arXiv subjects

Guido Sanguinetti

Publications and source records attributed to Guido Sanguinetti.

At least 37 records · Page 2Linked 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

Estimating the impact of preventive quarantine with reverse epidemiology

The impact of mitigation or control measures on an epidemics can be estimated by fitting the parameters of a compartmental model to empirical data, and running the model forward with modified parameters that account for a specific measure. This approach has several drawbacks, stemming from biases or lack of availability of data and instability of parameter estimates. Here we take the opposite approach -- that we call reverse epidemiology. Given the data, we reconstruct backward in time an ensemble of networks of contacts, and we assess the impact of measures on that specific realization of the contagion process. This approach is robust because it only depends on parameters that describe the evolution of the disease within one individual (e.g. latency time) and not on parameters that describe the spread of the epidemics in a population. Using this method, we assess the impact of preventive quarantine on the ongoing outbreak of Covid-19 in Italy. This gives an estimate of how many infected could have been avoided had preventive quarantine been enforced at a given time.

q-bio.PE↗

arXiv2019

Geometric fluid approximation for general continuous-time Markov chains

Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a dynamics for the approximating process. We construct here a general method based on spectral analysis of the transition matrix of the CTMC, without the need for a population structure. Specifically, we use the popular manifold learning method of diffusion maps to analyse the transition matrix as the operator of a hidden continuous process. An embedding of states in a continuous space is recovered, and the space is endowed with a drift vector field inferred via Gaussian process regression. In this manner, we construct an ODE whose solution approximates the evolution of the CTMC mean, mapped onto the continuous space (known as the fluid limit).

eess.SY↗

arXiv2019

Parameter estimation for biochemical reaction networks using Wasserstein distances

We present a method for estimating parameters in stochastic models of biochemical reaction networks by fitting steady-state distributions using Wasserstein distances. We simulate a reaction network at different parameter settings and train a Gaussian process to learn the Wasserstein distance between observations and the simulator output for all parameters. We then use Bayesian optimization to find parameters minimizing this distance based on the trained Gaussian process. The effectiveness of our method is demonstrated on the three-stage model of gene expression and a genetic feedback loop for which moment-based methods are known to perform poorly. Our method is applicable to any simulator model of stochastic reaction networks, including Brownian Dynamics.

q-bio.QM↗

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

Gene regulatory network inference: an introductory survey

Gene regulatory networks are powerful abstractions of biological systems. Since the advent of high-throughput measurement technologies in biology in the late 90s, reconstructing the structure of such networks has been a central computational problem in systems biology. While the problem is certainly not solved in its entirety, considerable progress has been made in the last two decades, with mature tools now available. This chapter aims to provide an introduction to the basic concepts underpinning network inference tools, attempting a categorisation which highlights commonalities and relative strengths. While the chapter is meant to be self-contained, the material presented should provide a useful background to the later, more specialised chapters of this book.

q-bio.QM↗

arXiv2018

Probabilistic Model Checking for Continuous Time Markov Chains via Sequential Bayesian Inference

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while statistical approaches require a large number of samples to estimate the desired properties with high confidence. Here, we show how model checking of time-bounded path properties can be recast exactly as a Bayesian inference problem. In this novel formulation the problem can be efficiently approximated using techniques from machine learning. Our approach is inspired by a recent result in statistical physics which derived closed form differential equations for the first-passage time distribution of stochastic processes. We show on a number of non-trivial case studies that our method achieves both high accuracy and significant computational gains compared to statistical model checking.

cs.LO↗

arXiv2017

Efficient Low-Order Approximation of First-Passage Time Distributions

We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem for an auxiliary observation process. The solution can be approximated efficiently by solving a closed set of coupled ordinary differential equations (for the low-order moments of the process) whose size scales with the number of species. We apply it to an epidemic model and a trimerisation process, and show good agreement with stochastic simulations.

physics.comp-ph↗

arXiv2017

Statistical abstraction for multi-scale spatio-temporal systems

Spatio-temporal systems exhibiting multi-scale behaviour are common in applications ranging from cyber-physical systems to systems biology, yet they present formidable challenges for computational modelling and analysis. Here we consider a prototypic scenario where spatially distributed agents decide their movement based on external inputs and a fast-equilibrating internal computation. We propose a generally applicable strategy based on statistically abstracting the internal system using Gaussian Processes, a powerful class of non-parametric regression techniques from Bayesian Machine Learning. We show on a running example of bacterial chemotaxis that this approach leads to accurate and much faster simulations in a variety of scenarios.

