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PhD in Modeling and Data Science

Università degli studi di Torino

A call for 5 fully funded PhD scholarships in the framework of the PhD in Modeling and Data Science https://dottorato-mds.campusnet.unito.it/do/home.pl at the University of Turin (Italy) will open on 28 April 2022 (date TBC). The scholarship is for three years, starting in October 2022.

The PhD program is interdisciplinary, and it involves branches of mathematics, informatics, economics, statistics, and physics. The candidate will choose one of the PhD topics listed below, according to their taste and background knowledge.

We are looking for expressions of interests for the PhD Program, and we welcome full applications once the call is live. Please contact the coordinator of the PhD Program, Prof Laura Sacerdote at laura.sacerdote@unito.it, or the supervisor of one of the individual projects for more information.

Further information, including the official call and all relevant (confirmed) deadlines, can be found here https://dottorato-mds.campusnet.unito.it/do/home.pl/View?doc=/content/Admission.html.

Admission details and the list of projects can be found here https://www.dottorato.unito.it/do/documenti.pl/ShowFile?_id=g3ot;field=file;key=JbqgKqg0lroYaYMa8BXEFYBVz1z8MXSdAKr7fGFtPR2;t=3298.

After the application is open, all interested candidates should submit their application online via the apply button. Deadline for applying is 30 May 2022 (date TBC). Notice that the application requires two reference letters, which should be submitted via the same link by the referees before the application deadline. The referees will be able to submit their letters only after the candidate has input all the required information and closed their (part of the) application. If the letters are not submitted by the deadline the application will not be valid.

List of PhD projects

  1. Duality methods in Bayesian inference for hidden Markov models
  2. Supporting Visually Impaired People in Exploring Structured Data
  3. Modeling human-nature relationships via multimodal deep learning architectures
  4. Interacting particle systems as microscopic stochastic representation of partial differential equations
  5. Future HPC solutions for cloud hybrid application
  6. Federated learning and beyond
  7. Time changed multivariate models: calibration and fit on financial data
  8. Stochastic modelling of subsurface water flow
  9. Numerical approximations of non-local parabolic equations based on stochastic and finite elements methods and applications
  10. Investigation with multi-agent system models, within the framework of the H2020 Green Cities pillar, of urban permeability to butterflies motion and of their diffusion in mixed urban areas (buildings and green spaces).

More details on the above projects can be found here.

1. Supervisor(s):Matteo Ruggiero

Title: Duality methods in Bayesian inference for hidden Markov models

Abstract:
The project deals with Bayesian inference on the trajectory of a diffusion process or on the parameters that characterize its drift and volatility, under the assumption of a hidden Markov model framework with noisy data collection. The target of inference is the trajectory of the diffusion, called signal, which in this framework is assumed to be unobserved and to modulate the so called emission distribution, namely the conditional distribution of the data given the current value of the process. Duality typically allows to write the conditional distributions of the signal given the data in simpler forms than those obtained through the transition density of the signal, especially when the latter is only available as a series expansion. In particular, when the dual process lives on a discrete space, these distributions become finite or countable mixtures of kernels that belong to the same family of the emission distribution. These can be shown to characterise the filtering and, under additional assumptions, the smoothing distribution and the likelihood. These quantities then can in turn be used to set up MCMC strategies that target the estimation of the parameters of the diffusion.


The current project aims at expanding on the results obtained in [1,2,3] and related papers, investigating new scenarios which may include different signals or different type of dualities, approximations of exact results and other acceleration techniques, both from the theoretical point of view and concerning the implementations for inference.

[1] Papaspiliopoulos, O. and Ruggiero, M. (2014). Optimal filtering and the dual process. Bernoulli 20, 1999-2019.
[2] Papaspiliopoulos, O., Ruggiero, M., and Spanò, D. (2016). Conjugacy properties of time-evolving Dirichlet and gamma random measures. Electronic Journal of Statistics 10, 3452-3489.
[3] Kon Kam King, G., Papaspiliopoulos, O. and Ruggiero, M. (2021). Exact inference for a class of hidden Markov models on general state spaces. Electronic Journal of Statistics 15, 2832-2875.

2. Supervisor(s):Luca Anselma e Alessandro Mazzei

Title: Supporting Visually Impaired People in Exploring Structured Data

Abstract:
This project intends to address the issue of accessibility to scientific information contained in graphic structures for people with visual disabilities. Today’s assistive technologies provide a number of tools to support visually impaired people, however these technologies often present severe limitations in non strictly textual contexts. In fact, scientific texts very often contain "structured" graphic information such as tables or diagrams representing large amounts of structured data usually employed in scientific analysis. The idea behind this project is to use Natural Language Processing and in particular conversational interfaces technologies to allow visually impaired people to navigate scientific diagrams towards a conversation with a chatbot.

