Related papers: Score Operator Newton transport
Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
We consider the problem of estimating the transition dynamics $T^*$ from near-optimal expert trajectories in the context of offline model-based reinforcement learning. We develop a novel constraint-based method, Inverse Transition Learning,…
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix,…
In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
We consider Newton's method for finding zeros of mappings from a manifold $\mathcal X$ into a vector bundle $\mathcal E$. In this setting a connection on $\mathcal E$ is required to render the Newton equation well defined, and a retraction…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…
Hard-thresholding-based algorithms have seen various advantages for sparse optimization in controlling the sparsity and allowing for fast computation. Recent research shows that when techniques of the Newton-type methods are integrated,…
Thresholding algorithms for sparse optimization problems involve two key components: search directions and thresholding strategies. In this paper, we use the compressed Newton direction as a search direction, derived by confining the…
In this paper, we propose a distributed Newton method for consensus optimization. Our approach outperforms state-of-the-art methods, including ADMM. The key idea is to exploit the sparsity of the dual Hessian and recast the computation of…
Let $\pi_{0}$ and $\pi_{1}$ be two distributions on the Borel space $(\mathbb{R}^{d},\mathcal{B}(\mathbb{R}^{d}))$. Any measurable function $T:\mathbb{R}^{d}\rightarrow\mathbb{R}^{d}$ such that $Y=T(X)\sim\pi_{1}$ if $X\sim\pi_{0}$ is…
This paper presents novel methods for achieving stable and efficient convergence in multivariable extremum seeking control (ESC) using sliding mode techniques. Drawing inspiration from both classical sliding mode control and more recent…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
We consider constrained linear-quadratic dynamic games arising in autonomous vehicle platooning, intersection crossing and other cooperative driving scenarios. Infinite-horizon Nash equilibria are reformulated as receding-horizon affine…