Andrea Patane

AAAI Conference 2026 Conference Paper

Flow-Induced Diagonal Gaussian Processes

• Moule Lin
• Andrea Patane
• Weipeng Jing
• Shuhao Guan
• Goetz Botterweck

We present Flow-Induced Diagonal Gaussian Processes (FiD-GP), a compression framework that incorporates a compact inducing weight matrix to project a neural network’s weight uncertainty into a lower-dimensional subspace. Critically, FiD-GP relies on normalising flow variational posterior and spectral regularisations to augment its expressiveness and align the inducing subspace with feature-gradient geometry through a numerically stable projection mechanism objective. Furthermore, we demonstrate how the prediction framework in FiD-GP can help to design a single pass projection for Out-of-Distribution (OoD) detection. Our analysis shows that FiD-GP improves uncertainty estimation ability on various tasks compared with SVGP-based baselines, satisfies tight spectral residual bounds with theoretically guaranteed OoD detection, and significantly compresses the neural network’s storage requirements at the cost of increased inference computation dependent on the number of inducing weights employed. Specifically, in a comprehensive empirical study spanning regression, image classification, semantic segmentation, and Out-of-Distribution detection benchmarks, it significantly cuts Bayesian training cost, compresses parameters by roughly 51%, reduces model size by about 75%, and matches state-of-the-art accuracy and uncertainty estimation.

AIJ Journal 2024 Journal Article

Probabilistic reach-avoid for Bayesian neural networks

• Matthew Wicker
• Luca Laurenti
• Andrea Patane
• Nicola Paoletti
• Alessandro Abate
• Marta Kwiatkowska

ICML Conference 2023 Conference Paper

BNN-DP: Robustness Certification of Bayesian Neural Networks via Dynamic Programming

• Steven Adams
• Andrea Patane
• Morteza Lahijanian
• Luca Laurenti

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper bounds on the BNN’s predictions for all the points in $T$. The framework is based on an interpretation of BNNs as stochastic dynamical systems, which enables the use of Dynamic Programming (DP) algorithms to bound the prediction range along the layers of the network. Specifically, the method uses bound propagation techniques and convex relaxations to derive a backward recursion procedure to over-approximate the prediction range of the BNN with piecewise affine functions. The algorithm is general and can handle both regression and classification tasks. On a set of experiments on various regression and classification tasks and BNN architectures, we show that BNN-DP outperforms state-of-the-art methods by up to four orders of magnitude in both tightness of the bounds and computational efficiency.

JBHI Journal 2023 Journal Article

Physiologically-Informed Gaussian Processes for Interpretable Modelling of Psycho-Physiological States

• Shadi Ghiasi
• Andrea Patane
• Luca Laurenti
• Claudio Gentili
• Enzo Pasquale Scilingo
• Alberto Greco
• Marta Kwiatkowska

The widespread popularity of Machine Learning (ML) models in healthcare solutions has increased the demand for their interpretability and accountability. In this paper, we propose the Physiologically-Informed Gaussian Process ( PhGP ) classification model, an interpretable machine learning model founded on the Bayesian nature of Gaussian Processes (GPs). Specifically, we inject problem-specific domain knowledge of inherent physiological mechanisms underlying the psycho-physiological states as a prior distribution over the GP latent space. Thus, to estimate the hyper-parameters in PhGP, we rely on the information from raw physiological signals as well as the designed prior function encoding the physiologically-inspired modelling assumptions. Alongside this new model, we present novel interpretability metrics that highlight the most informative input regions that contribute to the GP prediction. We evaluate the ability of PhGP to provide an accurate and interpretable classification on three different datasets, including electrodermal activity (EDA) signals collected during emotional, painful, and stressful tasks. Our results demonstrate that, for all three tasks, recognition performance is improved by using the PhGP model compared to competitive methods. Moreover, PhGP is able to provide physiological sound interpretations over its predictions.

