Explicit Learning Curves for Transduction and Application to Clustering and Compression Algorithms

Inductive learning is based on inferring a general rule from a finite data set and using it to label new data. In transduction one attempts to solve the problem of using a labeled training set to label a set of unlabeled points, which are given to the learner prior to learning. Although transduction seems at the outset to be an easier task than induction, there have not been many provably useful algorithms for transduction. Moreover, the precise relation between induction and transduction has not yet been determined. The main theoretical developments related to transduction were presented by Vapnik more than twenty years ago. One of Vapnik's basic results is a rather tight error bound for transductive classification based on an exact computation of the hypergeometric tail. While tight, this bound is given implicitly via a computational routine. Our first contribution is a somewhat looser but explicit characterization of a slightly extended PAC-Bayesian version of Vapnik's transductive bound. This characterization is obtained using concentration inequalities for the tail of sums of random variables obtained by sampling without replacement. We then derive error bounds for compression schemes such as (transductive) support vector machines and for transduction algorithms based on clustering. The main observation used for deriving these new error bounds and algorithms is that the unlabeled test points, which in the transductive setting are known in advance, can be used in order to construct useful data dependent prior distributions over the hypothesis space

Bureya-Jiamusi Superterrane: Tectonic and Geodynamic Processes in Late Mesozoic - Cenozoic

Bureya-Jiamusi superterrane (BJS) is a component of the Amur plate. This is one of the most complex and controversial structures of the eastern Asia. The bulk of the “body” superterrane is located in China, where it is actively researched by the Chinese scientists. The northern border of the structure is directly on the territory of the Amur region and is defined by the boundary of the Mongol-Okhotsk orogenic belt. By Parfenov, the superterrane is bordered by the Paleozoic-early Mesozoic orogenic belts and the North China plate. But there are other ideas about the spatial location of the BJS. All the suggested geodynamic reconstructions of the studied region take into account the interdependence between North-Asian and China-Korea plates and plates of the Pacific basin oceanic crust. The suggested work attempts to show the dependence of the evolution of the Bureya-Jiamusi superterrane on the surrounding geological objects in the late Cretaceous-Cenozoic interval

THE ROLE OF MESOZOIC GEODYNAMIC EVENTS IN FORMATION OF SEDIMENTARY BASINS ON THE FRAMING OF THE EASTERN MONGOL-OKHOTSK OROGENIC BELT

The Mongol-Okhotsk orogenic belt, finally formed in the end of the Mesozoic as a result of later tectonic events, is divided into two flanks: western and eastern. Its formation is obviously due to a regular change in geodynamic events significantly obscured by late tectonic and magmatic processes in the western flank and more clearly defined in the eastern flank from both magmatic and stratified formations. The early changes in geodynamic environment are most clearly determined by the formation of magmatic complexes whose completion is usually accompanied by the strata formation. Stratons framing the eastern flank of the Mongol-Okhotsk orogenic belt in the Mesozoic were formed in sedimentary basins, which are currently isolated to the Krestovkinsky and Ogodzhinsky basins along the southern border and to the Strelkinsky, Malotyndinsky, Toromsky and Udsky basins along the northern border. The deposition environment varied from deep-sea marine to continental. The article attempts to correlate the cross-sections of sedimentary basins on the framing of the eastern Mongol-Okhotsk orogenic belt and considers similarity or difference in their structure, conditions of sedimentation, tectonic positions and dependence of their evolution on geodynamic processes in the regio

Позднемезозойские адакитовые граниты южного обрамления восточного звена Монголо-Охотского орогенного пояса: вещественный состав, геодинамические условия формирования

