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±¨¸æ1£ºNeural Optimal Transport
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Evgeny BurnaevÊǶíÂÞ˹˹¿Æ¶û¿ÆÎֿƼ¼´óѧ£¨Skoltech£©µÄÈ«Ö°½ÌÊÚ£¬²©Ê¿Éúµ¼Ê¦£¬Ò²ÊǸÃУӦÓÃÈ˹¤ÖÇÄÜÖÐÐĵÄÖ÷ÈΡ£Evgeny Burnaev½ÌÊÚÓÚ2006ÄêÔÚĪ˹¿ÆÎïÀí¼¼Êõ´óѧ£¨MIPT£©»ñµÃÀíѧ˶ʿѧ룬2008ÄêÔÚÐÅÏ¢´«²¥ÎÊÌâÑо¿Ëù»ñµÃ²©Ê¿Ñ§Î»£¬2022ÄêÔÚĪ˹¿ÆÎïÀí¼¼Êõ´óѧ£¨MIPT£©ÓÖ»ñµÃÎïÀíÓëÊýѧ²©Ê¿Ñ§Î»¡£Evgeny Burnaev½ÌÊÚµÄÑо¿ÐËȤ°üÀ¨ÃæÏò3DÊý¾Ý·ÖÎöµÄÉî¶Èѧϰ¡¢Éú³É½¨Ä£ºÍÁ÷ÐΣ¨manifold£©Ñ§Ï°¡¢Ìæ´ú½¨Ä£ºÍ¹¤ÒµÏµÍ³ÓÅ»¯µÈ£¬Ïà¹ØÑо¿±»¼ÆËã»ú¿ÆѧµÄ¶¥¼¶»áÒéÈçICML, ICLR, NeurIPS, CVPR, ICCV, ECCVºÍÆÚ¿¯½ÓÊÕ·¢±í¡£
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Solving optimal transport (OT) problems with neural networks has become widespread in machine learning. The majority of existing methods compute the OT cost and use it as the loss function to update the generator in generative models (Wasserstein GANs). In this presentation, I will discuss the absolutely different and recently appeared direction - methods to compute the OT plan (map) and use it as the generative model itself. Recent advances in this field demonstrate that they provide comparable performance to WGANs. At the same time, these methods have a wide range of superior theoretical and practical properties.
The presentation will be mainly based on our recent pre-print "Neural Optimal Transport" https://arxiv.org/abs/2201.12220. I am going to present a neural algorithm to compute OT plans (maps) for weak & strong transport costs. For this, I will discuss important theoretical properties of the duality of OT problems that make it possible to develop efficient practical learning algorithms. Besides, I will prove that neural networks actually can approximate transport maps between probability distributions arbitrarily well. Practically, I will demonstrate the performance of the algorithm on the problems of unpaired image-to-image style transfer and image super-resolution.
±¨¸æ2£ºSemi-Levy driven CARMA process: Estimation and Prediction
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Saeid Rezakhah ÊÇÒÁÀʵºÚÀ¼°¢Ã׶û¿¨±È¶ûÀí¹¤´óѧ¸±½ÌÊÚ£¬²©Ê¿Éúµ¼Ê¦£¬1996ÄêÈ¡µÃÓ¢¹úÂ׶شóѧÂêÀö»ÊºóºÍΤ˹ÌطƶûµÂѧԺ£¨Queen Mary and Westfield College, University of London£©¸ÅÂÊͳ¼Æ²©Ê¿Ñ§Î»£¬ÏȺóÔÚÃÀ¹úÃÜЪ¸ùÖÝÁ¢´óѧºÍÓ¢¹úÂ׶شóѧ×ö·ÃÎʽÌÊÚ¡£Saeid Rezakhah½ÌÊÚÑо¿ÐËȤ°üÀ¨Selfsimilar Process; Hidden Markov Mixture models, Periodically Correlated Processes, Stable distributions, Random Polynomials; Time-Series Analysis; Stable ProcessºÍ Information TheoryµÈµÈ£¬Ä¿Ç°ÔÚ¹ú¼ÊѧÊõÆÚ¿¯·¢±ísci¼ìË÷ÂÛÎÄ40Óàƪ¡£
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The Levy driven Continuous-time ARMA (CARMA) models are restricted for modeling stationary processes. In this talk, we introduce semi-Levy driven CARMA (SL-CARMA) process as a generalized form of SL-CAR model which establishes a class of periodically correlated process. By a new representation of the semi-Levy process, we provide a ? discretized state-vector process with independent periodically identically distributed noise corresponding to high-frequency data. Then, we estimate
the parameters of the SL-CARMA process by Kalman filtering method. By simulation studies, the accuracy of the estimated parameters of a general form of semi-Levy and a special case of Normal inverse Gaussian backdriving processes are evaluated. Finally, the SL-CARMA process have much better fitting to the periodically correlated process in compare to the retrieved Levy driven CARMA models by applying periodic sample from the Apnea-ECG database and the percent log returns of Dow-Jones Industrial Average indices by mean absolute error criteria and Diebold-Mariano test.
