arXiv subjects

Luca Bortolussi

Publications and source records attributed to Luca Bortolussi.

At least 73 records · Page 4Linked to original sources

arXiv2020

Robustness of Bayesian Neural Networks to Gradient-Based Attacks

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, the problem remains open. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparametrized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in the limit BNN posteriors are robust to gradient-based adversarial attacks. Experimental results on the MNIST and Fashion MNIST datasets with BNNs trained with Hamiltonian Monte Carlo and Variational Inference support this line of argument, showing that BNNs can display both high accuracy and robustness to gradient based adversarial attacks.

cs.LG↗

arXiv2020

Bounding Mean First Passage Times in Population Continuous-Time Markov Chains

We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population models is notoriously difficult since typically neither state-based numerical approaches nor methods based on stochastic sampling give efficient and accurate results. Here, we propose a technique that extends recently developed methods using semi-definite programming to determine bounds on mean first passage times. We further apply the technique to hybrid models and demonstrate its accuracy and efficiency for some examples from biology.

eess.SY↗

arXiv2019

Rejection-Based Simulation of Non-Markovian Agents on Complex Networks

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often the preferred - sometimes the only feasible - way to investigate such systems. Previous research focused primarily on Markovian models where the random time until an interaction happens follows an exponential distribution. In this work, we study a general framework to model systems where each agent is in one of several states. Agents can change their state at random, influenced by their complete neighborhood, while the time to the next event can follow an arbitrary probability distribution. Classically, these simulations are hindered by high computational costs of updating the rates of interconnected agents and sampling the random residence times from arbitrary distributions. We propose a rejection-based, event-driven simulation algorithm to overcome these limitations. Our method over-approximates the instantaneous rates corresponding to inter-event times while rejection events counterbalance these over-approximations. We demonstrate the effectiveness of our approach on models of epidemic and information spreading.

cs.SI↗

arXiv2019

Reducing Spreading Processes on Networks to Markov Population Models

Stochastic processes on complex networks, where each node is in one of several compartments, and neighboring nodes interact with each other, can be used to describe a variety of real-world spreading phenomena. However, computational analysis of such processes is hindered by the enormous size of their underlying state space. In this work, we demonstrate that lumping can be used to reduce any epidemic model to a Markov Population Model (MPM). Therefore, we propose a novel lumping scheme based on a partitioning of the nodes. By imposing different types of counting abstractions, we obtain coarse-grained Markov models with a natural MPM representation that approximate the original systems. This makes it possible to transfer the rich pool of approximation techniques developed for MPMs to the computational analysis of complex networks' dynamics. We present numerical examples to investigate the relationship between the accuracy of the MPMs, the size of the lumped state space, and the type of counting abstraction.

cs.SI↗

arXiv2019

Control Variates for Stochastic Simulation of Chemical Reaction Networks

Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires the generation of a large number of simulation runs, which is computationally expensive. To reduce the number of necessary runs, we propose a variance reduction technique based on control variates. We exploit constraints on the statistical moments of the stochastic process to reduce the estimators' variances. We develop an algorithm that selects appropriate control variates in an on-line fashion and demonstrate the efficiency of our approach on several case studies.

q-bio.QM↗

arXiv2019

Monitoring Mobile and Spatially Distributed Cyber-Physical Systems

Cyber-Physical Systems~(CPS) consist of collaborative, networked and tightly intertwined computational (logical) and physical components, each operating at different spatial and temporal scales. Hence, the spatial and temporal requirements play an essential role for their correct and safe execution. Furthermore, the local interactions among the system components result in global spatio-temporal emergent behaviors often impossible to predict at the design time. In this work, we pursue a complementary approach by introducing STREL a novel spatio-temporal logic that enables the specification of spatio-temporal requirements and their monitoring over the execution of mobile and spatially distributed CPS. Our logic extends the Signal Temporal Logic with two novel spatial operators reach and escape from which is possible to derive other spatial modalities such as everywhere, somewhere and surround. These operators enable a monitoring procedure where the satisfaction of the property at each location depends only on the satisfaction of its neighbours, opening the way to future distributed online monitoring algorithms. We propose both a qualitative and quantitative semantics based on constraint semirings, an algebraic structure suitable for constraint satisfaction and optimisation. We prove that, for a subclass of models, all the spatial properties expressed with reach and escape, using euclidean distance, satisfy all the model transformations using rotation, reflection and translation. Finally, we provide an offline monitoring algorithm for STREL and, to demonstrate the feasibility of our approach, we show its application using the monitoring of a simulated mobile ad-hoc sensor network as running example.

