Scalable Learning of Bayesian Networks Using Feedback Arc Set-Based Heuristics

Bayesianske nettverk er en viktig klasse av probabilistiske grafiske modeller. De består av en struktur (en rettet asyklisk graf) som beskriver betingede uavhengighet mellom stokastiske variabler og deres parametere (lokale sannsynlighetsfordelinger). Med andre ord er Bayesianske nettverk generative modeller som beskriver simultanfordelingene på en kompakt form. Den største utfordringen med å lære et Bayesiansk nettverk skyldes selve strukturen, og på grunn av den kombinatoriske karakteren til asyklisitetsegenskapen er det ingen overraskelse at strukturlæringsproblemet generelt er NP-hardt. Det eksisterer algoritmer som løser dette problemet eksakt: dynamisk programmering og heltalls lineær programmering er de viktigste kandidatene når man ønsker å finne strukturen til små til mellomstore Bayesianske nettverk fra data. På den annen side er heuristikk som bakkeklatringsvarianter ofte brukt når man forsøker å lære strukturen til større nettverk med tusenvis av variabler, selv om disse heuristikkene vanligvis ikke har teoretiske garantier og ytelsen i praksis kan bli uforutsigbar når man arbeider med storskala læring. Denne oppgaven tar for seg utvikling av skalerbare metoder som takler det strukturlæringsproblemet av Bayesianske nettverk, samtidig som det forsøkes å opprettholde et nivå av teoretisk kontroll. Dette ble oppnådd ved bruk av relaterte kombinatoriske problemer, nemlig det maksimale asykliske subgrafproblemet (maximum acyclic subgraph) og det duale problemet (feedback arc set). Selv om disse problemene er NP-harde i seg selv, er de betydelig mer håndterbare i praksis. Denne oppgaven utforsker måter å kartlegge Bayesiansk nettverksstrukturlæring til maksimale asykliske subgrafforekomster og trekke ut omtrentlige løsninger for det første problemet, basert på løsninger oppnådd for det andre. Vår forskning tyder på at selv om økt skalerbarhet kan oppnås på denne måten, er det adskillig mer utfordrende å opprettholde den teoretisk forståelsen med denne tilnærmingen. Videre fant vi ut at å lære strukturen til Bayesianske nettverk basert på maksimal asyklisk subgraf kanskje ikke er den beste metoden generelt, men vi identifiserte en kontekst - lineære strukturelle ligningsmodeller - der vi eksperimentelt kunne validere fordelene med denne tilnærmingen, som fører til rask og skalerbar identifisering av strukturen og med mulighet til å lære komplekse strukturer på en måte som er konkurransedyktig med moderne metoder.Bayesian networks form an important class of probabilistic graphical models. They consist of a structure (a directed acyclic graph) expressing conditional independencies among random variables, as well as parameters (local probability distributions). As such, Bayesian networks are generative models encoding joint probability distributions in a compact form. The main difficulty in learning a Bayesian network comes from the structure itself, owing to the combinatorial nature of the acyclicity property; it is well known and does not come as a surprise that the structure learning problem is NP-hard in general. Exact algorithms solving this problem exist: dynamic programming and integer linear programming are prime contenders when one seeks to recover the structure of small-to-medium sized Bayesian networks from data. On the other hand, heuristics such as hill climbing variants are commonly used when attempting to approximately learn the structure of larger networks with thousands of variables, although these heuristics typically lack theoretical guarantees and their performance in practice may become unreliable when dealing with large scale learning. This thesis is concerned with the development of scalable methods tackling the Bayesian network structure learning problem, while attempting to maintain a level of theoretical control. This was achieved via the use of related combinatorial problems, namely the maximum acyclic subgraph problem and its dual problem the minimum feedback arc set problem. Although these problems are NP-hard themselves, they exhibit significantly better tractability in practice. This thesis explores ways to map Bayesian network structure learning into maximum acyclic subgraph instances and extract approximate solutions for the first problem, based on the solutions obtained for the second. Our research suggests that although increased scalability can be achieved this way, maintaining theoretical understanding based on this approach is much more challenging. Furthermore, we found that learning the structure of Bayesian networks based on maximum acyclic subgraph/minimum feedback arc set may not be the go-to method in general, but we identified a setting - linear structural equation models - in which we could experimentally validate the benefits of this approach, leading to fast and scalable structure recovery with the ability to learn complex structures in a competitive way compared to state-of-the-art baselines.Doktorgradsavhandlin

Coherent population trapping in a Raman atom interferometer

We investigate the effect of coherent population trapping (CPT) in an atom inter-ferometer gravimeter based on the use of stimulated Raman transitions. We find that CPT leads to significant phase shifts, of order of a few mrad, which may compromise the accuracy of inertial measurements. We show that this effect is rejected by the k-reversal technique, which consists in averaging inertial measurements performed with two opposite orientations of the Raman wavevector k, provided that internal states at the input of the interferometer are kept identical for both configurations

Stability comparison of two absolute gravimeters: optical versus atomic interferometers

We report the direct comparison between the stabilities of two mobile absolute gravimeters of different technology: the LNE-SYRTE Cold Atom Gravimeter and FG5X\#216 of the Universit\'e du Luxembourg. These instruments rely on two different principles of operation: atomic and optical interferometry. The comparison took place in the Walferdange Underground Laboratory for Geodynamics in Luxembourg, at the beginning of the last International Comparison of Absolute Gravimeters, ICAG-2013. We analyse a 2h10 duration common measurement, and find that the CAG shows better immunity with respect to changes in the level of vibration noise, as well as a slightly better short term stability.Comment: 6 page

