Free energy Sequential Monte Carlo, application to mixture modelling

We introduce a new class of Sequential Monte Carlo (SMC) methods, which we call free energy SMC. This class is inspired by free energy methods, which originate from Physics, and where one samples from a biased distribution such that a given function $\xi(\theta)$ of the state $\theta$ is forced to be uniformly distributed over a given interval. From an initial sequence of distributions $(\pi_t)$ of interest, and a particular choice of $\xi(\theta)$, a free energy SMC sampler computes sequentially a sequence of biased distributions $(\tilde{\pi}_{t})$ with the following properties: (a) the marginal distribution of $\xi(\theta)$ with respect to $\tilde{\pi}_{t}$ is approximatively uniform over a specified interval, and (b) $\tilde{\pi}_{t}$ and $\pi_{t}$ have the same conditional distribution with respect to $\xi$. We apply our methodology to mixture posterior distributions, which are highly multimodal. In the mixture context, forcing certain hyper-parameters to higher values greatly faciliates mode swapping, and makes it possible to recover a symetric output. We illustrate our approach with univariate and bivariate Gaussian mixtures and two real-world datasets.Comment: presented at "Bayesian Statistics 9" (Valencia meetings, 4-8 June 2010, Benidorm

Comments on "Particle Markov chain Monte Carlo" by C. Andrieu, A. Doucet, and R. Hollenstein

This is the compilation of our comments submitted to the Journal of the Royal Statistical Society, Series B, to be published within the discussion of the Read Paper of Andrieu, Doucet and Hollenstein.Comment: 7 pages, 4 figure

Potential and constraints for applying the "4 per 1000 Initiative" in the Caribbean: the case of Guadeloupe

This paper assesses the feasibility of the 4 per 1000 initiative for agricultural soils in the tropics more specifically in Guadeloupe, as a representative case study of the Caribbean and other tropical regions. We used a locally adapted and calibrated model describing soil organic carbon dynamics under the impact of climate change and a broad range of scenarios combining increased use of organic amendments, reduced soil tillage, and increased land area for the local market. We found that, in its current state, only 26% of agricultural area could achieve a 4 parts per thousand year(-1) increase in soil organic carbon (SOC) stocks in the coming 30 years, due mainly to perennial cropping systems (sugarcane, banana, orchards) occupying soils with the lowest SOC stocks. Implementing reduced tillage with increased use of locally produced composts would increase the agricultural area reaching the 4 per 1000 target to 31%. However, at territory scale, all scenarios tested showed an annual decrease in SOC stocks varying from - 0.1 to - 3.2 parts per thousand. The limited area on which the 4 per 1000 target is feasible and generalized SOC losses were mainly linked to the current high SOC stocks in volcanic and calcareous soils on the island and lack of practices capable of further increasing C inputs in current cropping systems. We concluded that C sequestration potential in the Caribbean is rather limited and that increasing SOC stocks, even lower than 4 per 1000, should be the primary target in adaptation to climate change, by increasing the resilience of cropping systems based mainly on SOC-poor soils

PAC-Bayesian Offline Contextual Bandits With Guarantees

This paper introduces a new principled approach for off-policy learning in contextual bandits. Unlike previous work, our approach does not derive learning principles from intractable or loose bounds. We analyse the problem through the PAC-Bayesian lens, interpreting policies as mixtures of decision rules. This allows us to propose novel generalization bounds and provide tractable algorithms to optimize them. We prove that the derived bounds are tighter than their competitors, and can be optimized directly to confidently improve upon the logging policy offline. Our approach learns policies with guarantees, uses all available data and does not require tuning additional hyperparameters on held-out sets. We demonstrate through extensive experiments the effectiveness of our approach in providing performance guarantees in practical scenarios.Comment: Accepted to ICML 202

SMC^2: an efficient algorithm for sequential analysis of state-space models

We consider the generic problem of performing sequential Bayesian inference in a state-space model with observation process y, state process x and fixed parameter theta. An idealized approach would be to apply the iterated batch importance sampling (IBIS) algorithm of Chopin (2002). This is a sequential Monte Carlo algorithm in the theta-dimension, that samples values of theta, reweights iteratively these values using the likelihood increments p(y_t|y_1:t-1, theta), and rejuvenates the theta-particles through a resampling step and a MCMC update step. In state-space models these likelihood increments are intractable in most cases, but they may be unbiasedly estimated by a particle filter in the x-dimension, for any fixed theta. This motivates the SMC^2 algorithm proposed in this article: a sequential Monte Carlo algorithm, defined in the theta-dimension, which propagates and resamples many particle filters in the x-dimension. The filters in the x-dimension are an example of the random weight particle filter as in Fearnhead et al. (2010). On the other hand, the particle Markov chain Monte Carlo (PMCMC) framework developed in Andrieu et al. (2010) allows us to design appropriate MCMC rejuvenation steps. Thus, the theta-particles target the correct posterior distribution at each iteration t, despite the intractability of the likelihood increments. We explore the applicability of our algorithm in both sequential and non-sequential applications and consider various degrees of freedom, as for example increasing dynamically the number of x-particles. We contrast our approach to various competing methods, both conceptually and empirically through a detailed simulation study, included here and in a supplement, and based on particularly challenging examples.Comment: 27 pages, 4 figures; supplementary material available on the second author's web pag

