Nonparametric inference of interaction laws in systems of agents from trajectory data

Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or assumption about their analytical form, from data consisting trajectories of interacting agents. We demonstrate the effectiveness of our learning approach both by providing theoretical guarantees, and by testing the approach on a variety of prototypical systems in various disciplines. These systems include homogeneous and heterogeneous agents systems, ranging from particle systems in fundamental physics to agent-based systems modeling opinion dynamics under the social influence, prey-predator dynamics, flocking and swarming, and phototaxis in cell dynamics

Robust PDE Identification from Noisy Data

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential terms in a prescribed dictionary. Noisy data make such identification particularly challenging. Our objective is to develop methods which are robust against a high level of noise, and to approximate the underlying noise-free dynamics well. We first introduce a Successively Denoised Differentiation (SDD) scheme to stabilize the amplified noise in numerical differentiation. SDD effectively denoises the given data and the corresponding derivatives. Secondly, we present two algorithms for PDE identification: Subspace pursuit Time evolution error (ST) and Subspace pursuit Cross-validation (SC). Our general strategy is to first find a candidate set using the Subspace Pursuit (SP) greedy algorithm, then choose the best one via time evolution or cross validation. ST uses multi-shooting numerical time evolution and selects the PDE which yields the least evolution error. SC evaluates the cross-validation error in the least squares fitting and picks the PDE that gives the smallest validation error. We present a unified notion of PDE identification error to compare the objectives of related approaches. We present various numerical experiments to validate our methods. Both methods are efficient and robust to noise

Valuing buildings energy efficiency through Hedonic Prices Method: are spatial effects relevant?

The primary goal of this work is to employ a spatial econometric model joined with a basic Hedonic Prices Method (HPM) to estimate the implicit marginal price, as measure of willingness to pay for buildings energy performance in Turin City. The recent debate about environmental costs of energy waste justifies the implementation of different policies focused on buildings energy efficiency. The application of seven models on a large data–set of residential properties values shows the necessity to carefully control the coherence between spatial and econometric approaches. At the same time, findings of the exploration of an exemplary case study can help researchers and policymakers in the definition of innovative urban models in the context of the post-carbon city

Characterising and modeling the co-evolution of transportation networks and territories

The identification of structuring effects of transportation infrastructure on territorial dynamics remains an open research problem. This issue is one of the aspects of approaches on complexity of territorial dynamics, within which territories and networks would be co-evolving. The aim of this thesis is to challenge this view on interactions between networks and territories, both at the conceptual and empirical level, by integrating them in simulation models of territorial systems.Comment: Doctoral dissertation (2017), Universit\'e Paris 7 Denis Diderot. Translated from French. Several papers compose this PhD thesis; overlap with: arXiv:{1605.08888, 1608.00840, 1608.05266, 1612.08504, 1706.07467, 1706.09244, 1708.06743, 1709.08684, 1712.00805, 1803.11457, 1804.09416, 1804.09430, 1805.05195, 1808.07282, 1809.00861, 1811.04270, 1812.01473, 1812.06008, 1908.02034, 2012.13367, 2102.13501, 2106.11996

Quantitative Models in Life Science Business

This open access book explores the field of life science business from a multidisciplinary perspective. Applying statistical, mathematical, game-theoretic, and data science tools to pharmaceutical and biotechnology business endeavors, the book describes value creation, value maintenance, and value realization in the life sciences as a sequence of processes using the quantitative language of applied mathematics. Written by experts from a variety of fields, the contributions illustrate the shift from a deterministic to a stochastic view of the processes involved, offering a new perspective on life sciences economics. The book covers topics such as valuing and managing intellectual property in life science, licensing in the pharmaceutical business, outsourcing pharmaceutical R&D, and stochastic modelling of a pharmaceutical supply chain. The book will appeal to scholars of economics and the life sciences, as well as to professionals in chemical and pharmaceutical industries

On-line estimation of steam boiler plant dynamics

Imperial Users onl

Interpretable Machine Learning for Electro-encephalography

While behavioral, genetic and psychological markers can provide important information about brain health, research in that area over the last decades has much focused on imaging devices such as magnetic resonance tomography (MRI) to provide non-invasive information about cognitive processes. Unfortunately, MRI based approaches, able to capture the slow changes in blood oxygenation levels, cannot capture electrical brain activity which plays out on a time scale up to three orders of magnitude faster. Electroencephalography (EEG), which has been available in clinical settings for over 60 years, is able to measure brain activity based on rapidly changing electrical potentials measured non-invasively on the scalp. Compared to MRI based research into neurodegeneration, EEG based research has, over the last decade, received much less interest from the machine learning community. But generally, EEG in combination with sophisticated machine learning offers great potential such that neglecting this source of information, compared to MRI or genetics, is not warranted. In collaborating with clinical experts, the ability to link any results provided by machine learning to the existing body of research is especially important as it ultimately provides an intuitive or interpretable understanding. Here, interpretable means the possibility for medical experts to translate the insights provided by a statistical model into a working hypothesis relating to brain function. To this end, we propose in our first contribution a method allowing for ultra-sparse regression which is applied on EEG data in order to identify a small subset of important diagnostic markers highlighting the main differences between healthy brains and brains affected by Parkinson's disease. Our second contribution builds on the idea that in Parkinson's disease impaired functioning of the thalamus causes changes in the complexity of the EEG waveforms. The thalamus is a small region in the center of the brain affected early in the course of the disease. Furthermore, it is believed that the thalamus functions as a pacemaker - akin to a conductor of an orchestra - such that changes in complexity are expressed and quantifiable based on EEG. We use these changes in complexity to show their association with future cognitive decline. In our third contribution we propose an extension of archetypal analysis embedded into a deep neural network. This generative version of archetypal analysis allows to learn an appropriate representation where every sample of a data set can be decomposed into a weighted sum of extreme representatives, the so-called archetypes. This opens up an interesting possibility of interpreting a data set relative to its most extreme representatives. In contrast, clustering algorithms describe a data set relative to its most average representatives. For Parkinson's disease, we show based on deep archetypal analysis, that healthy brains produce archetypes which are different from those produced by brains affected by neurodegeneration

Quantitative Models in Life Science Business

This open access book explores the field of life science business from a multidisciplinary perspective. Applying statistical, mathematical, game-theoretic, and data science tools to pharmaceutical and biotechnology business endeavors, the book describes value creation, value maintenance, and value realization in the life sciences as a sequence of processes using the quantitative language of applied mathematics. Written by experts from a variety of fields, the contributions illustrate the shift from a deterministic to a stochastic view of the processes involved, offering a new perspective on life sciences economics. The book covers topics such as valuing and managing intellectual property in life science, licensing in the pharmaceutical business, outsourcing pharmaceutical R&D, and stochastic modelling of a pharmaceutical supply chain. The book will appeal to scholars of economics and the life sciences, as well as to professionals in chemical and pharmaceutical industries

Efficient Sparse Bayesian Learning using Spike-and-Slab Priors

In the context of statistical machine learning, sparse learning is a procedure that seeks a reconciliation between two competing aspects of a statistical model: good predictive power and interpretability. In a Bayesian setting, sparse learning methods invoke sparsity inducing priors to explicitly encode this tradeoff in a principled manner

Singing voice resynthesis using concatenative-based techniques

Tese de Doutoramento. Engenharia Informática. Faculdade de Engenharia. Universidade do Porto. 201