cs.LO↗

arXiv2019

Intrinsic Geometric Vulnerability of High-Dimensional Artificial Intelligence

The success of modern Artificial Intelligence (AI) technologies depends critically on the ability to learn non-linear functional dependencies from large, high dimensional data sets. Despite recent high-profile successes, empirical evidence indicates that the high predictive performance is often paired with low robustness, making AI systems potentially vulnerable to adversarial attacks. In this report, we provide a simple intuitive argument suggesting that high performance and vulnerability are intrinsically coupled, and largely dependent on the geometry of typical, high-dimensional data sets. Our work highlights a major potential pitfall of modern AI systems, and suggests practical research directions to ameliorate the problem.

cs.LG↗

arXiv2018

Signal Convolution Logic

We introduce a new logic called Signal Convolution Logic (SCL) that combines temporal logic with convolutional filters from digital signal processing. SCL enables to reason about the percentage of time a formula is satisfied in a bounded interval. We demonstrate that this new logic is a suitable formalism to effectively express non-functional requirements in Cyber-Physical Systems displaying noisy and irregular behaviours. We define both a qualitative and quantitative semantics for it, providing an efficient monitoring procedure. Finally, we prove SCL at work to monitor the artificial pancreas controllers that are employed to automate the delivery of insulin for patients with type-1 diabetes.

cs.LO↗

arXiv2018

A Robust Genetic Algorithm for Learning Temporal Specifications from Data

We consider the problem of mining signal temporal logical requirements from a dataset of regular (good) and anomalous (bad) trajectories of a dynamical system. We assume the training set to be labeled by human experts and that we have access only to a limited amount of data, typically noisy. We provide a systematic approach to synthesize both the syntactical structure and the parameters of the temporal logic formula using a two-steps procedure: first, we leverage a novel evolutionary algorithm for learning the structure of the formula; second, we perform the parameter synthesis operating on the statistical emulation of the average robustness for a candidate formula w.r.t. its parameters. We compare our results with our previous work [{BufoBSBLB14] and with a recently proposed decision-tree [bombara_decision_2016] based method. We present experimental results on two case studies: an anomalous trajectory detection problem of a naval surveillance system and the characterization of an Ineffective Respiratory effort, showing the usefulness of our work.

cs.AI↗

arXiv2018

Central Limit Model Checking

We consider probabilistic model checking for continuous-time Markov chains (CTMCs) induced from Stochastic Reaction Networks (SRNs) against a fragment of Continuous Stochastic Logic (CSL) extended with reward operators. Classical numerical algorithms for CSL model checking based on uniformisation are limited to finite CTMCs and suffer from the state sapce explosion problem. On the other hand, approximate techniques such as mean-field approximations and simulations combined with statistical inference are more scalable, but can be time consuming and do not support the full expressiveness of CSL. In this paper we employ a continuous-space approximation of the CTMC in terms of a Gaussian process based on the Central Limit Approximation (CLA), also known as the Linear Noise Approximation (LNA), whose solution requires solving a number of differential equations that is quadratic in the number of species and independent of the population size. We then develop efficient and scalable approximate model checking algorithms on the resulting Gaussian process, where we restrict the target regions for probabilistic reachability to convex polytopes. This allows us to derive an abstraction in terms of a time-inhomogeneous discrete-time Markov chain (DTMC), whose dimension is independent of the number of species, on which model checking is performed. Using results from probability theory, we prove the convergence in distribution of our algorithms to the corresponding measures on the original CTMC. We implement the techniques and, on a set of examples, demonstrate that they allow us to overcome the state space explosion problem, while still correctly characterizing the stochastic behaviour of the system. Our methods can be used for formal analysis of a wide range of distributed stochastic systems, including biochemical systems, sensor networks and population protocols.

cs.LO↗

arXiv2018

Lumping the Approximate Master Equation for Multistate Processes on Complex Networks

Complex networks play an important role in human society and in nature. Stochastic multistate processes provide a powerful framework to model a variety of emerging phenomena such as the dynamics of an epidemic or the spreading of information on complex networks. In recent years, mean-field type approximations gained widespread attention as a tool to analyze and understand complex network dynamics. They reduce the model's complexity by assuming that all nodes with a similar local structure behave identically. Among these methods the approximate master equation (AME) provides the most accurate description of complex networks' dynamics by considering the whole neighborhood of a node. The size of a typical network though renders the numerical solution of multistate AME infeasible. Here, we propose an efficient approach for the numerical solution of the AME that exploits similarities between the differential equations of structurally similar groups of nodes. We cluster a large number of similar equations together and solve only a single lumped equation per cluster. Our method allows the application of the AME to real-world networks, while preserving its accuracy in computing estimates of global network properties, such as the fraction of nodes in a state at a given time.

cs.SI↗

arXiv2017

Lumping of Degree-Based Mean Field and Pair Approximation Equations for Multi-State Contact Processes

