Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are statistically inefficient as estimators of the true parameter value. To address these tw…
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48 results for “proximal average”
Optimal scaling for proximal MALA in high dimensions confirmed.
problem Optimizing sampling efficiency in high-dimensional target densities.
method Introduced and analyzed the proximal MALA algorithm, showing it maintains optimal scaling.
result Proximal MALA achieves optimal scaling in high dimensions with an average acceptance probability of 0.574.
This paper studies the lower bound complexity for the optimization problem whose objective function is the average of 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…
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.
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…
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…
Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.
problem Lower complexity bounds for finite-sum optimization problems with various component functions.
method Developed novel approach to construct hard instances and analyzed PIFO algorithms.
result Established lower complexity bounds for convex-concave and nonconvex-strongly-concave objectives.
ALP outperforms other data descriptors in one-class classification.
problem Challenges in one-class classification using data descriptors.
method Determined optimal default hyperparameters for data descriptors, proposed ALP, evaluated using leave-one-dataset-out procedure.
result ALP outperforms other data descriptors, including IF and SVM.
Efficient solver for nonconvex tensor regularization reduces computational cost.
problem Computational inefficiency in extending nonconvex regularization to tensor learning.
method Proximal average algorithm with adaptive momentum, maintaining sparse plus low-rank structure.
result Shows good statistical performance and accuracy on tensor completion problems.
The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a non-trivial proximit…
ProxSARAH: An Efficient Algorithmic Framework for Stochastic Composite Nonconvex Optimizationmath.OC
We propose a new stochastic first-order algorithmic framework to solve stochastic composite nonconvex optimization problems that covers both finite-sum and expectation settings. Our algorithms rely on the SARAH estimator introduced in (Nguyen et al, 2017) and consist of two steps: a proximal gradient and an averaging s…
Paper improves a method for fast global and local convergence in optimization.
problem Slow global convergence in optimization methods with noisy Hessian estimates.
method Stochastic Newton Proximal Extragradient method using HPE framework.
result Faster global linear rate and superlinear convergence in fewer iterations.
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has…
The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in…
Quantile regression using random forest proximities improves prediction and uncertainty quantification.
problem Forecasting corporate bond volume with uncertainty quantification.
method Introduced a novel approach to compute quantile regressions from random forests using proximity metrics.
result Superior performance in approximating conditional target distributions and prediction intervals.
Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal stochastic gradient descent (DAP-SGD), to minimize an objective function that is the…
We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is the first time such a method is proposed. In the special case when the number of…
Extends robust methods for causal inference, improving estimator performance.
problem Estimating causal effects in the presence of latent confounders.
method Minimax kernel machine learning for doubly robust functionals.
result Proposed method leads to robust and high-performance estimators.
We consider saddle point problems which objective functions are the average of strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence guarantees. However, these methods have a slow convergence when the condition n…
Random Forest proximity measures for multi-view classification.
problem Combining multiple heterogeneous data views for classification.
method Building dissimilarity representations for each view, fusing them dynamically.
result Dynamic View Selection improves multi-view classification performance.
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial intelligence and machine learning, such as fused Lasso, fused logistic regression, a…
Improved Last-Iterate Convergence of Shuffling Gradient Methods for Nonsmooth Convex Optimizationmath.OC
Improved shuffling gradient methods converge faster for nonsmooth convex optimization.
problem Improving convergence rates for nonsmooth convex optimization problems.
method Analysis of shuffling gradient methods, focusing on Random Reshuffle and Single Shuffle strategies.
result Shuffling gradient methods, particularly Random Reshuffle and Single Shuffle, converge faster than Proximal Gradient Descent for nonsmooth convex optimization.
Due to the recent advancements in wearables and sensing technology, health scientists are increasingly developing mobile health (mHealth) interventions. In mHealth interventions, mobile devices are used to deliver treatment to individuals as they go about their daily lives. These treatments are generally designed to im…
In this paper we present an optimization-based view of distributed parameter estimation and observational social learning in networks. Agents receive a sequence of random, independent and identically distributed (i.i.d.) signals, each of which individually may not be informative about the underlying true state, but the…
A framework to compare federated learning algorithms in high-dimensional settings.
problem Comparing the performance of federated learning algorithms in high-dimensional settings.
method Formulating federated learning as a multi-criterion objective and analyzing a linear regression model.
result Federated Averaging with simple client fine-tuning achieves the same asymptotic risk as more intricate approaches and outperforms without personalization.
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…
Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogatesmath.OC
Paper extends SMM to weakly convex and multi-convex surrogates for non-convex optimization.
problem Non-convex optimization with weakly convex or multi-convex surrogates.
method Stochastic majorization-minimization with proximal regularization or block-minimization.
result Convergence rates for empirical and expected losses under non-i.i.d. data.
The posterior variance of Gaussian processes is a valuable measure of the learning error which is exploited in various applications such as safe reinforcement learning and control design. However, suitable analysis of the posterior variance which captures its behavior for finite and infinite number of training data is …
Accelerated Randomized Mirror Descent Algorithms For Composite Non-strongly Convex Optimizationmath.OC
We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem with the assumption that the sum is strongly convex, few methods support the non-…
BinaryConnect is generalized and proven to converge.
problem Understanding and improving neural network quantization.
method Refined analysis of BC, introduction of ProxConnect.
result ProxConnect achieves competitive performance.
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual subspace ascent. This is the first time momentum variants of several of these metho…
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.
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 framework uses deep RL to aggregate expert advice for better portfolio management.
problem Improving portfolio management through expert advice and deep reinforcement learning.
method Convolutional networks for signal aggregation and historical price data, Proximal Policy Optimization algorithm.
result Our framework can achieve 90% of the best expert's profit on average.
Algorithm solves robust linear regression with block Lewis weights.
problem Group distributionally robust least squares problem.
method Algorithm based on geometric construction and block Lewis weights, using accelerated proximal methods.
result Improves over known methods for moderate accuracy regimes and matches state-of-the-art guarantees.
LassoFlexNet improves deep learning performance on tabular data.
problem Deep learning underperforms tree-based models on tabular data.
method Incorporates five inductive biases and uses Tied Group Lasso for variable selection.
result LassoFlexNet matches or outperforms leading tree-based models on 52 datasets.
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.
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 present a method for training multi-label, massively multi-class image classification models, that is faster and more accurate than supervision via a sigmoid cross-entropy loss (logistic regression). Our method consists in embedding high-dimensional sparse labels onto a lower-dimensional dense sphere of unit-normed …
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.
AutoAnchor uses cross-attention to improve text-to-image model unlearning.
problem Mitigating harmful or copyrighted content in text-to-image models.
method Two-stage framework that automatically synthesizes manifold-proximal anchors using cross-attention consistency loss.
result Effective robust and unbiased unlearning across various baselines.
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.
New adaptive methods solve weakly convex stochastic optimization problems.
problem Solving weakly convex stochastic optimization problems.
method Adaptive first and zeroth-order methods using exponential moving averages.
result Established non-asymptotic convergence rates for nonsmooth and nonconvex problems.
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.
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.
Proposes P-learner for estimating treatment effects with proxy variables.
problem Estimating treatment effect heterogeneity in settings with unverifiable exchangeability.
method Two-stage loss function for learning heterogeneous treatment effects with proxy variables.
result P-learner satisfies an oracle bound on estimated error.