JMLR Journal 2022 Journal Article

Adversarial Robustness Guarantees for Gaussian Processes

• Andrea Patane
• Arno Blaas
• Luca Laurenti
• Luca Cardelli
• Stephen Roberts
• Marta Kwiatkowska

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this paper we present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations. Given a compact subset of the input space $T\subseteq \mathbb{R}^d$, a point $x^*$ and a GP, we provide provable guarantees of adversarial robustness of the GP by computing lower and upper bounds on its prediction range in $T$. We develop a branch-and-bound scheme to refine the bounds and show, for any $\epsilon > 0$, that our algorithm is guaranteed to converge to values $\epsilon$-close to the actual values in finitely many iterations. The algorithm is anytime and can handle both regression and classification tasks, with analytical formulation for most kernels used in practice. We evaluate our methods on a collection of synthetic and standard benchmark data sets, including SPAM, MNIST and FashionMNIST. We study the effect of approximate inference techniques on robustness and demonstrate how our method can be used for interpretability. Our empirical results suggest that the adversarial robustness of GPs increases with accurate posterior estimation. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2022. ( edit, beta )

UAI Conference 2021 Conference Paper

Certification of iterative predictions in Bayesian neural networks

• Matthew Wicker
• Luca Laurenti
• Andrea Patane
• Nicola Paoletti
• Alessandro Abate
• Marta Kwiatkowska

We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds for the probability that trajectories of the BNN model reach a given set of states while avoiding a set of unsafe states. We use the lower bounds in the context of control and reinforcement learning to provide safety certification for given control policies, as well as to synthesize control policies that improve the certification bounds. On a set of benchmarks, we demonstrate that our framework can be employed to certify policies over BNNs predictions for problems of more than $10$ dimensions, and to effectively synthesize policies that significantly increase the lower bound on the satisfaction probability.

UAI Conference 2020 Conference Paper

Probabilistic Safety for Bayesian Neural Networks

• Matthew Wicker
• Luca Laurenti
• Andrea Patane
• Marta Kwiatkowska

We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq R^m$, we study the probability w. r. t. the BNN posterior that all the points in $T$ are mapped to the same region $S$ in the output space. In particular, this can be used to evaluate the probability that a network sampled from the BNN is vulnerable to adversarial attacks. We rely on relaxation techniques from non-convex optimization to develop a method for computing a lower bound on probabilistic safety for BNNs, deriving explicit procedures for the case of interval and linear function propagation techniques. We apply our methods to BNNs trained on a regression task, airborne collision avoidance, and MNIST, empirically showing that our approach allows one to certify probabilistic safety of BNNs with millions of parameters.

AAAI Conference 2019 Conference Paper

Robustness Guarantees for Bayesian Inference with Gaussian Processes

• Luca Cardelli
• Marta Kwiatkowska
• Luca Laurenti
• Andrea Patane

Bayesian inference and Gaussian processes are widely used in applications ranging from robotics and control to biological systems. Many of these applications are safety-critical and require a characterization of the uncertainty associated with the learning model and formal guarantees on its predictions. In this paper we define a robustness measure for Bayesian inference against input perturbations, given by the probability that, for a test point and a compact set in the input space containing the test point, the prediction of the learning model will remain δ−close for all the points in the set, for δ > 0. Such measures can be used to provide formal probabilistic guarantees for the absence of adversarial examples. By employing the theory of Gaussian processes, we derive upper bounds on the resulting robustness by utilising the Borell-TIS inequality, and propose algorithms for their computation. We evaluate our techniques on two examples, a GP regression problem and a fully-connected deep neural network, where we rely on weak convergence to GPs to study adversarial examples on the MNIST dataset.

IJCAI Conference 2019 Conference Paper

Statistical Guarantees for the Robustness of Bayesian Neural Networks

• Luca Cardelli
• Marta Kwiatkowska
• Luca Laurenti
• Nicola Paoletti
• Andrea Patane
• Matthew Wicker

We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a measure can be used, for instance, to quantify the probability of the existence of adversarial examples. Building on statistical verification techniques for probabilistic models, we develop a framework that allows us to estimate probabilistic robustness for a BNN with statistical guarantees, i. e. , with a priori error and confidence bounds. We provide experimental comparison for several approximate BNN inference techniques on image classification tasks associated to MNIST and a two-class subset of the GTSRB dataset. Our results enable quantification of uncertainty of BNN predictions in adversarial settings.