3. Supervisor(s): Rossano Schifanella

Title: Modeling human-nature relationships via multimodal deep learning architectures

Abstract

Our daily urban experiences are the product of perceptions and emotional states that are triggered by the physical and social contexts around us, yet a complete modeling of these aspects is strikingly absent from urban studies. Mobile devices and sensors produce digital traces at an unprecedented spatial and temporal granularity and they enable innovative forms to model human behavior, characterizing where, when, and how people interact. In addition, crowdsourced data and geo-referenced online content add the human component to the underlying technological infrastructure and they present an invaluable tool to capture the invisible image of a city.

This project will leverage online feeds and the associated metadata to build an alternative cartography weighted for positive emotions, adding a layer where citizens opinions and emotions are modeled in time and space at scale. This will enable the implementation of new forms of services, e.g., an emotions-driven routing engine that is able to suggest a environmentally friendly path over the shortest, and urban design policies that favor the human factor over a city built around efficiency, predictability, and security alone.

This activity will be carried within the framework of the H2020 that plans to position European cities as world ambassadors of urban sustainability augmenting nature based-solutions, urban design with the goal of fostering a positive human-nature relationship, flourishing nature connectedness and promoting citizen engagement through digital, educational and behavioural innovation.

4. Supervisor(s): Elena Issoglio (with Francesco Russo, ENSTA Paris)

A co-tutorship between Torino and Paris will be formalized for this project aiming to release of the double title between the two universities

Title: Interacting particle systems as microscopic stochastic representation of partial differential equations

Abstract:

A stochastic interacting particle system is a system of particles (also known as agents) whose stochastic dynamics is dependent on the other particles. This system of stochastic equations describes the interactions between the particles at the microscopic level. Interacting particle systems find applications in many fields, such as biology (herds), sociology (herding behaviour), energy markets (price formation), etc. The drawback of this description is the complexity of the model, however it is known that, under suitable conditions, if we let the number of particles tend to infinity, then the (infinite) system will converge, in a suitable sense, to a partial differential equation known as Fokker-Planck equation. This limiting procedure is known as ''propagation of chaos''. The limiting equation corresponds to the macroscopic description of the stochastic system and it is much less complex (being a single equation instead of a large system), at least from a computational point of view.

This PhD project will focus on the study of stochastic interacting particle systems with singular coefficients, for example when the drift of each particle dynamics is highly non smooth. Singular coefficients would account for the singular nature of the dynamics of each particle, that could be due to exogenous factors (the environment) or endogenous ones (the particles themselves). In this specific framework, we will investigate the limit as the number of particles tends to infinity and prove a propagation of chaos result, hence establish the link between the microscopic and the macroscopic view. Afterwards, we will add a control variable to the system and/or to the limit partial differential equation. In terms of modelling, adding a control variable amounts to allow each particle (or agent) to modify its dynamics, for example changing the drift, upon paying a cost. The aim of each agent is to optimize their dynamics and at the same time minimize their cost. Thus this problem becomes a stochastic optimization problem with a large number of agents with singular and stochastic dynamics, which is the microscopic view. The corresponding macroscopic view is conjectured to be a controlled Fokker-Planck equation with singular coefficients. Our aim will be to formalize this mathematically and establish the propagation of chaos result in this more involved setting.

We observe that this mathematical formulation opens the door to many applications, especially with the help of data science and deep learning algorithms. Indeed, when the number of particles is large and/or the dimension of the underlying space is large, then fitting this model to real data becomes a data science problem. One possible tool that could be used to fit this high-dimensional model would be deep learning. Using this, one could investigate numerically the goodness of the approximation of the particle system with its limit equation, i.e. check the validity of the propagation of chaos result in real-life examples. This however will not be part of the current PhD project and it is left as future work after the completion of this PhD project.

5. Supervisor(s): Marco Aldinucci

Title: Future HPC solutions for cloud hybrid application

Project funded by Leonardo Company

Abstract

The project aims at developing methods and tools for digital twins, i.e. a digital replica of a living or nonliving physical entity (i.e., "the system") that allows us to simulate the effects of a natural event or human intervention on the system itself. Digital twins are workflows of modular, composable, portable, scalable cloud services embedding high-performance simulations, AI-based data analysis stages and possibly specialized Quantum kernels. The project will extend the Common Workflow Language (CWL) open standard and its Streamflow implementation to match the need of future generation digital twins.

