arXiv research

This paper studies fixed sets in ribbon complexes using descriptive proximity spaces.

New method for efficient proximal mapping of 1-path-norm in shallow networks.

Inserts proximal mapping into deep networks for better regularization.

New EZ-structure maps mapping class group actions.

Low-rank inducing unitarily invariant norms have been introduced to convexify problems with low-rank/sparsity constraint. They are the convex envelope of a unitary invariant norm and the indicator function of an upper bounding rank constraint. The most well-known member of this family is the so-called nuclear norm. To …

New algorithm proves convergence for MAP estimation with denoisers.

Proximal Diffusion Models improve generative model efficiency.

Innovative method solves nonconvex optimization on manifolds.

Proper proximality proved for various groups on non-positive curvature spaces.

We generalize Newton-type methods for minimizing smooth functions to handle a sum of two convex functions: a smooth function and a nonsmooth function with a simple proximal mapping. We show that the resulting proximal Newton-type methods inherit the desirable convergence behavior of Newton-type methods for minimizing s…

A new method reformulates Optimal Transport Conditional Flow Matching using proximal operators.

This paper extends the Good Covering Theorem and Jordan Curve Theorem for proximal Alexandrov spaces.

A new method solves convex optimization problems on manifolds efficiently.

We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the distance function to a closed subset $C$ of $M$; 2) solvability and implicit func…

Introduces a new divergence measure for optimal transport.

Variational Proximal Policy Optimization improves reinforcement learning from human feedback.

We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole objective function is strongly convex. Such problems often arise in machine lea…

Enhances counterfactual explanations with more valid and informative saliency maps.

Unified framework for training neural networks with non-smooth, non-convex regularizers.

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and the non-smooth part is equipped with a simple proximal mapping. We propose a pr…

We consider a class of nonconvex nonsmooth optimization problems whose objective is the sum of a smooth function and a finite number of nonnegative proper closed possibly nonsmooth functions (whose proximal mappings are easy to compute), some of which are further composed with linear maps. This kind of problems arises …

Paper proposes a new method for supervised manifold learning using random forest proximities.

We develop a projected Nesterov's proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov's momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a conv…

In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy proximal mappings. However, many problems arising from statistics, image processi…

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 constraints. Split feasibility generalizes important inverse problems including con…

Paper extends Brouwer Fixed Point Theorem with amiable and almost amiable fixed sets.

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in …

Study evaluates deep learning models for solar flare prediction with interpretability analysis.

We propose a new optimization method for training feed-forward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feed-forward neural network by adding the proximal operators to the objective function as penalties, hence we call the lifted proximal operator machin…

The total variation (TV) penalty, as many other analysis-sparsity problems, does not lead to separable factors or a proximal operatorwith a closed-form expression, such as soft thresholding for the $\ell\_1$ penalty. As a result, in a variational formulation of an inverse problem or statisticallearning estimation, it l…

Paper introduces a new reinforcement learning method with improved performance.

BinaryConnect is generalized and proven to converge.

Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization assumes convexity or strong convexity of each function. In this paper, we extend t…

Magnetic resonance imaging (MRI) has been proposed as a complimentary method to measure bone quality and assess fracture risk. However, manual segmentation of MR images of bone is time-consuming, limiting the use of MRI measurements in the clinical practice. The purpose of this paper is to present an automatic proximal…

We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane block-coordinate Frank-Wolfe method that takes advantage of the specific structure of …

In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…

Unified view connects CoCoA and ADMM for distributed ERM.

We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal M$, with the proximal mappings of $τP$, $τ> 0$, simple to compute. This problem i…

In Random Forests, proximity distances are a metric representation of data into decision space. By observing how changes in input map to the movement of instances in this space we are able to determine the independent contribution of each feature to the decision-making process. For binary feature vectors, this process …

Improves time series classification with forest proximities.

A new framework solves complex optimization problems with continuous worst-case distributions.

We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We proposed the stochastic ADMM to solve this complicated objective. In order to find an $ε$ stationary point where the expected norm of the subgradient of corresponding augmented Lag…

Improved sampling guarantees for weakly log-concave distributions.

New sampling methods for constrained and composite distributions.

MAP-Elites generates diverse trading strategies for improved execution performance.

Fix a finite set of points in Euclidean $n$-space $\euc^n$, thought of as a point-cloud sampling of a certain domain $D\subset\euc^n$. The Rips complex is a combinatorial simplicial complex based on proximity of neighbors that serves as an easily-computed but high-dimensional approximation to the homotopy type of $D$. …

CFR-Pro enhances treatment effect estimation by incorporating local proximity.

Improved random forest proximities capture data geometry.