q-bio.QM↗

arXiv2017

Approximation and inference methods for stochastic biochemical kinetics - a tutorial review

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

q-bio.QM↗

arXiv2016

Property-driven State-Space Coarsening for Continuous Time Markov Chains

Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however, focus on a priori state aggregation based on similarities in transition rates, which is not necessarily reflected in similar behaviours at the level of trajectories. We propose a way to coarsen the state-space of a system which optimally preserves the satisfaction of a set of logical specifications about the system's trajectories. Our approach is based on Gaussian Process emulation and Multi-Dimensional Scaling, a dimensionality reduction technique which optimally preserves distances in non-Euclidean spaces. We show how to obtain low-dimensional visualisations of the system's state-space from the perspective of properties' satisfaction, and how to define macro-states which behave coherently with respect to the specifications. Our approach is illustrated on a non-trivial running example, showing promising performance and high computational efficiency.

eess.SY↗

arXiv2016

Cox process representation and inference for stochastic reaction-diffusion processes

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

cond-mat.stat-mech↗

arXiv2016

Expectation propagation for continuous time stochastic processes

We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using variational approximate inference. We then show how the approximation can be extended to a wide class of discrete-state Markov jump pro- cesses by making use of the chemical Langevin equation. Our empirical results show that the proposed method is computationally efficient and provides good approximations for these classes of inverse problems.

stat.ML↗

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

Unbiased Bayesian Inference for Population Markov Jump Processes via Random Truncations

We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we propose a novel efficient algorithm for joint state / parameter posterior sampling in population Markov Jump processes. We introduce a class of pseudo-marginal sampling algorithms based on a random truncation method which enables a principled treatment of infinite state spaces. Extensive evaluation on a number of benchmark models shows that this approach achieves considerable savings compared to state of the art methods, retaining accuracy and fast convergence. We also present results on a synthetic biology data set showing the potential for practical usefulness of our work.

stat.ML↗

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↗

arXiv2016

Higher order methylation features for clustering and prediction in epigenomic studies

Motivation: DNA methylation is an intensely studied epigenetic mark, yet its functional role is incompletely understood. Attempts to quantitatively associate average DNA methylation to gene expression yield poor correlations outside of the well-understood methylation-switch at CpG islands. Results: Here we use probabilistic machine learning to extract higher order features associated with the methylation profile across a defined region. These features quantitate precisely notions of shape of a methylation profile, capturing spatial correlations in DNA methylation across genomic regions. Using these higher order features across promoter-proximal regions, we are able to construct a powerful machine learning predictor of gene expression, significantly improving upon the predictive power of average DNA methylation levels. Furthermore, we can use higher order features to cluster promoter-proximal regions, showing that five major patterns of methylation occur at promoters across different cell lines, and we provide evidence that methylation beyond CpG islands may be related to regulation of gene expression. Our results support previous reports of a functional role of spatial correlations in methylation patterns, and provide a mean to quantitate such features for downstream analyses. Availability: https://github.com/andreaskapou/BPRMeth

q-bio.GN↗

arXiv2016

Statistical modeling of isoform splicing dynamics from RNA-seq time series data

Isoform quantification is an important goal of RNA-seq experiments, yet it remains prob- lematic for genes with low expression or several isoforms. These difficulties may in principle be ameliorated by exploiting correlated experimental designs, such as time series or dosage response experiments. Time series RNA-seq experiments, in particular, are becoming in- creasingly popular, yet there are no methods that explicitly leverage the experimental design to improve isoform quantification. Here we present DICEseq, the first isoform quantification method tailored to correlated RNA-seq experiments. DICEseq explicitly models the corre- lations between different RNA-seq experiments to aid the quantification of isoforms across experiments. Numerical experiments on simulated data sets show that DICEseq yields more accurate results than state-of-the-art methods, an advantage that can become considerable at low coverage levels. On real data sets, our results show that DICEseq provides substan- tially more reproducible and robust quantifications, increasing the correlation of estimates from replicate data sets by up to 10% on genes with low or moderate expression levels (bot- tom third of all genes). Furthermore, DICEseq permits to quantify the trade-off between temporal sampling of RNA and depth of sequencing, frequently an important choice when planning experiments. Our results have strong implications for the design of RNA-seq ex- periments, and offer a novel tool for improved analysis of such data sets. Python code is freely available at http://diceseq.sf.net.

q-bio.GN↗