Granitoids of the Magdagachi complex were studied using new and published petrochemical, geochemical and isotopic (Sm-Nd, Rb-Sr) data. Granitoid samples were taken from the southern frame of the eastern flank of the Mongol-Okhotsk orogenic belt (MOOB). Their analysis shows increased concentrations of Sr, Ba, Eu; reduced concentrations of Nb, Ta; abnormally low concentrations of HREE, Y and Yb; significant fractionation of REE; and high Sr/Y ratios. Therefore, the Magdagachi granitoids are "classical" adakites that may have formed at a depth of more than 45 km due to melting of eclogite with a garnet content of 20–50 %. Such conditions could exist under subduction as a result of melting of the frontal or lateral parts of the slab in subduction windows formed during oblique subduction at an orthogonal sinking angle. Highly metamorphosed lower crust Precambrian formations were also melted, and a source of parental melts could have been composed of both the mantle and crustal materials. Two tectonic scenarios are proposed that could have been accompanied by the formation of Magdagachi granitoids. Both scenarios refer to subduction processes, but differ in interactions between various regional structures in the Late Mesozoic. Согласно новым и уже опубликованным петрохимическим, геохимическим и изотопным (Sm-Nd, Rb-Sr) данным, для гранитоидов магдагачинского комплекса южного обрамления восточного звена Монголо-Охотского орогенного пояса установлено, что они характеризуются повышенными концентрациями Sr, Ba, Eu и пониженными содержаниями Nb, Ta, аномально низкими концентрациями HREE, Y и Yb; значительным фракционированием редкоземельных элементов; высокими соотношениями Sr/Y. Эти данные говорят о принадлежности пород комплекса к «классическим» адакитам. Предполагается, что они формировались на глубине более 45 км за счет плавления эклогита с содержанием граната 20–50 %. Такие условия могли существовать в обстановке субдукции в результате плавления фронтальной составляющей или боковых частей слэба в субдукционных окнах, образующихся при косой субдукции и ортогональном угле погружения. При этом плавлению подвергались также высокометаморфизованные нижнекоровые докембрийские образования, а в составе источника родоначальных расплавов принимало участие как мантийное, так и коровое вещество. Предложено два тектонических сценария, которые могли сопровождаться становлением гранитоидов магдагачинского комплекса. Оба сценария соответствуют условиям субдукционных процессов, но отличаются взаимодействием различных региональных структур в позднемезозойское время.

РОЛЬ МЕЗОЗОЙСКИХ ГЕОДИНАМИЧЕСКИХ СОБЫТИЙ В ФОРМИРОВАНИИ ОСАДОЧНЫХ БАССЕЙНОВ ОБРАМЛЕНИЯ ВОСТОЧНОГО ФЛАНГА МОНГОЛО-ОХОТСКОГО ОРОГЕННОГО ПОЯСА

The Mongol-Okhotsk orogenic belt, finally formed in the end of the Mesozoic as a result of later tectonic events, is divided into two flanks: western and eastern. Its formation is obviously due to a regular change in geodynamic events significantly obscured by late tectonic and magmatic processes in the western flank and more clearly defined in the eastern flank from both magmatic and stratified formations. The early changes in geodynamic environment are most clearly determined by the formation of magmatic complexes whose completion is usually accompanied by the strata formation. Stratons framing the eastern flank of the Mongol-Okhotsk orogenic belt in the Mesozoic were formed in sedimentary basins, which are currently isolated to the Krestovkinsky and Ogodzhinsky basins along the southern border and to the Strelkinsky, Malotyndinsky, Toromsky and Udsky basins along the northern border. The deposition environment varied from deep-sea marine to continental. The article attempts to correlate the cross-sections of sedimentary basins on the framing of the eastern Mongol-Okhotsk orogenic belt and considers similarity or difference in their structure, conditions of sedimentation, tectonic positions and dependence of their evolution on geodynamic processes in the regionМонголо-Охотский орогенный пояс, окончательно сформировавшийся в конце мезозоя, в результате более поздних тектонических событий был разделен на два фланга: западный и восточный. В его формировании прослеживается закономерное изменение геодинамических процессов, которые в пределах западного фланга значительно «затушеваны» поздними тектоническими и магматическими событиями, тогда как в пределах восточного фланга эти процессы менее искажены и фиксируются по наличию как магматических, так и стратифицированных образований. Начало изменения геодинамических условий наиболее четко определяется по формированию магматических комплексов, а их завершение, как правило, сопровождается образованием стратонов. Стратоны в обрамлении восточного фланга Монголо-Охотского орогенного пояса в мезозое формировались в осадочных бассейнах, фрагменты которых в настоящее время обособлены вдоль южной границы в Крестовкинский и Огоджинский бассейны, а вдоль северной – в Стрелкинский, Малотындинский, Торомский и Удский бассейны. Накопление осадков происходило в различных условиях: от глубоководных морских до континентальных. В статье выполнена корреляция разрезов осадочных бассейнов в обрамлении восточного фланга Монголо-Охотского орогенного пояса; рассматривается сходство или различие составов, возраста, условий осадконакопления, тектонических позиций и зависимость их эволюции от изменения геодинамических процессов в регионе