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We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional functions ("mixtures") of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and post-intervention views or temporal structure; places restrictive assumptions, such as linearity, on the mixing function or latent causal model; or requires partial knowledge of the generative process, such as the causal graph or the intervention targets. We instead consider the general setting in which both the causal model and the mixing function are nonparametric. The learning signal takes the form of multiple datasets, or environments, arising from unknown interventions in the underlying causal model. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data. We study the fundamental setting of two causal variables and prove that the observational distribution and one perfect intervention per node suffice for identifiability, subject to a genericity condition. This condition rules out spurious solutions that involve fine-tuning of the intervened and observational distributions, mirroring similar conditions for nonlinear cause-effect inference. For an arbitrary number of variables, we show that two distinct paired perfect interventions per node guarantee identifiability. Further, we demonstrate that the strengths of causal influences among the latent variables are preserved by all equivalent solutions, rendering the inferred representation appropriate for drawing causal conclusions from new data. Our study provides the first identifiability results for the general nonparametric setting with unknown interventions, and elucidates what is possible and impossible for causal representation learning without more direct supervision.

Independent Component Analysis (ICA) aims to recover independent latent variables from observed mixtures thereof. Causal Representation Learning (CRL) aims instead to infer causally related (thus often statistically dependent) latent variables, together with the unknown graph encoding their causal relationships. We introduce an intermediate problem termed Causal Component Analysis (CauCA). CauCA can be viewed as a generalization of ICA, modelling the causal dependence among the latent components, and as a special case of CRL. In contrast to CRL, it presupposes knowledge of the causal graph, focusing solely on learning the unmixing function and the causal mechanisms. Any impossibility results regarding the recovery of the ground truth in CauCA also apply for CRL, while possibility results may serve as a stepping stone for extensions to CRL. We characterize CauCA identifiability from multiple datasets generated through different types of interventions on the latent causal variables. As a corollary, this interventional perspective also leads to new identifiability results for nonlinear ICA -- a special case of CauCA with an empty graph -- requiring strictly fewer datasets than previous results. We introduce a likelihood-based approach using normalizing flows to estimate both the unmixing function and the causal mechanisms, and demonstrate its effectiveness through extensive synthetic experiments in the CauCA and ICA setting.

The solubility of 2,2′-(1,2-ethenediyldi-4,1-phenylene) bis-benzoxazole (OB-1) in four monosolvents (chlorobenzene, N-methyl-2-pyrrolidone (NMP), N,N-dimethylformamide (DMF), and water) and four di...

