Florian Angeletti

2020

Of Zipper and Types,

F. Angeletti, Internet, (2020),

High-level error messages for modules through diffing,

F. Angeletti, G. Radanne, ICFP,OCaml workshop, Internet, (2020),

Abstract

Modules are one of the most complex features of ML languages. This complexity is reflected in error messages. Whenever two module types are mismatched,it is hard to identify and report the exact source of the error. Consequently,typecheckers often resort to printing the whole module types,and hope that the human user will navigate the sea of definitions. We propose to improve module error messages by coupling classical typechecking with a diffing algorithm. The typechecker deals with the gritty details of the ML module system whereas the diffing algorithm summarizes the error through a higher level view. The large literature on diffing algorithms allows us to pick and choose the exact algorithm adapted for signatures,functors applications,submodules,etc.

2019

Codept: a whole-project dependency analyzer for OCaml,

F. Angeletti, ICFP,OCaml workshop, Berlin, (2019),

Abstract

Computing accurate dependencies from source code is a complex task in OCaml. The canonical OCaml tool ocamldep tries to compute an over-approximation of dependencies. Codept is a new tool that goes one step further by using whole-project analysis to guarantee that inferred dependencies are exact in the absence of warnings.

2016

Diffusions conditioned on occupation measures,

F. Angeletti, NITheP seminar, Stellenbosch, (2016),

Abstract

How can we study the fluctuations far away from equilibrium of a Markov process? Echoes of this question appears in numerous applications: metastable states,quasi-stationary distributions or conditioned random walks. A simple example of Markov process is a diffusion process confined by a harmonic potential. At equilibrium this system spends most of this time oscillating around the potential minimum. What happens when this system goes far away from this equilibrium situation and spends an atypical amount of time inside a particular interval? To answer this question,this seminar shall explore a method based on the construction of a driven Markov process to approximate the conditioned process.

2015

Matrix-correlated random variables: a statistical physics and signal processing dialogue,

F. Angeletti, Séminaire LPT Toulouse, Toulouse, (2015),

Abstract

Finding statistical descriptions of non-equilibrium stationary state is often an arduous task. For specific systems,like ASEP or 1D diffusion-reaction systems,stationary solutions have been characterized using matrix product representations. These representations generalize the product structure of independent random variable to matrices; the non-commutativity of matrices generates correlation while preserving many of the algebraic properties of expectation. Depending on the matrix structure,the correlation can vary from short-range to long-range correlation. Moreover,from a signal processing perspective,these matrix-correlated random variables can be recast as specific Hidden Markov Models. In this talk,we propose to investigate the general statistical properties of this mathematical framework,with the long-term hope to improve our understanding of related physical systems. In particular,we shall focus on the statistical properties of sums of such random variables. Do we have a large deviation principle for this sum? Can we find analogous of the law of large number or the central limit theorem?

Matrix-correlated random variables: a statistical physics and signal processing dialogue,

F. Angeletti, Séminaire LPTMS Orsay, Orsay, (2015),

Abstract

Finding statistical descriptions of non-equilibrium stationary state is often an arduous task. For specific systems,like ASEP or 1D diffusion-reaction systems,stationary solutions have been characterized using matrix product representations. These representations generalize the product structure of independent random variable to matrices; the non-commutativity of matrices generates correlation while preserving many of the algebraic properties of expectation. Depending on the matrix structure,the correlation can vary from short-range to long-range correlation. Moreover,from a signal processing perspective,these matrix-correlated random variables can be recast as specific Hidden Markov Models. In this talk,we propose to investigate the general statistical properties of this mathematical framework,with the long-term hope to improve our understanding of related physical systems. In particular,we shall focus on the statistical properties of sums of such random variables. Do we have a large deviation principle for this sum? Can we find analogous of the law of large number or the central limit theorem?

Diffusions conditioned on occupation measures,

F. Angeletti, Club Journal LPT, Orsay, (2015),

Critical order for moment estimation : insights from statistical physics.,

F. Angeletti, Club journal LPT Orsay, Orsay, (2015),

Abstract

Moment estimation is one of the most basic question in statistical signal processing. For i.i.d. random variables and a infinite number of observations,the law of large numbers implies that the classical moment estimator converges towards the theoretical moment. However,these hypothesis are not really satisfied in practical settings where only a finite number of observations is available and most data are correlated. It is therefore quite natural to ask ourselves: up to which order can moments be reliably estimated from a given number of observation? In this presentation,I will show how the notion of glassy phase transition developed for studying disordered systems in statistical physics can help to answer such a question.

Matrix-correlated random variables: A statistical physics and signal processing duet,

F. Angeletti, Séminaire I2M, Marseille, (2015),

2014

Matrix-correlated random variables: A statistical physics and signal processing duet,

F. Angeletti, Séminaire GPS, Nancy, (2014),

Large deviation for matrix-correlated random variables,

F. Angeletti, NIThep Workshop on large deviations in statistical physics, Stellenbosch, (2014),

Abstract

Inspired by out-of-equilibrium physics,matrix-correlated random variables generalize the product structure of independent random variables to matrices. The non-commutativity of matrices generates correlation while preserving many of the algebraic properties of expectation. Moreover,depending on the matrix structure,the correlation can vary from short-range correlation to long-range correlation. These matrix-correlated random variables constitutes therefore an interesting framework to study the effect of long-range correlation on the large deviation function or the limit distributions of the sum. In particular,it is possible to construct strongly correlated random variable whose sum admits non strictly convex rate functions.

2013

Random vectors with a matrix representation: a framework for out-of-equilibrium systems,

F. Angeletti, NIThep seminary, Stellenbosch, (2013),

Abstract

The Matrix Product Ansatz has become a classical tool for the study of the stationary distribution of out-of-equilibrium physical systems. In particular,the ASEP model and its many variants admits an exact solution using this Matrix Product Ansatz. In this talk,we propose a reversal of perspective and investigate the general statistical properties of random vectors whose joint pdf can be described with a matrix representation. In particular,we show that these random vectors can be recast as a specific non-homogeneous Hidden Markov Model. This dual representation opens interesting ways to characterize the correlation structure or synthesize random vector with prescribed statistical properties. An other application of this framework is the study of the sum of random variables with matrix representation. Depending on the nature of the correlation,non-standard extension of the law of large numbers and the central limit theorems can be constructed. Similarly,the derivation of a large deviation principle leads to non-convex or flat rate function in presence of long-range correlations.

Vecteurs aléatoires à représentation matricielle: Une rencontre entre Matrix Product Ansatz et Hidden Markov Models,

F. Angeletti, Séminaire LPMA, Paris, (2013),

Critical order for moment estimation : insights from statistical physics.,

F. Angeletti, LATP seminary, Marseille, (2013),

Abstract

Moment estimation is one of the most basic question in statistical signal processing. For i.i.d. random variables and a infinite number of observations,the law of large numbers implies that the classical moment estimator converges towards the theoretical moment. However,these hypothesis are not really satisfied in practical settings where only a finite number of observations is available and most data are correlated. It is therefore quite natural to ask ourselves: up to which order can moments be reliably estimated from a given number of observation? In this presentation,I will show how the notion of glassy phase transition developed for studying disordered systems in statistical physics can help to answer such a question.

Random vectors with matrix representation: Insights from statistical physics,

F. Angeletti, Max Planck Institute for the Physics of Complex Systems, Dresden, (2013),