Effective velocity distribution in an atom gravimeter: effect of the convolution with the response of the detection

We present here a detailed study of the influence of the transverse motion of the atoms in a free-fall gravimeter. By implementing Raman selection in the horizontal directions at the beginning of the atoms free fall, we characterize the effective velocity distribution, ie the velocity distribution of the detected atom, as a function of the laser cooling and trapping parameters. In particular, we show that the response of the detection induces a pronounced asymetry of this effective velocity distribution that depends not only on the imbalance between molasses beams but also on the initial position of the displaced atomic sample. This convolution with the detection has a strong influence on the averaging of the bias due to Coriolis acceleration. The present study allows a fairly good understanding of results previously published in {\it Louchet-Chauvet et al., NJP 13, 065025 (2011)}, where the mean phase shift due to Coriolis acceleration was found to have a sign different from expected

Développement d'un système analytique pour la datation in situ des roches martiennes par la méthode K-Ar

Sur Mars, la datation par comptage de densité de cratères est actuellement la seule méthode utilisée pour dater les surfaces planétaires. Cependant, sur Mars, elle n a pas encore été corrigé et complété par des datations absolues. Ce travail consiste à développer un prototype démontrant le potentiel d une nouvelle approche expérimentale basée sur la méthode K-Ar pour dater les roches martiennes in situ. L objectif à terme est de proposer une solution instrumentale de datation absolue pour un futur rover d exploration.Un laser Nd :YAG quadruplé pour tirer à 266 nm ablate un échantillon basaltique mis sous vide secondaire. L observation du plasma par Laser Induced Breakdown Spectroscopy apporte des informations sur la concentration en K et sur la nature chimique et minéralogique de la cible. Puisque l ablation est faite par un laser UV et sous vide secondaire, l ablation est reproductible par minéralogie. La reconnaissance stoechiométrique permet donc d estimer la masse vaporisée. Après purification des gaz libérés, un spectromètre de masse quadripolaire détermine la quantité d argon.L ensemble de ces mesures pourvoit un âge avec une incertitude théorique de 13% dans les meilleures conditions.Les calibrations du dispositif expérimental ont apporté de nombreuses informations sur des effets sur les spectres LIBS provoqués par l ablation sous vide secondaire. L augmentation de la pression e tla variation de géométrie du cratère d ablation ont des effets opposés sur les pics des éléments.Nous avons aussi démontré que l instrument était capable de mesurer l âge de la mésostase de roche basaltique et qu il offre des perspectives intéressantes sur certaines phases minérales comme la biotite.Crater counting is the only method used on Mars to give relative geochronological information but it never had been fitted and corrected by absolute geochronology. This work is about the development of a new prototype demonstrating the ability of a protocol using in situ K-Ar dating. The goal is to propose a solution of an absolute geochronology for the next explorations rovers. A quadrupled Nd:YAG laser at 266 nm ablates a basaltic sample under high vacuum. The light collection by a spectrometer (Laser Induced Breakdown Spectroscopy) gives the rate of potassium and the chemical or the mineralogy of the target. Thanks to the specificities of the ablation in highvacuum and with a UV laser, the ablated mass has a good reproducibility per mineralogy. Thus, theLIBS identification gives an estimation of the ablated mass. After the purification of the released gas,a quadrupole mass spectrometer determines the quantity of argon. All these measures give an age with a theoretical uncertainty of 13% in the best conditions.The calibration of the experiment had given new information about the effects on LIBS spectrarelated to the ablation under high vacuum. The rise of the pressure and the variation of geometry of the pit have opposite effects on the elements peaks. We also demonstrated that the instrument was capable of measuring the age of the groundmass of basalt and has some interesting perspectives on some mineral phases such as biotite.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Metrology with Atom Interferometry: Inertial Sensors from Laboratory to Field Applications

Developments in atom interferometry have led to atomic inertial sensors with extremely high sensitivity. Their performances are for the moment limited by the ground vibrations, the impact of which is exacerbated by the sequential operation, resulting in aliasing and dead time. We discuss several experiments performed at LNE-SYRTE in order to reduce these problems and achieve the intrinsic limit of atomic inertial sensors. These techniques have resulted in transportable and high-performance instruments that participate in gravity measurements, and pave the way to applications in inertial navigation.Comment: 7 pages, 5 figure

Sequential updating of a new dynamic pharmacokinetic model for caffeine in premature neonates

International audienceCaffeine treatment is widely used in nursing care to reduce the risk of apnoea in premature neonates. To check the therapeutic efficacy of the treatment against apnoea, caffeine concentration in blood is an important indicator. The present study was aimed at building a pharmacokinetic model as a basis for a medical decision support tool. In the proposed model, time dependence of physiological parameters is introduced to describe rapid growth of neonates. To take into account the large variability in the population, the Pharmacokinetic model is embedded in a population structure. The whole model is inferred within a Bayesian framework. To update caffeine concentration predictions as data of an incoming patient are collected, we propose a fast method that can be used in a medical context. This involves the sequential updating of model parameters (at individual and population levels) via a stochastic particle algorithm. Our model provides better predictions than the ones obtained with models previously published. We show, through an example, that sequential updating improves predictions of caffeine concentration in blood (reduce bias and length of credibility intervals). The update of the pharmacokinetic model using body mass and caffeine concentration data is studied. It shows how informative caffeine concentration data are in contrast to body mass data. This study provides the methodological basis to predict caffeine concentration in blood, after a given treatment if data are collected on the treated neonate