134 citations · 185 across the 22 of their papers we have counts for
11 papers · 1 filter
On the Wasserstein alignment problem
Soumik Pal, Bodhisattva Sen, Ting-Kam Leonard Wong
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces -- namely the…
Adapted optimal transport between Gaussian processes in discrete time
Madhu Gunasingam, Ting-Kam Leonard Wong
We derive explicitly the adapted -Wasserstein distance between non-degenerate Gaussian distributions on and characterize the optimal bicausal coupling(s). This le…
Bregman-Wasserstein divergence: geometry and applications
Amanjit Singh Kainth, Cale Rankin, Ting-Kam Leonard Wong
The Bregman-Wasserstein divergence is the optimal transport cost when the underlying cost function is given by a Bregman divergence, and arises naturally in fields such as statisti…
Tsallis and Rényi deformations linked via a new -duality
Ting-Kam Leonard Wong, Jun Zhang
Tsallis and Rényi entropies, which are monotone transformations of each other, are deformations of the celebrated Shannon entropy. Maximization of these deformed entropies, under s…
Random concave functions
Peter Baxendale, Ting-Kam Leonard Wong
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonpar…
Multiplicative Schrödinger problem and the Dirichlet transport
Soumik Pal, Ting-Kam Leonard Wong
We consider an optimal transport problem on the unit simplex whose solutions are given by gradients of exponentially concave functions and prove two main results. First, we show th…
Random walks and induced Dirichlet forms on compact spaces of homogeneous type
Shi-Lei Kong, Ka-Sing Lau, Ting-Kam Leonard Wong
We extend our study of random walks and induced Dirichlet forms on self-similar sets [arXiv:1604.05440, 1612.01708] to compact spaces of homogeneous type . A successive p…
Logarithmic divergences from optimal transport and Rényi geometry
Ting-Kam Leonard Wong
Divergences, also known as contrast functions, are distance-like quantities defined on manifolds of non-negative or probability measures. Using the duality in optimal transport, we…
Exponentially concave functions and a new information geometry
Soumik Pal, Ting-Kam Leonard Wong
A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps…
Random walks and induced Dirichlet forms on self-similar sets
Shi-Lei Kong, Ka-Sing Lau, Ting-Kam Leonard Wong
Let be a self-similar set satisfying the open set condition. Following Kaimanovich's elegant idea, it has been proved that on the symbolic space of a natural augmented…
Induced measures of simple random walks on Sierpinski graphs
Ting Kam Leonard Wong
In \cite{[K]}, Kaimanovich defined an augmented rooted tree corresponding to the Sierpinski gasket , and showed that the Martin boundary of the simple random walk $\{Z_…