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information spreading. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), like degree-based mean field (DBMF), approximate master equation (AME), or pair approximation (PA). The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we extend AME and PA, which has been proposed only for the binary state case, to a multi-state setting and provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

cs.SI↗

arXiv2017

Model Checking Markov Population Models by Stochastic Approximations

Many complex systems can be described by population models, in which a pool of agents interacts and produces complex collective behaviours. We consider the problem of verifying formal properties of the underlying mathematical representation of these models, which is a Continuous Time Markov Chain, often with a huge state space. To circumvent the state space explosion, we rely on stochastic approximation techniques, which replace the large model by a simpler one, guaranteed to be probabilistically consistent. We show how to efficiently and accurately verify properties of random individual agents, specified by Continuous Stochastic Logic extended with Timed Automata (CSL-TA), and how to lift these specifications to the collective level, approximating the number of agents satisfying them using second or higher order stochastic approximation techniques.

cs.LO↗

arXiv2017

An Active Learning Approach to the Falsification of Black Box Cyber-Physical Systems

Search-based testing is widely used to find bugs in models of complex Cyber-Physical Systems. Latest research efforts have improved this approach by casting it as a falsification procedure of formally specified temporal properties, exploiting the robustness semantics of Signal Temporal Logic. The scaling of this approach to highly complex engineering systems requires efficient falsification procedures, which should be applicable also to black box models. Falsification is also exacerbated by the fact that inputs are often time-dependent functions. We tackle the falsification of formal properties of complex black box models of Cyber-Physical Systems, leveraging machine learning techniques from the area of Active Learning. Tailoring these techniques to the falsification problem with time-dependent, functional inputs, we show a considerable gain in computational effort, by reducing the number of model simulations needed. The goodness of the proposed approach is discussed on a challenging industrial-level benchmark from automotive.

cs.LO↗

arXiv2016

Location Aggregation of Spatial Population CTMC Models

In this paper we focus on spatial Markov population models, describing the stochastic evolution of populations of agents, explicitly modelling their spatial distribution, representing space as a discrete, finite graph. More specifically, we present a heuristic approach to aggregating spatial locations, which is designed to preserve the dynamical behaviour of the model whilst reducing the computational cost of analysis. Our approach combines stochastic approximation ideas (moment closure, linear noise), with computational statistics (spectral clustering) to obtain an efficient aggregation, which is experimentally shown to be reasonably accurate on two case studies: an instance of epidemic spreading and a London bike sharing scenario.

cs.MA↗

arXiv2016

Policy learning for time-bounded reachability in Continuous-Time Markov Decision Processes via doubly-stochastic gradient ascent

Continuous-time Markov decision processes are an important class of models in a wide range of applications, ranging from cyber-physical systems to synthetic biology. A central problem is how to devise a policy to control the system in order to maximise the probability of satisfying a set of temporal logic specifications. Here we present a novel approach based on statistical model checking and an unbiased estimation of a functional gradient in the space of possible policies. The statistical approach has several advantages over conventional approaches based on uniformisation, as it can also be applied when the model is replaced by a black box, and does not suffer from state-space explosion. The use of a stochastic gradient to guide our search considerably improves the efficiency of learning policies. We demonstrate the method on a proof-of-principle non-linear population model, showing strong performance in a non-trivial task.

eess.SY↗

arXiv2016

Matching models across abstraction levels with Gaussian Processes

Biological systems are often modelled at different levels of abstraction depending on the particular aims/resources of a study. Such different models often provide qualitatively concordant predictions over specific parametrisations, but it is generally unclear whether model predictions are quantitatively in agreement, and whether such agreement holds for different parametrisations. Here we present a generally applicable statistical machine learning methodology to automatically reconcile the predictions of different models across abstraction levels. Our approach is based on defining a correction map, a random function which modifies the output of a model in order to match the statistics of the output of a different model of the same system. We use two biological examples to give a proof-of-principle demonstration of the methodology, and discuss its advantages and potential further applications.

stat.ML↗

arXiv2015

Distribution approximations for the chemical master equation: comparison of the method of moments and the system size expansion

The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the temporal evolution of the system in terms of a chemical master equation (CME). In this paper we study two approaches for approximating the underlying probability distributions of the CME. The first approach is based on an integration of the statistical moments and the reconstruction of the distribution based on the maximum entropy principle. The second approach relies on an analytical approximation of the probability distribution of the CME using the system size expansion, considering higher-order terms than the linear noise approximation. We consider gene expression networks with unimodal and multimodal protein distributions to compare the accuracy of the two approaches. We find that both methods provide accurate approximations to the distributions of the CME while having different benefits and limitations in applications.

q-bio.QM↗