­Reprendre la leçon, renouer le temps didactique : spiralité du temps du savoir et ajustement contractuel de début de séance en physique seconde

L’article convoque le modèle de l’hétérogénéisation (Sarrazy, 2002 ; Chopin 2007, 2011) et les recherches sur la mémoire didactique (Brousseau & Centeno, 1991) pour mettre en évidence la dimension spiralaire du temps de la diffusion des savoirs dans la classe, rarement prise en compte dans les recherches sur l’enseignement. L’analyse d’une leçon de physique en classe de seconde supporte la démonstration. Elle permet de montrer, par l’examen statistique des mentions temporelles jalonnant la séance observée (évocation du passé, anticipation de l’à-venir), la manière dont professeur et élèves sont co-impliqués dans le projet de construction d’une temporalité commune, nécessitant, en vue de sa clôture, un retour minimal et partagé sur le passé didactique de la classe.This article summons up the model of heterogenisation (Sarrazy, 2002 ; Chopin 2007, 2011) and the research on didactic memory (Brousseau & Centeno, 1991). It aims to show evidence of the spiral dimension of the time of knowledge within the class, which is rarely taken into account among educational research. The analysis of a physics lesson in Fifth Form (10th grade USA) supports the demonstration. The statistic examinal of temporal mentions which mark out the observed lesson (evocation of past, anticipation of future) reveals how teacher and pupils are co-implicated in the project of building a common temporality, needing a minimal and shared feedback on class’ didactic past in order to be closed

Les usages du « temps » dans les recherches sur l’enseignement

Les perspectives praxéologiques, voire prescriptives, s’esquissant à partir de la question temporelle dans le champ scolaire sont nombreuses et hétéroclites : allongement ou raccourcissement du temps d’enseignement, rationalisation du temps de travail des professeurs, individualisation des temps d’apprentissage des élèves, etc. Leitmotiv tenace, la thématique du temps surgit régulièrement dans les discours sur l’école, suscitant à chaque fois d’intenses espoirs de changement. Le recensement des travaux menés à son propos fait apparaître ce phénomène de répétition/recomposition. Il constitue également une étape indispensable à la clarification des fondements et des limites de l’entreprise visant à instituer le temps comme une variable-clé de l’amélioration du système d’enseignement.There are numerous and disparate praxeological, even prescriptive perspectives that are drawn from the question of time at school: Longer or shorter school-days; rationalizing the teachers’ work-time; individualizing the students’ learning periods, etc. The time issue is a tenacious leitmotif and regularly comes back in debates over schools. Each time it raises intense hope of change. Inventorying the works on this subject has revealed its repetition/reconstructing element. It is also a necessary step to clarify the basis and limits for initiatives aiming at setting time as a key-element to the betterment of the teaching system.Las perspectivas praxeológicas, incluso prescriptivas, que se esbozan a partir de la cuestión temporal en el campo escolar son numerosas y heteróclitas: tiempo de enseñanza que se alarga o se acorta, racionalización del tiempo laboral de los docentes, individualización de los tiempos de aprendizaje de los alumnos, etc. Leitmotiv tenaz, la temática del tiempo surge de manera regular en los discursos sobre la escuela y suscita cada vez intensas esperanzas de cambio. El inventario de los trabajos realizados a su propósito hace aparecer ese fenómeno de repetición/recomposición. Asimismo constituye una etapa imprescindible para la clarificación de los fundamentos y de los límites de la empresa que trata de instituir el tiempo como una variable clave del mejoramiento del sistema de enseñanza.Die praxeologischen, ja sogar vorschriftsmäßigen Perspektiven, die man aus der Zeitfrage im schulischen Rahmen herleiten kann, sind zahlreich und vielförmig: Verlängerung oder Verkürzung der Lehrzeit, Rationalisierung der Arbeitszeit der Lehrer, Individualisierung der Lernzeit der Schüler, usw. Die Thematik der Zeit ist ein hartnäckiges Leitmotiv, taucht oft in Reden über die Schule auf und schürt dabei jedes Mal erneut große Hoffnungen auf Veränderung. Ein Überblick über diesbezügliche Forschungsarbeiten lässt dieses Phänomen der Wiederholung/Neugestaltung erscheinen. Es stellt ebenso eine unentbehrliche Etappe in der Klärung der Grundlagen und Grenzen des Unternehmens dar, das dazu tendiert, die Zeit als eine Schlüsselvariable in der Verbesserung des Schulsystems einzurichten