Échantillonnage de Gibbs | EPFL Graph Search

L' est une méthode MCMC. Étant donné une distribution de probabilité sur un univers , cet algorithme définit une chaîne de Markov dont la distribution stationnaire est . Il permet ainsi de tirer aléatoirement un élément de selon la loi (on parle d'échantillonnage). Introduction Comme pour toutes les méthodes de Monte-Carlo à chaîne de Markov,

on se place dans un espace vectoriel Ɛ de dimension finie n ;
on veut générer aléatoirement N vecteurs x(i) suivant une distribution de probabilité π ;
pour simplifier le problème, on détermine une distribution qx(i) permettant de générer aléatoirement x(i + 1) à partir de x(i). La spécificité de l'échantillonnage de Gibbs consiste à « découper » qx(i) en n probabilités conditionnelles :
la première composante du vecteur, x(i + 1)1, est générée à partir de la probabilité conditionnelle π(x1|x(i)2, x(i)3, …, x(i)n) ;
la seconde composante du vecteur, x(i + 1)2, est générée à partir de la probabilité conditionnelle π(x2|

Subtree-based bounds and simulation-based estimations for the partition function

Mehdi Molkaraie

Many different algorithms developed in statistical physics, coding theory, signal processing, and artificial intelligence can be expressed by graphical models and solved (either exactly or approximately) with iterative message-passing algorithms on the model. One quantity of interest in these algorithms is the partition function. In graphical models without cycle (trees), the partition function can be computed efficiently by means of message-passing algorithms, like GDL or the sum-product algorithm. In contrast, when graphical models contain cycles, the computation of the partition function is in general intractable. Our contributions in this dissertation are: deriving deterministic upper and lower bounds on partition function, and developing methods to approximate this quantity with Monte Carlo methods. Specifically, we obtain subtree-based upper and lower bounds which lead to theoretical results on optimality properties of the minimum entropy sub-tree and finally lead to a greedy algorithm. At last, we introduce and analyze a number of estimators that use Gibbs sampling to draw samples from different target distributions to estimate the value of the partition function. In one estimator, we demonstrate a novel strategy which combines Gibbs sampling and message-passing algorithms on trees.

EPFL2007

Work fluctuations in the active Ornstein-Uhlenbeck particle model

Francesco Cagnetta

We study the large deviations of the power injected by the active force for an active Ornstein-Uhlenbeck particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by (a) direct sampling of the active work in numerical solutions of the AOUP equations and (b) Legendre-Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system's dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods (a) and (b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation-dissipation theorem.

IOP Publishing Ltd2021

A neural probe to sample brain fluid in nanoliter volumes for quantitative molecular studies

Joan Teixidor

Neural functions operate in tightly controlled conditions that are mediated by multiple electrical and chemical phenomena. Brain disorders such as Parkinson's Disease and Alzheimer's Disease perturb these conditions and cause a loss of neurons, which impairs the motor and cognitive functions. Thus, an access to the concentration of the neurochemicals in the brain and to their temporal evolution would be an asset to understand these diseases better and develop treatments that could stop their progression and even restore neural functions.Among the techniques to measure neurochemicals in the brain, fluid sampling approaches such as microdialysis allow the continuous collection of molecules from the extracellular fluid (ECF), by diffusion in a perfusate that can be retrieved and analyzed offline. However, these experiments can be long and the real concentration of the molecules in the ECF cannot be quantified directly from the samples. This thesis aims to propose a solution to these limitations; thus, a new sampling approach called Droplet on Demand (DoD) and a neural probe for it were developed.The DoD approach is inspired by the theoretical foundations of microdialysis and by the limitations of continuous sampling methods. Thus, it is proposed as a sequential sampling method in steps: a perfusion step to create a pocket of perfusate in the brain, a diffusion step to capture molecules in this pocket, a sampling step to collect the pocket and the molecules in a droplet, and a phase to let the concentration in the ECF equilibrate. This offers a way to collect samples that closely reflect the molecular concentration in the ECF for quantitative molecular studies. Moreover, the DoD can be applied on-demand, to probe the molecules in the ECF at specific experimental times, punctually or repeatedly.The neural probe was fabricated with polyimide and SU-8 technologies to implement the DoD approach during acute experiments in the brain of mice. It integrates microfluidic channels, droplet-sensing electrodes, and a stimulation electrode in its 320 µm wide and 80 µm thick needle. An optical fiber was also added to it for optical stimulation.The concepts of the DoD were illustrated in simulations and confirmed in experiments in agarose brain phantoms in vitro. They showed that the diffusion time allows tuning the concentration of the molecules collected in the samples, with stable characteristics over repeated sampling events. Acute in vivo experiments were also performed in mice and samples of typically 24.4 nL were collected every 1 to 2 minutes, 20 minutes after inserting the probe. The samples were stored in a capillary and an analytical procedure with mass spectrometry was developed to confirm the properties of the DoD for the quantification of glucose in the brain. This also allowed the detection of acetylcholine and glutamate. Finally, a module for chronoamperometric measurement of dopamine (DA) was developed with pyrolyzed carbon electrodes, and proof-of-concept experiments showed that it could be coupled to the outlet of the probe for DA measurement in droplets.By combining the probe and the DoD with the appropriate analytical methods, quantitative molecular studies of neurotransmitters, metabolites, proteins, or even ribonucleic acids (RNAs) could now be envisioned. They would benefit from the electrical, chemical, and optical stimulation features of the probe and from the accurate chemical recording enabled by the DoD approach.

EPFL2022

A neural probe to sample brain fluid in nanoliter volumes for quantitative molecular studies

Joan Teixidor

EPFL2022