6. Supervisor(s): Marco Aldinucci

Title: Federated learning and beyond

Abstract:

Federated Learning has been proposed to develop better AI systems without compromising the privacy of final users and the legitimate interests of private companies. Federated learning can be coupled with other learning techniques, such as continual and adversarial learning, and could be a real game-changer for analyzing inherently distributed critical data. The project aims to explore the boundary of distributed and federated learning techniques.

7. Supervisor(s): Elvira Di Nardo

Title: Time changed multivariate models: calibration and fit on financial data

Abstract

Multi-asset derivative pricing is still an active field of research in financial modeling, calling for multivariate stochastic models that reproduce well-known stylized facts such as skewness and excess kurtosis of marginal return distributions.

The objectives of this research project are to build stochastic models for financial assets, develop calibration procedures and simulation methods. Simulations are necessary to price derivatives if analytical pricing formulas are not available, and they are also necessary to generate future scenarios for out-of-sample evaluation.

A class of models widely used in finance are Markov processes. Among them, Lévy processes, which are characterized by independent and time-homogeneous increments, are widely used because of their analytical tractability and good fit on financial data. These processes are recently used to build multivariate models able to incorporate linear and non-linear dependencies among assets. In fact, both linear and non-linear dependence may affect the price of a multi-asset derivative or the risk associated with a financial position.

One of the objectives of the present project is to build and characterize multivariate stochastic processes able to reproduce well-known stylized facts and with a flexible dependence structure. A way to build multivariate stochastic models in finance is to subordinate a Lévy process or, more in general, a Markov process.

Subordination has the nice economic interpretation of a change of time. The underlying idea is that the time runs fast when there are a lot of orders, while it slows down when trade is stale. If both the processes are of Lèvy type the resulting process is also Lèvy, otherwise we introduce time inhomogeneity using more general change of time.

Once the model has been built the objective becomes to calibrate the models on real data, and evaluate its fit properties.

8. Supervisor(s): Bruno Toaldo with Stefano Ferraris

A co-tutorship between Torino and Chambery USMB will be formalized for this project aiming to release of the double title between the two universities

Title: Stochastic modelling of subsurface water flow

Abstract:

The subsurface water flow in natural formations with multiscale heterogeneities exhibit complex patterns. Our aim is to efficiently represent this motion by resorting to stochastic models for anomalous transport (e.g., continuous time random walks, Lévy flights, Lévy walks). Validation of the models will be conducted with statistical methods and simulations.

The data will be available from two critical zone observatories. One is in the grassland of the Gran Paradiso national park at 2600 meters above sea level, the other is in an Alpi Cozie park forested catchment between 2000 and 600 m asl. The main measured variables are precipitation, snow height, discharge, water temperature, electrical conductivity, anions, cations, and stable isotope contents.

We develop models to analyse the data taken in both streams and springs. The final objective is to quantify and model the old water paradox, stating that the age of water parcels in river discharge can span from hours to years. This is a key issue to design and manage the hydroelectric energy plants, beside drinking water problems. In fact the time variability of river discharge is often very strong, especially as a consequence of climate change. Hydroelectric plants furnish fully renewable energy, and allow the storage of relevant quantity of potential energy at very low environmental costs. 

9. Supervisor(s):Bruno Toaldo

A co-tutorship between Torino and Pau, in the framework of UNITA- Universitas Montium,  will be formalized for this project aiming to release of the double title between the two universities

Title: Numerical approximations of non-local parabolic equations based on stochastic and finite elements methods and applications.

Abstract

Non-local equations in time arise in several applications, especially for modeling anomalous diffusion. In this context, it is very rare to have explicit solutions to the equations governing an anomalous diffusive phenomenon. However, numerical methods and stochastic representation can provide suitable approximations. The aim of this project is to determine whether stochastic representations and numerical approximations can be used in this context, and to compare the two approaches, whenever possible.

10. Supervisor(s): Marco Maggiora

Title: Investigation with multi-agent system models, within the framework of the H2020 Green Cities pillar, of urban permeability to butterflies motion and of their diffusion in mixed urban areas (buildings and green spaces).

Abstract

Experimental data recently collected on butterflies motion in Turin could be exploited, profiting as well of data available from different sources on buildings, green areas, water sources and traffic, in order to develop Multi Agents Systems that could later provide predictions and optimisation tools to design location, type and size of new green areas in European Cities.

A research group composed of Biologists and Physicists aims in fact to develop those tools needed to design cities in order to, within the framework of the H2020 Green Cities pillar, allow for and optimise the permeability of urban ecosystem to butterflies and other insects needed to sustain pollination for most of vegetables in urban environment.

Qualification Type: PhD
Location: Turin - Italy
Funding for: UK Students, EU Students, International Students
Funding amount: Not Specified
Hours: Full Time
Placed On: 20th April 2022
Closes: 30th May 2022
   
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