相关论文: The Generalized Bregman Distance

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…

We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that…

We use duality techniques - specifically Siegmund and Bernstein duality - as tools to analyse ergodic and recurrence properties of $[0,1]$-valued Markov processes. These dualities enable the derivation of sharp bounds on the distance to…

The pointwise estimates of the deviations $\widetilde{T}_{n,A,B}^{\text{}%}f\left(\cdot \right) -\widetilde{f}(\cdot)$ and $\widetilde{T}_{n,A,B}^{% \text{}}f\left(\cdot \right) -\widetilde{f}(\cdot,\varepsilon)$ in terms of moduli of…

We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…

We study the problem of minimizing a relatively-smooth convex function using stochastic Bregman gradient methods. We first prove the convergence of Bregman Stochastic Gradient Descent (BSGD) to a region that depends on the noise (magnitude…

The continuous Frechet distance between two polygonal curves is classically computed by exploring their free space diagram. Recently, Har-Peled, Raichel, and Robson [SoCG'25] proposed a radically different approach: instead of directly…

Many problems in statistical learning, imaging, and computer vision involve the optimization of a non-convex objective function with singularities at the boundary of the feasible set. For such challenging instances, we develop a new…

The conditions of relative smoothness and relative strong convexity were recently introduced for the analysis of Bregman gradient methods for convex optimization. We introduce a generalized left-preconditioning method for gradient descent,…

Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…

Consider the twin problems of estimating the connection probability matrix of an inhomogeneous random graph and the graphon of a W-random graph. We establish the minimax estimation rates with respect to the cut metric for classes of block…

We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…

We introduce the discrete Fr\'echet gap and its variants as an alternative measure of similarity between polygonal curves. We believe that for some applications the new measure (and its variants) may better reflect our intuitive notion of…

Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…

We characterize proximity operators, that is to say functions that map a vector to a solution of a penalized least squares optimization problem. Proximity operators of convex penalties have been widely studied and fully characterized by…

We propose a variant of the approximate Bregman proximal gradient (ABPG) algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. ABPG is known to converge globally to a stationary point even when the…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

Many problems in machine learning write as the minimization of a sum of individual loss functions over the training examples. These functions are usually differentiable but, in some cases, their gradients are not Lipschitz continuous, which…

In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…