded range, we recover a strengthened version of Catoni's bound that holds uniformly for all parameter values. This…

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a…

We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework…

Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of…

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to…

Fairness is crucial for neural networks which are used in applications with important societal implication. Recently, there have been multiple attempts on improving fairness of neural networks, with a focus on fairness testing (e.g.,…

We give a general recipe for derandomising PAC-Bayesian bounds using margins, with the critical ingredient being that our randomised predictions concentrate around some value. The tools we develop straightforwardly lead to margin bounds for…

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

The reliable measurement of confidence in classifiers' predictions is very important for many applications and is, therefore, an important part of classifier design. Yet, although deep learning has received tremendous attention in recent…

The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…

Let $f(\theta, X_1),$ $ \dots,$ $ f(\theta, X_n)$ be a sequence of random elements, where $f$ is a fixed scalar function, $X_1, \dots, X_n$ are independent random variables (data), and $\theta$ is a random parameter distributed according to…

Extensive research on formal verification of machine learning systems indicates that learning from data alone often fails to capture underlying background knowledge, such as specifications implicitly available in the data. Various neural…

In this paper we derive a Probably Approxilmately Correct(PAC)-Bayesian error bound for linear time-invariant (LTI) stochastic dynamical systems with inputs. Such bounds are widespread in machine learning, and they are useful for…

We introduce a new PAC-Bayes oracle bound for unbounded losses that extends Cram\'er-Chernoff bounds to the PAC-Bayesian setting. The proof technique relies on controlling the tails of certain random variables involving the Cram\'er…