학과 세미나 및 콜로퀴엄
Many of real-world data, e.g., the VGGFace2 dataset, which is a collection of multiple portraits of individuals, come with nested
structures due to grouped observation. The Ornstein auto-encoder (OAE) is an emerging framework for representation learning from nested data, based on an optimal transport distance between random processes. An attractive feature of OAE is its ability to generate new variations nested within an observational unit, whether or not the unit is known to the model. A previously proposed algorithm for OAE, termed the random-intercept OAE (RIOAE), showed an impressive performance in learning nested representations, yet lacks theoretical justification.
In this work, we show that RIOAE minimizes a loose upper bound of the employed optimal transport distance. After identifying several issues with RIOAE, we present the product-space OAE (PSOAE) that minimizes a tighter upper bound of the distance and achieves orthogonality in the representation space. PSOAE alleviates the instability of RIOAE and provides more flexible representation of nested data. We demonstrate the high performance of PSOAE in the three key tasks of generative models: exemplar generation, style transfer, and new concept generation. This is a joint work with Dr. Youngwon Choi (UCLA) and Sungdong Lee (SNU).
(전체일정: 7/28, 7/29, 8/3, 8/5)
In 2d first-passage percolation, we let (t_e) be a family of i.i.d. weights associated to the edges of the square lattice, and let T = T(x,y) be the induced weighted graph metric on Z^2. If we let p be the probability that a weight takes the value 0, then there is a transition in the large-scale behavior of T depending on the value of p. Specifically, when p < 1/2, T grows linearly, but when p > 1/2, T is stochastically bounded. In these lectures, I will describe some of the standard questions of FPP in the case p < 1/2, and then focus on the "critical" case, where p = 1/2. Regarding this case, I will show some of my work over the last few years including exact asymptotics for T, universality results, and recent work on a dynamical version of the model. The work I will present was done in collaboration with J. Hanson, D. Harper, W.-K. Lam, P. Tang, and X. Wang.
Lec 4: Critical FPP: the general case
(전체일정: 7/26, 7/27, 8/2, 8/4)
Lec 4: Information Percolation
In this final lecture, we discuss the celebrated technique known as the information percolation introduced by Lubetzky and Sly. Then, we explain the application of this technique to Glauber dynamics of the Ising model on lattice, and of the Random cluster model. The last result is a joint work with Shirshendu Ganguly.
(전체일정: 7/28, 7/29, 8/3, 8/5)
In 2d first-passage percolation, we let (t_e) be a family of i.i.d. weights associated to the edges of the square lattice, and let T = T(x,y) be the induced weighted graph metric on Z^2. If we let p be the probability that a weight takes the value 0, then there is a transition in the large-scale behavior of T depending on the value of p. Specifically, when p < 1/2, T grows linearly, but when p > 1/2, T is stochastically bounded. In these lectures, I will describe some of the standard questions of FPP in the case p < 1/2, and then focus on the "critical" case, where p = 1/2. Regarding this case, I will show some of my work over the last few years including exact asymptotics for T, universality results, and recent work on a dynamical version of the model. The work I will present was done in collaboration with J. Hanson, D. Harper, W.-K. Lam, P. Tang, and X. Wang.
Lec 3: Critical FPP: the Bernoulli case
(전체일정: 7/26, 7/27, 8/2, 8/4)
Lec 3: Cut-off phenomenon for mean-field spin systems
In this third lecture, we explain the cut-off phenomenon for the Glauber dynamics of the mean-field Ising or Potts model and general strategy to prove it.