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.
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.
A new method tackles nonconvex optimization with penalties and proximal terms.
problem Nonconvex optimization problems with equality and inequality constraints.
method Inexact proximal augmented Lagrangian method (P-ALM) with adaptive penalty and proximal parameters.
result Effective convergence properties and numerical superiority over traditional methods.
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…
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.
Extends multidimensional scaling to analyze three-way asymmetric proximities.
problem Analyzing asymmetric and three-way proximities in a Euclidean space.
method Unified h-plot methodology for three-way asymmetric proximities, including symmetric and conditional frameworks.
result Identification of archetypal profiles and clustering structures.
The paper analyzes two ISGD modes for statistical inference, deriving error bounds and confidence intervals.
problem Statistical inference with implicit SGD for smooth convex functions.
method Proximal Robbins-Monro (proxRM) and proximal Polyak-Ruppert (proxPR) procedures for ISGD.
result Derives non-asymptotic error bounds and confidence interval estimators for model parameters.
RFX accelerates and compresses Random Forests for large datasets.
problem Memory bottleneck in proximity matrices limits Random Forest analysis.
method QLORA compression, CPU TriBlock storage, GPU batch sizing, 3D MDS visualization.
result Proximity-based Random Forest analysis on larger datasets is feasible.
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties of this method, both in the exact and inexact setting, in the case when the obje…
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.
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…
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a unified analysis as approximations of the classical proximal point method for solving…
Proximal Mediation Analysis with Hidden Recanting Witnesses
problem Identifying path-specific effects in mediation analysis when recanting witnesses are unknown
method Proximal causal inference and semiparametric inference framework
result Developed three novel identification strategies and a semiparametric inference framework
Stochastic version of proximal distance algorithm analyzed and validated.
problem Optimization of constrained estimation problems.
method Stochastic proximal distance algorithm, with convergence guarantees and finite error bounds.
result Convergence guarantees and finite error bounds for the first time.
Paper introduces a new reinforcement learning method with improved performance.
problem Designing and analyzing efficient reinforcement learning algorithms.
method Proximal gradient temporal difference learning (GTD) with accelerated algorithm GTD2-MP.
result GTD algorithms have linear complexity and improved convergence rate.
New method reduces variance in stochastic optimization with high confidence.
problem Achieving high-probability guarantees in stochastic optimization with weaker noise assumptions.
method Stochastic proximal point method combining proximal subproblem solver and probability booster.
result Demonstrates convergence with low sample complexity under bounded variance assumptions.
DE-PSGLD samples from constrained distributions in a decentralized manner.
problem Sampling from log-concave distributions with constraints.
method Decentralized Proximal Stochastic Gradient Langevin Dynamics with proximal regularization.
result DE-PSGLD converges to a regularized Gibbs distribution and maintains posterior concentration.
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.
The paper addresses nonconvex penalized LAD estimation in partial linear models using DNNs.
problem Challenges in nonconvex penalized LAD estimation with DNNs in partial linear models.
method Parameterizes nonparametric term with DNNs, formulates penalized LAD problem, introduces proximal subgradient method.
result Establishes consistency, convergence rate, and asymptotic normality of the estimator.
The need for parameter estimation with massive datasets has reinvigorated interest in stochastic optimization and iterative estimation procedures. Stochastic approximations are at the forefront of this recent development as they yield procedures that are simple, general, and fast. However, standard stochastic approxima…
Randomized SINDy learns dynamic data structures using probabilistic methods.
problem Learning time-dependent data structures in dynamic systems.
method Sequential machine learning with a probabilistic approach, incorporating feature augmentation and Tikhonov regularization.
result Demonstrated effectiveness in regression and binary classification using real-world data.
Proximal gradient method has been playing an important role to solve many machine learning tasks, especially for the nonsmooth problems. However, in some machine learning problems such as the bandit model and the black-box learning problem, proximal gradient method could fail because the explicit gradients of these pro…
Two strategies for embedding new data points from proximity data are explored.
problem Embedding new data points using proximity data.
method Two competing strategies: projection and restricted reconstruction.
result Projection and restricted reconstruction can be derived from kernel methods.
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Sinc…
Improved analysis for fair federated learning reduces dependence on noise floor.
problem Asymptotic stationarity in group fair federated learning with reduced noise floor dependence.
method DS FedProxGrad framework with inexact local proximal solutions and fairness regularization.
result Algorithm converges asymptotically to stationarity without dependence on a noise floor.
