Descrizione del progetto
Oltre l’integrazione di Monte Carlo
Il concetto alla base degli esperimenti di Monte Carlo, un’ampia classe di algoritmi computazionali che si basano su ripetuti campionamenti casuali per ottenere risultati numerici, è quello di utilizzare la casualità per risolvere problemi che in linea di principio possono essere deterministici. Il progetto BLACKJACK, finanziato dall’UE, si propone di fornire metodi Monte Carlo che consentono l’inferenza per modelli costosi in biologia, affrontando direttamente la scarsa velocità di convergenza e la parallelizzazione degli stessi. In ultimo, il progetto prevede di abbattere la velocità di Monte Carlo, per introdurre la repulsione tra i nodi in quadratura, producendo un nuovo strumento per gli statistici applicati, i processori di segnale e i dispositivi di apprendimento automatico.
Obiettivo
Expensive computer simulations have become routine in the experimental sciences. Astrophysicists design complex models of the evolution of galaxies, biologists develop intricate models of cells, ecologists model the dynamics of ecosystems at a world scale. A single evaluation of such complex models takes minutes or hours on today's hardware. On the other hand, fitting these models to data can require millions of serial evaluations. Monte Carlo methods, for example, are ubiquitous in statistical inference for scientific data, but they scale poorly with the number of model evaluations. Meanwhile, the use of parallel computing architectures for Monte Carlo is often limited to running independent copies of the same algorithm. Blackjack will provide Monte Carlo methods that unlock inference for expensive models in biology by directly addressing the slow rate of convergence and the parallelization of Monte Carlo methods.
The key to take down the Monte Carlo rate is to introduce repulsiveness between the quadrature nodes. For instance, we recently proved that determinantal point processes, a prototypal repulsive distribution introduced in physics, improve the Monte Carlo convergence rate, just like electrons lead to low-variance estimation of volumes by efficiently filling a box. Such results lead to open computational and statistical challenges. We propose to solve these challenges, and make repulsive processes a novel tool for applied statisticians, signal processers, and machine learners.
Still with repulsiveness as a hammer, we will design the first parallel Markov chain Monte Carlo algorithms that are qualitatively different from running independent copies of known algorithms, i.e. that explicitly improve the order of convergence of the single-machine algorithm. To this end, we will turn mathematical tools such as repulsive particle systems and non-colliding processes into computationally cheap, communication-efficient Monte Carlo schemes with fast convergence.
Campo scientifico
Programma(i)
Argomento(i)
Meccanismo di finanziamento
ERC-STG - Starting GrantIstituzione ospitante
75794 Paris
Francia