L’oggetto di questa tesi è stato lo studio della mineralogia dei sedimenti fluviali ed eolici attuali generati dall’erosione della catena Himalayana, con lo scopo di definire con precisione le segnature composizionali dei diversi domini tettono-stratigrafici dell’orogene. All’approccio basato sulla identificazione e quantificazione delle associazioni di minerali pesanti (densità > 2.90 g/cm3), sono stati affiancate diverse tecniche analitiche complementari, che comprendono la petrografia e la geochimica del sedimento totale, lo studio di dettaglio al microscopio elettronico a scansione e allo spettroscopio Raman delle caratteristiche minerochimiche dei quattro principali gruppi di minerali pesanti che caratterizzano i sedimenti himalayani e orogenici in generale (anfiboli, epidoti, granati, e pirosseni), l’ analisi dei rapporti isotopici di samario e neodimio scolta in collaborazione con Peter Clift presso l’ Istituto Oceanigrafico Woods Hole, oltre all’ analisi geocronologica su zirconi detritici svolta in collaborazione con Pieter Vermeesch presso l’Università di Londra (UCL) affiancata anche da dati analoghi su rutilo, monazite, e titanite ottenuti con la collaborazione di Xiumian Hu e Ronghua Guo presso l’ Università di Nanjing. Le principali aree di studio hanno compreso il Deserto di Thal nel Pakistan centro-settentrionale e gli affluenti del Fiume Indo nel suo corso di montagna dal Ladakh fino al Punjab e gli affluenti principali del Fiume Yarlung (il nome tibetano del Brahmaputra) in Tibet meridionale. Sono stati studiati anche campioni di arenarie Cenozoiche provenienti sia dalle Alpi Occidentali che dal Tibet meridionale. I risultati presentati in questa tesi sono stati pubblicati a primo nome in un volume speciale della rivista internazionale Minerals, sono stati sottomessi nel mese di Settembre e sempre a primo nome a Sedimentary Geology, o sono in preparazione per una prossima sottomissione ad altra prestigiosa rivista internazionale. Sediments and sedimentary rocks can be considered as geological archives that faithfully reflect their provenance information if the bias introduced by physical and chemical processes during transport and deposition can be properly recognized and corrected for. The sediment provenance analysis both in modern and ancient settings is crucial to trace the sediment sources, reconstruct paleoclimate and paleoenvironment, and interpret the evolution of the Earth’s surface. Modern sediments, unaffected by diagenesis and eroded, tansported and deposited under climatic conditions that are fully known, can provide valuable information on the interactions among the different controlling factors that govern source-to-sink systems. Rivers draining the Himalayan orogen provide the good opportunity to trace the source fingerprinting that is documented in modern fluvial and eolian sand and how these signatures reflect the erosion patterns of the modern and paleo-river systems. A multidisciplinary approach based on petrography, minerology, geochemistry and geochronology is emphasized in this research, in order to obtain a comprehensive provenance information. Our research area focused on the modern sands from two river system: Yarlung River and Indus River. In the Yarlung River system, the Nian River was chosen to investigate the petrographic, mineralogical and chronological signature of sediments from Tethys Himalaya, Greater Himalaya, Kangmar gneiss dome and Transhimalayan ophiolitic suture. Different tectonic domains are characterized by distinct heavy mineral assemblages, e.g., the first-cycle sillimanite and garnet in Greater Himalaya, and clinopyroxene, olivine and enstatite in the forearc ophiolites. Sand carried by the Nian River and its major tributaries, mainly reflects Tethys Himalayan characteristics, consistent with the geochronological results. Erosion rates were also evaluated and circumscribed in the middle Yarlung River catchment. The average erosion rate in the Nianchu catchment is estimated at 0.07-0.10 mm/a, twice as that in the middle Yarlung and Lhasa River catchments, which is principally ascribed to the high erodibility of Tethys Himalayan strata. In the Indus River system, minerochemical analysis of amphibole, garnet, epidote and pyroxene grains, and geochronological analysis of detrital zircons, associated with analysis on petrography, bulk-sediment geochemistry and isotopic geochemistry, in aolian sand from Thal Desert and fluvial sand in selected tributaries draining one specific tectonic domain in the upper Indus catchment, were carried out to discriminate compositional signatures, decipher the provenance information, and trace the erosional evolution of the western Himalaya syntaxis. The compositional fingerprints of Thal Desert sand are characterized by litho-feldspatho-quartzose to quartzo-feldspatho-lithic detrital modes and very rich amphibole-dominated heavy-mineral assemblages. The high heavy mineral concentration, less negative εNd, abundant zircon ages at 40-100 Ma, and specific mineral varietal fingerprints, consistently reflect that the Kohistan arc has acted as the main sediment source. Karakorum appears to contribute less while Himalaya shows higher influence on the Thal Desert sands than modern river sands from the Indus. As a Quaternary repository of wind-reworked Indus River sand at the entry point in the Himalayan foreland basin, Thal Desert sands document higher erosion rates than today in the glaciated areas formed largely by batholites granitoids of the Asian active margin. The close compositional and chronological connection between the Thal Desert and the ancient Indus Delta and Fan deposits, shed new light on the reconstructing of paleodrainage and the understanding of relationship between climatic and tectonic forcing that controlled the erosional evolution of the western Himalayan-Karakorum orogen.

Daihai Lake lies in the transitional area from semi-humid to semi-arid region, and also in the north margin of the East Asia monsoon. The analysis of 65 pollen samples from the surface sediment of Daihai Lake and alluvium of its inflow rivers revealed the characteristics of pollen distribution and different transport vectors. Most pollen grains in Daihai Lake come from its inflow rivers, although rain-out and wind are also important. Activities of insects, birds and humans may also carry pollen into the lake. The pollen assemblages are consistent with the regional vegetation in general. The variance of pollen assemblages in different parts of the lake reflects changes of local vegetation near the lakeshore. Pollen concentrations in the lake sediment surface are lower than that in fresh alluvium in its inflow rivers, and the highest percentages and concentrations of major pollen types mainly appear in the margin part of the lake. DCA demonstrated that there are more similarities between lake sediments and the inflow rivers than there are differences.