New sampling method using regularized Wasserstein proximal for Gibbs distributions.
problem Sampling from Gibbs distributions with numerical stability and efficiency.
method Preconditioned regularized Wasserstein proximal operator.
result Discrete-time convergence analysis and explicit bias characterization.
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 ℓ_1 penalty. As a result, in a variational formulation of an inverse problem or statisticallearning estimation, it l…
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of n individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex case, we prove such an algorith…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better recovery performance. However, the resultant optimization pro…
We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly non-differentiable but convex component. We propose a proximal stochastic gradie…
Modern proximal and stochastic gradient descent (SGD) methods are believed to efficiently minimize large composite objective functions, but such methods have two algorithmic challenges: (1) a lack of fast or justified stop conditions, and (2) sensitivity to the objective function's conditioning. In response to the firs…
New method finds linear relationships across multiple data blocks using proximal gradient descent with ℓ1 constraint.
problem Finding leading generalized eigenvectors for multi-block CCA.
method Proximal gradient descent with ℓ1 constraint. result Rate-optimal solution under suitable assumptions.
Study evaluates deep learning models for solar flare prediction with interpretability analysis.
problem Lack of interpretability in deep learning models for solar flare prediction.
method Proximity-based metric for analyzing attribution maps generated by Guided Grad-CAM.
result Models' predictions align with active region characteristics, offering insights into their behavior.
Accelerates sampling from Gibbs distributions using ARWP method.
problem Sampling from Gibbs distributions efficiently.
method ARWP method, combining Nesterov acceleration and regularized Wasserstein proximal.
result ARWP exhibits higher contraction rate and faster tail exploration.
Paper proposes a new method for sparse spectral clustering on Stiefel manifold.
problem Sparse spectral clustering on Stiefel manifold with nonsmooth and nonconvex objective.
method Proposes a manifold proximal linear method (ManPL) to solve the original SSC formulation.
result Demonstrates the advantage of ManPL over existing methods on single-cell RNA sequencing data.
We analyze Riemannian accelerated methods using a new framework.
problem Understanding Riemannian accelerated gradient methods.
method Riemannian A-HPE framework, focusing on Euclidean A-HPE insights and metric distortion control.
result Characterization of acceleration for various Riemannian methods.
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…
This paper accelerates TV regularization algorithms by unrolling proximal gradient descent.
problem Solving Total Variation (TV) regularized problems with iterative algorithms.
method Unrolling proximal gradient descent solvers to learn their parameters.
result Two approaches to compute derivatives through proximal operators improve performance.
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.
Two new algorithms improve federated optimization under second-order similarity.
problem Federated learning under communication constraints and second-order similarity.
method SVRP and Catalyzed SVRP algorithms combining proximal point evaluations, client sampling, and variance reduction.
result Achieves superior performance and uniformly improves upon existing algorithms for federated optimization under second-order similarity and strong convexity.
Stochastic Gradient Descent has been widely studied with classification accuracy as a performance measure. However, these stochastic algorithms cannot be directly used when non-decomposable pairwise performance measures are used such as Area under the ROC curve (AUC) which is a common performance metric when the classe…
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 ℓ2,0-norm condition. New Langevin Monte Carlo algorithms for sampling from nonsmooth distributions.
problem Sampling from distributions with nonsmooth convex composite potentials.
method Leveraging Bregman--Moreau envelopes and proximal operators in mirror descent.
result Efficiency in sampling from nonsmooth distributions, extending existing methods.
Two new methods solve nonsmooth optimization on Riemannian Stiefel manifold.
problem Optimization over nonsmooth, non-differentiable functions on Riemannian manifolds.
method R-ProxSGD and R-ProxSPB, generalizing proximal SGD and SpiderBoost.
result R-ProxSPB finds ε-stationary points with IFO complexity of Ø(ε^(-3)) in online and Ø(n + √nε^(-2)) in finite-sum cases.
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient descent, coordinate gradient descent, proximal coordinate gradient, and Newton's …
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS…
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.
A new algorithm speeds up convex clustering.
problem Optimizing clustering with convex optimization and avoiding local minima.
method Smoothing proximal gradient algorithm (Sproga) for convex clustering.
result Sproga is faster and uses less memory than existing methods.