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Hi, I'm Pier! I am a PhD student at Princeton University, part of ORFE department and the ML theory group.
My interests lie in Machine Learning Theory and the mathematics to develop it. I'm fortunate to be advised by
Prof. Boris Hanin and
Prof. Jason D. Lee.
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I am a mathematician working on the theory of machine learning.
My work is motivated by enabling the deployment of machine learning techniques in safety critical contexts.
I believe that developing a theory for deep learning is key to assessing when its use is harmful and to what extent.
So, my long term objective is to understand which machine learning model works in what setting, how well, and why.
Currently, I am working towards this goal by trying to gain a theoretical understanding of what neural networks we find by studying the optimization problem behind them.
More precisely, I am investigating the implicit effect of SGD as it is a fundamental step towards understanding the generalization capabilities of neural networks.
Check out my new paper: On the Trajectories of SGD Without Replacement |
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On the Trajectories of SGD Without Replacement.
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Deep neural network approximation theory for high-dimensional functions.
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High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations.
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Optimization
, Princeton University, Spring 2024.
Audience: Students from various bachelors. Tasks: Teach Precepts, Hold office hours, grade homeworks and exams, organization. Contents: An introduction to several fundamental and practically-relevant areas of modern optimization and numerical computing. Topics include computational linear algebra, first and second order descent methods, convex sets and functions, basics of linear and semidefinite programming, optimization for statistical regression and classification, and techniques for dealing with uncertainty and intractability in optimization problems. Extensive hands-on experience with high-level optimization software. Applications drawn from operations research, statistics and machine learning, economics, control theory, and engineering. |
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Computing and Optimization for the Physical and Social Sciences
, Princeton University, Fall 2023.
Audience: Students from various bachelors. Tasks: Hold office hours, grade homeworks and exams, organization. Contents: An introduction to several fundamental and practically-relevant areas of modern optimization and numerical computing. Topics include computational linear algebra, first and second order descent methods, convex sets and functions, basics of linear and semidefinite programming, optimization for statistical regression and classification, and techniques for dealing with uncertainty and intractability in optimization problems. Extensive hands-on experience with high-level optimization software. Applications drawn from operations research, statistics and machine learning, economics, control theory, and engineering. |
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Analysis of Big Data, Princeton University, Spring 2023.
Audience: Students from various bachelors. Tasks: Head TA. Teach the precepts, hold office hours, grade homeworks and exams. Contents: This course is a theoretically oriented introduction to the statistical tools that underpin modern machine learning, whose hallmarks are large datasets and/or complex models. Topics include a rigorous analysis of dimensionality reduction, a survey of models ranging from regression to neural networks, and an analysis of learning algorithms. |
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Analysis of Big Data, Princeton University, Spring 2022.
Audience: Students from various bachelors. Tasks: Teach the precepts, hold office hours, grade homeworks and exams. Contents: This course is a theoretically oriented introduction to the statistical tools that underpin modern machine learning, whose hallmarks are large datasets and/or complex models. Topics include a rigorous analysis of dimensionality reduction, a survey of models ranging from regression to neural networks, and an analysis of learning algorithms. |
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Energy and Commodities Markets, Princeton University, Fall 2021.
Audience: Master in Finance and BSc in Operations Research and Financial Engineering. Tasks: Teach the precepts, hold office hours, grade homeworks and exams (Python, Excel, and theory). Contents: This course is an introduction to commodities markets (oil, gas, metals, electricity, etc.), and quantitative approaches to capturing uncertainties in their demand and supply. We start from a financial perspective, and traditional models of commodity spot prices and forward curves. Then we cover modern topics: game theoretic models of energy production (OPEC vs. fracking vs. renewables); quantifying the risk of intermittency of solar and wind output on the reliability of the electric grid (mitigating the duck curve); financialization of commodity markets; carbon emissions markets; cryptocurrencies as commodities. We also discuss economic and policy implications. |
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Numerical Methods for Partial Differential Equations, ETH Zurich, Spring 2020.
Audience: Master in Physics, Data Science, Computational Biology. Bachelor in Computational Science and Engineering. Tasks: Teach the precepts and grade the homeworks (C++ and theory). Contents: Derivation, properties, and implementation of fundamental numerical methods for a few key partial differential equations: convection-diffusion, heat equation, wave equation, conservation laws. Implementation in C++ based on a finite element library. |
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Computational Methods for Engineering Applications, ETH Zurich, Fall 2019.Audience: Bachelor in Mechanical Engineering. Tasks: Teach the precepts and grade the homeworks (C++ and theory). Contents: Introduction to the numerical methods for the solution of ordinary and partial differential equations that play a central role in engineering applications. Both basic theoretical concepts and implementation techniques necessary to understand and master the methods are addressed. |
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Lately, I'm getting increasingly interested in the ethical aspects of my job. I am contributing to the organization of multiple events to raise the awareness of the community around the responsibilities of modelers and statisticians for the high-stakes decisions and policies that are based on their work.
See
CEST-UCL Seminar series on responsible modelling and check out our conference.
I'm in the committee of the Princeton AI Club (PAIC)! Follow us on twitter! We'll host a lot of exciting talks featuring Yoshua Bengio, Max Welling, Chelsea Finn, Tamara Broderick, etc. |
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Last modified on Feb 23rd 2023. |
Template credits to Jon Barron! |