OxCSML seminar this week: Alessandro Barp
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Hai Dang Dau
Jan 29, 2024, 4:47:43 AM1/29/24
to oxc...@googlegroups.com, oxcsml...@googlegroups.com
Dear all,
This week we
welcome Alessandro Barp from Turing Institute to give a talk in our
OxCSML seminar entitled "What is a distribution? Constructing a
geometric backbone for statistical methodologies". The details are
below. Looking forward to seeing you there.
Kind regards,
Saif & Hai-Dang.
===============
Speaker: Alessandro Barp, Turing Institute
Time and date: 2pm-3pm, Friday 2 Feb
Place: Room LG03 (Small Lecture Theatre), Dept. of Statistics, Oxford
Title: What is a distribution? Constructing a geometric backbone for statistical methodologies
Abstract: Many powerful methods in statistics and machine learning, such as Hamiltonian/Langevin algorithms, flow matching, gradient descent, reproducing kernel methods, and score-based discrepancies, are inherently geometric. However, geometry remains notably absent from the curriculum of most statistics departments, underscoring the perception it isn’t an integral part of statistics. In this talk, we argue that this misconception stems from the formalisation of distributions as probability measures, which tends to isolate statistics from the rest of mathematics. Instead, we propose employing the powerful intrinsic geometry of smooth distributions as a mathematical backbone for statistics, upon which generalisations (e.g., discrete or non-commutative distributions) can be gradually constructed. In particular, we characterise the differential information of distributions used in score-based methods, explaining why it is not given by the log-density gradient, but rather by Lie algebroids that specify three differential operators, (i) the canonical Stein operator, (ii) the curl, which describes measure-preserving systems; (iii) and a covariant derivative that generate statistical discrepancies, providing a unified perspective on log-density derivatives, score-matching, and canonical Stein discrepancies. Remarkably, key abstract mathematical ideas (e.g., the dualities between gradient-driven mechanics and calculus, or between geometric spaces and function spaces) naturally emerge as we merely reflect on the structure of distributions, which helps us navigate the sporadic emergence of geometric tools across applications.
Zoom: https://zoom.us/j/99855897488?pwd=WnUxZVJ0ZHQ2UjVRK2xSVW9kN2xiZz09
Time and date: 2pm-3pm, Friday 2 Feb
Place: Room LG03 (Small Lecture Theatre), Dept. of Statistics, Oxford
Title: What is a distribution? Constructing a geometric backbone for statistical methodologies
Abstract: Many powerful methods in statistics and machine learning, such as Hamiltonian/Langevin algorithms, flow matching, gradient descent, reproducing kernel methods, and score-based discrepancies, are inherently geometric. However, geometry remains notably absent from the curriculum of most statistics departments, underscoring the perception it isn’t an integral part of statistics. In this talk, we argue that this misconception stems from the formalisation of distributions as probability measures, which tends to isolate statistics from the rest of mathematics. Instead, we propose employing the powerful intrinsic geometry of smooth distributions as a mathematical backbone for statistics, upon which generalisations (e.g., discrete or non-commutative distributions) can be gradually constructed. In particular, we characterise the differential information of distributions used in score-based methods, explaining why it is not given by the log-density gradient, but rather by Lie algebroids that specify three differential operators, (i) the canonical Stein operator, (ii) the curl, which describes measure-preserving systems; (iii) and a covariant derivative that generate statistical discrepancies, providing a unified perspective on log-density derivatives, score-matching, and canonical Stein discrepancies. Remarkably, key abstract mathematical ideas (e.g., the dualities between gradient-driven mechanics and calculus, or between geometric spaces and function spaces) naturally emerge as we merely reflect on the structure of distributions, which helps us navigate the sporadic emergence of geometric tools across applications.
Zoom: https://zoom.us/j/99855897488?pwd=WnUxZVJ0ZHQ2UjVRK2xSVW9kN2xiZz09
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