<div>The rise of artificial intelligence (AI) hinges on the efficient training of modern deep neural networks (DNNs) for non-convex optimization and uncertainty quantification, which boils down to a non-convex Bayesian learning problem. A standard tool to handle the problem is Langevin Monte Carlo, which proposes to approximate the posterior distribution with theoretical guarantees. However, non-convex Bayesian learning in real big data applications can be arbitrarily slow and often fails to capture the uncertainty or informative modes given a limited time. As a result, advanced techniques are still required.</div><div><br></div><div>In this thesis, we start with the replica exchange Langevin Monte Carlo (also known as parallel tempering), which is a Markov jump process that proposes appropriate swaps between exploration and exploitation to achieve accelerations. However, the na\"ive extension of swaps to big data problems leads to a large bias, and the bias-corrected swaps are required. Such a mechanism leads to few effective swaps and insignificant accelerations. To alleviate this issue, we first propose a control variates method to reduce the variance of noisy energy estimators and show a potential to accelerate the exponential convergence. We also present the population-chain replica exchange and propose a generalized deterministic even-odd scheme to track the non-reversibility and obtain an optimal round trip rate. Further approximations are conducted based on stochastic gradient descents, which yield a user-friendly nature for large-scale uncertainty approximation tasks without much tuning costs. </div><div><br></div><div>In the second part of the thesis, we study scalable dynamic importance sampling algorithms based on stochastic approximation. Traditional dynamic importance sampling algorithms have achieved successes in bioinformatics and statistical physics, however, the lack of scalability has greatly limited their extensions to big data applications. To handle this scalability issue, we resolve the vanishing gradient problem and propose two dynamic importance sampling algorithms based on stochastic gradient Langevin dynamics. Theoretically, we establish the stability condition for the underlying ordinary differential equation (ODE) system and guarantee the asymptotic convergence of the latent variable to the desired fixed point. Interestingly, such a result still holds given non-convex energy landscapes. In addition, we also propose a pleasingly parallel version of such algorithms with interacting latent variables. We show that the interacting algorithm can be theoretically more efficient than the single-chain alternative with an equivalent computational budget.</div>

as English abstract / Oppressed by the severe surveillance of the Japanese police in Taiwan, short-lived Taiwanese Communist Party (TCP) (1928-1931) marked a significant step in the Taiwan’s anti-Japanese movement and social thought. The TCP was the first political organization in Taiwan to put forward the slogan of Taiwan’s independence. Following the Comintern’s activation in the East in 1920s, the first contacts between the Taiwan’s leftists and the Comintern representatives took place in early 1920s. Starting from 1927, the Comintern pursued the policy of activation of the communist movement in the colonies and establishment of communist parties in these countries. Established on the Comintern directive in Shanghai with the help of the Chinese Communist Party (CCP) and being subordinated to the Japanese Communist Party (JCP), the TCP was developing quite independently under the leadership of Xie Xuehong and in the close alliance with the Taiwan Cultural Association and the Taiwan Peasants Union, until the end of 1930 when the TCP established a contact with the Far Eastern Bureau (FEB) of the Comintern through the TCP Shanghai representative, Weng Zesheng, who served as liaison with the Comintern. As the result, the Comintern activated its work toward Taiwan, started dispatching emissaries to Taiwan who in the framework of the Comintern’s rhetoric of that time promoted the Party’s reform to eliminate the “opportunistic errors”. The activation of the Party’s work followed, the Union for Reorganization was established. The Comintern did not have chance to adjust the activity of the reformed TCP as within few months after the beginning of actual interaction between the Comintern and the TCP, the TCP was destroyed by arrests. The thesis is devoted to the Comintern’s role in the TCP’s establishment, development, reform, establishment of the Union for Reorganization, the Party’s activation and destruction. The research is based on the TCP files deposited in the former archive of the Comintern. The documents include the correspondence of the representative of the TCP, Weng Zesheng, with the Comintern FEB. The correspondence between Weng Zesheng and the FEB sheds light on the inner-party processes in the TCP, clarifies the essence of the inner-party struggle and reform, and explores the role of personal relations in the inner-party struggle which resulted in the UFR establishment without direct involvement of the Comintern. The available now text of the consultations of Weng Zesheng with the CCP representative Qu Qiubai makes it possible to clarify the CCP’s involvement in the TCP’s development and reform and to conclude as to whose directive it was to commence the struggle against Xie Xuehong. The TCP’s history was short but very intensive. Abandoned by its superior, the JCP, and not having relations with the international communist leadership, the TCP suffered lack of the financial and ideological support, and was left for the mercy of unpredictable fate of the exhausting inner factional struggle, still was able to survive under the “white terror” until the Party’s reorganization in 1931. According to the research results, the TCP inner-party struggles during 1928-1931 were in fact the result of resistance to emigrant party groupings who were attempting to take control over the TCP’s Taiwan based Party organization. Neither the JCP and the CCP, nor the Comintern had a real opportunity to influence the activities of the Taiwan-based communists. Taiwan’s communists overseas used the Comintern’s rhetoric and their contacts with the Comintern and the CCP to promote their agenda in the inner-party struggle. The implementation of the plans of Weng Zesheng and the opponents of Xie Xuehong in Taiwan on the Party’s reform and activation led to the Party’s destruction by the Japanese administration.

La tesi si concentra sul Partito Nazionalista Cinese negli anni Venti come punto privilegiato di osservazione del cambiamento politico della Cina dopo la Prima guerra mondiale. Questo decennio rappresentò un momento di definizione identitaria sia per i comunisti sia per i nazionalisti. La storiografia ne ha sottolineato numerosi aspetti, ma si è finora occupata del periodo 1919-1928 come una preistoria degli anni Trenta piuttosto che come un autonomo segmento di storia cinese. Studi recenti hanno superato implicitamente questo approccio criticando due date periodizzanti fondamentali per il Novecento cinese: la nascita della Repubblica nazionalista (1911) e la nascita della Repubblica Popolare (1949). A metà tra queste due date, gli anni Venti sono emersi come snodo decisivo nel passaggio da impero a Stato nazionale, durante cui si definì un nuovo spazio di discussione politica. Questo processo, pur interno, subì l’influsso delle strategie internazionali di sovietici e statunitensi dando vita a una nuova visione non soltanto della rivoluzione ma anche dello Stato post-rivoluzionario. Le classi dirigenti nazionalista e comunista, durante la collaborazione, si rivelarono dinamiche e tale “competizione” si trasferì anche all’interno di ciascun movimento diventando un fattore determinante per il successo o il fallimento del partito inteso come moderna formazione politica. / The thesis focuses on the Chinese Nationalist Party in the 1920s as a special standpoint to analyze the political changes in China after the World War I. That decade was crucial for shaping the identity of nationalists and communists. Many works have already examined some aspects, but they mostly considered the years 1919-1928 as a pre-history of the Thirties rather than an autonomous part of Chinese history. Recent studies have overcome this approach by criticizing two of the main periodization in the Chinese twentieth century: the birth of the nationalist Republic (1911) and the birth of the People’s Republic (1949). Halfway, the 1920s stood out as a critical juncture in the transition from empire to nation-state. A new space of political discussion was defined. The process, albeit internal, was under the influence of the USSR and US international strategies and gave birth not only to a new vision of the revolution, but also to a vision of the post-revolutionary state. Also, the nationalist and communist leaderships turned out to be dynamic. That "competition" may be seen also within the two political movements and became a shaping factor for the success or failure of the party as a modern political formation.