In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form solutions of proximal operators and envelope representations based on the Moreau, Fo…
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48 results for “close proximity”
New method for efficient proximal mapping of 1-path-norm in shallow networks.
problem Efficiently handling the 1-path-norm of shallow neural networks.
method Closed-form proximal operator for efficient computation and upper bound on Lipschitz constant.
result Proximal mapping allows robust training against adversarial perturbations.
Unified framework for training neural networks with non-smooth, non-convex regularizers.
problem Training neural networks with non-smooth, non-convex regularizers.
method ProxGen framework for stochastic proximal gradient descent.
result ProxGen framework achieves the same convergence rate as standard methods and outperforms subgradient-based approaches.
New method detects close contacts to prevent SARS-CoV-2 spread.
problem Detecting close contacts to prevent SARS-CoV-2 spread.
method Machine learning approach using BLE data.
result Reliable detection of close contacts reduces SARS-CoV-2 risk.
The p-Laplacian Transformer improves transformer models by assigning higher attention weights to tokens in close proximity.
problem The self-attention mechanism in transformers does not effectively distinguish attention weights between tokens in close and non-close proximity.
method Proposes a novel class of transformers, p-Laplacian Transformers, that use -Laplacian regularization to assign higher attention weights to tokens in close proximity.
result Empirically demonstrates that p-Laplacian Transformers outperform baseline transformers on various benchmark datasets.
This article introduces planar shape signatures derived from homology nerves, which are intersecting 1-cycles in a collection of homology groups endowed with a proximal relator (set of nearness relations) that includes a descriptive proximity. A 1-cycle is a closed, connected path with a zero boundary in a simplicial c…
Noise-free sampling method using Wasserstein proximal for faster convergence.
problem Sampling from distributions governed by potential functions.
method Deterministic score-based MCMC with regularized Wasserstein proximal.
result Improved mixing time bounds for Gaussian distributions compared to ULA and MALA.
New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.
problem The difficulty of sampling from heavy-tailed distributions using Gaussian versus stable oracles.
method Comparison of Gaussian and stable oracles for proximal samplers.
result Gaussian samplers have a fundamental barrier for high-accuracy guarantees in heavy-tailed sampling, while stable samplers excel.
Study shows tractable generalization in RL is impossible but possible with Strong Proximity.
problem RL agents struggle to generalize to new environments.
method Introduced Weak and Strong Proximity conditions to capture similarity between environments.
result Proved Strong Proximity is sufficient for efficient generalization.
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…
New algorithm proves convergence for MAP estimation with denoisers.
problem Proving convergence of MAP estimation methods using pretrained denoisers.
method A simple gradient descent algorithm on smoothed proximal objectives.
result Algorithm provably converges to the proximal operator under log-concavity.
The Alexandrov Soap Bubble Theorem asserts that the distance spheres are the only embedded closed connected hypersurfaces in space forms having constant mean curvature. The theorem can be extended to more general functions of the principal curvatures satisfying suitable conditions. In this paper…
New algorithm stabilizes RL policy learning through divergence regularization.
problem Stabilize policy learning and improve performance in RL.
method Proximity term constraining discounted state-action visitation distributions to be close to each other.
result Proposed algorithm improves stability and final performance in RL tasks.
Efficient algorithms solve joint graphical lasso problems.
problem Learning graphical models from sparse data.
method Proximal gradient procedures with ADMM backtracking option.
result Proposed algorithms achieve high accuracy and precision.
In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiable function and a proper closed convex function. Under the error bound condition used in [19] for analyzing the convergence of the proximal gradient algorithm, we show that there exists a thresho…
We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold . We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the distance function to a closed subset of ; 2) solvability and implicit func…
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …
Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector norm, whic…
The study examines hypersurfaces close to constant mean curvature and their proximity to spheres.
problem Understanding hypersurfaces close to constant mean curvature and their proximity to spheres.
method Quantitative stability results for hypersurfaces with mean curvature close to a constant.
result Hypersurfaces close to constant mean curvature are closely related to spheres, with quantitative descriptions of proximity.
ITSPACE improves covariance alignment faster than other methods.
problem Optimizing covariance matrices for machine learning tasks.
method Proximal majorization-minimization method that directly optimizes the Bures-Wasserstein objective.
result ITSPACE achieves lower BW gap solutions faster than other methods.
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 penalty. As a result, in a variational formulation of an inverse problem or statisticallearning estimation, it l…
The structure of return spillovers is examined by constructing Granger causality networks using daily closing prices of 20 developed markets from 2nd January 2006 to 31st December 2013. The data is properly aligned to take into account non-synchronous trading effects. The study of the resulting networks of over 94 sub-…
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 …
Sparse transformer architecture improves accuracy and speed in generative modeling and inverse problems.
problem Improving accuracy and speed in generative modeling and inverse problems.
method Proposes a sparse transformer architecture using regularized Wasserstein proximal operator with prior.
result Sparse transformer achieves higher accuracy and faster convergence than classical methods.
