134 citations · 185 across the 22 of their papers we have counts for
26 papers
Maximum likelihood estimation for the -exponential family
Xiwei Tian, Ting-Kam Leonard Wong, Jiaowen Yang +1
The -exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the…
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…
JKO schemes with general transport costs
Cale Rankin, Ting-Kam Leonard Wong
We modify the JKO scheme, which is a time discretization of Wasserstein gradient flows, by replacing the Wasserstein distance with more general transport costs on manifolds. We sho…
Information Geometry for the Working Information Theorist
Kumar Vijay Mishra, M. Ashok Kumar, Ting-Kam Leonard Wong
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic application…
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…
Conformal Mirror Descent with Logarithmic Divergences
Amanjit Singh Kainth, Ting-Kam Leonard Wong, Frank Rudzicz
The logarithmic divergence is an extension of the Bregman divergence motivated by optimal transport and a generalized convex duality, and satisfies many remarkable properties. Usin…
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…
Projections with logarithmic divergences
Zhixu Tao, Ting-Kam Leonard Wong
In information geometry, generalized exponential families and statistical manifolds with curvature are under active investigation in recent years. In this paper we consider the sta…
Functional portfolio optimization in stochastic portfolio theory
Steven Campbell, Ting-Kam Leonard Wong
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to op…
Scalable Gradients for Stochastic Differential Equations
Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen +1
The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing…
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…
Logarithmic divergences: geometry and interpretation of curvature
Ting-Kam Leonard Wong, Jiaowen Yang
We study the logarithmic -divergence which extrapolates the Bregman divergence and corresponds to solutions to novel optimal transport problems. We show that this logarith…
Time-consistent conditional expectation under probability distortion
Jin Ma, Ting-Kam Leonard Wong, Jianfeng Zhang
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond…
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…
On portfolios generated by optimal transport
Ting-Kam Leonard Wong
First introduced by Fernholz in stochastic portfolio theory, functionally generated portfolio allows its investment performance to be attributed to directly observable and easily i…
Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio
Christa Cuchiero, Walter Schachermayer, Ting-Kam Leonard Wong
Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant re…
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…
Universal portfolios in stochastic portfolio theory
Ting-Kam Leonard Wong
Consider a family of portfolio strategies with the aim of achieving the asymptotic growth rate of the best one. The idea behind Cover's universal portfolio is to build a wealth-wei…
Optimization of relative arbitrage
Ting-Kam Leonard Wong
In stochastic portfolio theory, a relative arbitrage is an equity portfolio which is guaranteed to outperform a benchmark portfolio over a finite horizon. When the market is divers…
The geometry of relative arbitrage
Soumik Pal, Ting-Kam Leonard Wong
Consider an equity market with stocks. The vector of proportions of the total market capitalizations that belong to each stock is called the market weight. The market weight de…