Paper extends Brouwer Fixed Point Theorem with amiable and almost amiable fixed sets.
problem Extending the Brouwer Fixed Point Theorem to approximate fixed sets.
method Introducing shape boundary regions in CW spaces as amiable and almost amiable fixed subsets of dpc maps.
result Variation of Jordan Curve Theorem and Fixed Cell Complex Theorem.
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…
Improves time series classification with forest proximities.
problem Time series classification accuracy and efficiency.
method PF-GAP, an extension of RF-GAP proximities to proximity forests, combined with Multi-Dimensional Scaling and Local Outlier Factors.
result Forest proximities show stronger connection between misclassified points and outliers.
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized co…
Learning Concave Bid Shading Strategies in Online Auctions via Measure-valued Proximal Optimizationcs.LG
This work optimizes bid strategies for online auctions using measure-valued optimization.
problem Optimizing bid strategies in first-price auctions to maximize expected surplus.
method Formulates the problem as convex optimization over the joint distribution of shading parameters, adapts the distribution after each auction using a Wasserstein-proximal update.
result The proposed algorithm encourages bids on values with high expected surplus.
Improved sampling guarantees for weakly log-concave distributions.
problem Sampling from distributions that are not strongly log-concave.
method Proximal sampler with convergence guarantees under weaker assumptions.
result New state-of-the-art sampling guarantees for various target distributions.
New sampling methods for constrained and composite distributions.
problem Sampling from log-concave distributions with constraints and composite structures.
method Proximal sampler applied to lifted convex sets with separation and subgradient oracles.
result Practical and unbiased samplers for constrained and composite distributions.
We develop a novel theoretical framework for understating OT schemes respecting a class structure. For this purpose, we propose a convex OT program with a sum-of-norms regularization term, which provably recovers the underlying class structure under geometric assumptions. Furthermore, we derive an accelerated proximal …
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak) derivative and divergence of a solution with respect to the observations. As such a so…
CFR-Pro enhances treatment effect estimation by incorporating local proximity.
problem Treatment selection bias in HTE estimation from observational data.
method Proximity-enhanced CounterFactual Regression (CFR-Pro) with pair-wise proximity regularizer and subspace projector.
result Significantly outperforms competitors in HTE estimation accuracy.
Paper analyzes convergence of PAM method for low-rank factorization models.
problem Convergence analysis of PAM method with subspace correction for low-rank factorization models.
method Majorized proximal alternating minimization (PAM) method with subspace correction.
result Established full convergence of PAM method under KL property and column -norm condition.
Improved random forest proximities capture data geometry.
problem Inaccurate random forest proximities do not reflect learned data geometry.
method Introduce RF-GAP: Geometry- and Accuracy-Preserving proximities.
result RF-GAP improves geometric representation in tasks like data imputation.
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 …
Introduces PPMM algorithm for nonconvex robust regression problems.
problem Nonconvex tuning-free robust regression problems.
method PPMM algorithm with inner subproblems solved by SSN-PPA.
result Converges to d-stationary point with KL property.
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a p…
Paper analyzes convergence of proximal algorithm in metric spaces without geodesic convexity.
problem Analyzing convergence of proximal algorithm in general metric spaces.
method Analysis of the Wasserstein proximal algorithm without geodesic convexity assumption.
result Establishes unbiased and linear convergence rate for proximal algorithm under natural Wasserstein inequality.
Extends RF proximities to all supervised distance-based machine learning contexts.
problem Limited utility of RF proximities in various machine learning tasks.
method Introduces generalized Proximity Forest (PF) model and variant for regression.
result Demonstrates unique advantages over RF and k-nearest neighbors models.
Clarifies when solutions to stochastic PDEs stay near given subsets.
problem Understanding the proximity of solutions to stochastic PDEs to given subsets.
method Analyzes distance between closed sets and solutions to stochastic PDEs.
result Clarifies conditions for solutions to stay near given subsets.
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…
Improved bounds for proximal gradient algorithms with computational errors.
problem Analyzing convergence of proximal gradient algorithms with inaccuracies.
method Deriving new tighter deterministic and probabilistic bounds for convex composite problems.
result Probabilistic bounds are more robust and accurate for algorithm verification and performance guarantees.
Good Coverings of Proximal Alexandrov Spaces. Homotopic Cycles in Jordan Curve Theorem Extensionmath.AT
Paper extends theorem on covering spaces and Jordan curves.
problem Covering and extending theorems for Alexandrov spaces.
method Introduces proximal homotopic cycles to extend the Mitsuishi-Yamaguchi theorem.
result Extensions of the Mitsuishi-Yamaguchi Good Covering Theorem and Jordan curve theorem.
Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
Innovative method solves nonconvex optimization on manifolds.
problem Nonconvex optimization problems on Riemannian manifolds.
method Intrinsic Riemannian proximal gradient method.
result Converges for nonconvex or nonembedded problems.
Unified Lagrangian-based methods for nonsmooth nonconvex optimization.
problem Minimizing nonsmooth nonconvex functions with constraints.
method Developed a unified framework for Lagrangian-based methods using subgradient updates.
result Global convergence guarantees for the proposed framework under mild conditions.