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.
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48 results for “Majorization--Minimization”
Proposes BMME for optimizing nonsmooth nonconvex problems with block structure.
problem Optimizing nonsmooth nonconvex problems with block structure.
method Block Alternating Bregman Majorization Minimization with Extrapolation (BMME).
result Subsequential convergence to a first-order stationary point under mild assumptions, global convergence under stronger conditions.
Paper proposes an efficient MM method for optimizing mean-reverting portfolios in finance.
problem Optimizing mean-reverting portfolios in financial markets considering mean-reversion strength, variance, and investment constraints.
method Majorization-Minimization (MM) method.
result The proposed method significantly outperforms other methods in financial market simulations.
We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is regularization, which is often used in compressed sensing, a technique for reconstructing sparse input signals from undersampled outputs. regularization impedes the …
Efficient algorithm solves sparse nonconvex regression problems.
problem Sparse nonconvex square-root-loss regression problems.
method Proximal majorization-minimization (PMM) algorithm with sparse semismooth Newton method.
result Converges to a d-stationary point with Kurdyka-Łojasiewicz property.
A new method for 1-bit matrix completion that is faster and more accurate.
problem Estimating a low-rank matrix from binary observations.
method Majorization-Minimization Gauss-Newton (MMGN) method.
result MMGN outperforms existing methods in accuracy and speed.
Non-convex optimization is ubiquitous in machine learning. Majorization-Minimization (MM) is a powerful iterative procedure for optimizing non-convex functions that works by optimizing a sequence of bounds on the function. In MM, the bound at each iteration is required to \emph{touch} the objective function at the opti…
New IRLS algorithms for SVM fitting via MM approach.
problem Fitting support vector machines (SVMs) via quadratic programming.
method Majorization--Minimization (MM) paradigm for iteratively-reweighted least-squares (IRLS) algorithms.
result IRLS algorithms for SVM risk minimization problems with various losses and penalties.
MM algorithms simplify solving machine learning and statistical problems.
problem Optimization problems in machine learning and statistics.
method Majorization-minimization framework applied to specific examples.
result Derivation and demonstration of MM algorithms for Gaussian mixtures, multinomial logistic, and SVM.
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal processing. In this paper, we intend to make this principle scalable. We introduc…
Unified approach for federated learning using MM optimization.
problem Scaling stochastic optimization to federated learning.
method Unified Majorize-Minimize (MM) framework for stochastic optimization, extended to federated learning.
result Unified algorithm \QSMM\ for federated learning that aggregates surrogate majorizing functions.
New algorithm for nonconvex optimization on constrained Riemannian manifolds converges quickly.
problem Optimization on constrained Riemannian manifolds.
method Block majorization-minimization (BMM) for smooth nonconvex objectives with Riemannian constraints.
result Converges to stationary points within iterations.
Paper proposes an efficient algorithm for nonnegative binary matrix factorization.
problem Decomposing binary data using matrix factorization.
method Majorization-minimization algorithm with Beta prior for improved performance.
result Proposed algorithm offers excellent trade-off between performance, complexity, and interpretability.
New algorithm speeds up NMF with -divergence.
problem Efficiently factorize nonnegative matrices with -divergence.
method Joint majorization-minimization with multiplicative updates.
result Significant reduction in computation time for NMF.
One of the most fundamental concepts in statistics is the concept of sample mean. Properties of the sample mean that are well-defined in Euclidean spaces become unwieldy or even unclear in graph spaces. Open problems related to the sample mean of graphs include: non-existence, non-uniqueness, statistical inconsistency,…
Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learningmath.OC
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective function downhill. Such a simple principle is widely applicable and has been very popu…
The paper improves IPS for modern optimization, scaling and regularizing it.
problem Improving iterative proportional scaling for modern optimization.
method Coordinate descent, majorization-minimization, optimization techniques, regularized variants.
result IPS can deliver coefficient estimates and handle log-affine models.
QMME balances cost and speed in convex optimization.
problem Slow convergence of first-order methods and high cost of second-order methods.
method Minimizing quadratic majorants with fixed curvature at each iteration.
result QMME framework achieves sequential convergence under standard assumptions.
Proposes MM-DUST for efficient generalized lasso solution paths.
problem Efficiently solve generalized lasso problems in large-scale and non-linear models.
method Majorization-minimization dual stagewise algorithm incorporating quadratic majorizers and stagewise learning.
result Established the uniform convergence of approximated solution paths.
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.
This paper proposes a new method for GLM estimation using distance penalties to handle constraints.
problem Handling constraints in generalized linear models (GLM) is complicated.
method The approach uses distance penalties to optimize the log-likelihood, avoiding shrinkage.
result Distance penalties provide a flexible and non-shrinking alternative to traditional penalties.
Paper proposes a method to improve graph clustering by integrating node textual metadata with node signals in GGMs.
problem Graph learning in Gaussian Graphical Models with auxiliary node metadata.
method Laplacian-constrained Gaussian Graphical Models with majorization-minimization algorithm.
result The proposed method outperforms state-of-the-art approaches that use either signals or metadata alone.
New algorithm improves on EM for streaming data, outperforming existing methods.
problem Processing high-volume, streaming data efficiently.
method Incremental stochastic Majorization-Minimization (MM) algorithm.
result The algorithm converges to a stationary point with vanishing gradient.
Entropy regularization improves power k-means for high-dimensional data.
problem Power k-means' tendency to get stuck in local minima and performance in high dimensions.
method Entropy regularization to learn feature relevance, combined with majorization-minimization algorithm.
result Consistent learning and scalable algorithm with closed-form updates and convergence guarantees.
BMM algorithm improves convergence for nonconvex optimization problems.
problem Constrained nonsmooth nonconvex optimization problems.
method Block majorization-minimization with diminishing radius.
result Improved convergence rate for nonconvex optimization problems.
Paper introduces a new regularization method for visual representations.
problem Learning sparse visual representations from over-complete data.
method Proposes leaky capped norm regularization (LCNR) and a majorization-minimization algorithm.
result LCNR outperforms regularization in monocular 3D shape recovery.
CCMM efficiently solves large-scale convex clustering problems.
problem Scalability and hierarchical structure in convex clustering.
method Majorization-minimization algorithm with cluster fusions and efficient updating.
result CCMM achieves efficient solutions for large datasets.
A new framework for predictive clustering and optimization.
problem Finding clusters of data that yield low error on a supervised target.
method Generalized optimization framework using MILP and MM for scalability.
result Models can uncover different interpretable discrete cluster structures.
Tyler's M-estimator's phase transition at DS-SNR = 1 is resolved.
problem Robust Subspace Recovery
method Tyler's M-estimator
result TME converges exactly to the true subspace for DS-SNR >= 1 under a new stability condition.
Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Informationmath.OC
Paper proposes a new method for SP with covariates using PADR and ERM.
problem Stochastic programming with covariate information.
method Empirical risk minimization (ERM) with nonconvex piecewise affine decision rules (PADR).
result The method provides theoretical consistency and computational tractability for nonconvex SP problems.
New algorithms improve ICA performance without manual tuning.
problem Improving Independent Component Analysis (ICA) performance.
method Developed majorization-minimization framework for non-convex loss function.
result Stochastic algorithms guarantee loss function decrease at each iteration.
A new framework evaluates large language models efficiently and accurately.
problem Evaluation of large language models is challenging due to stochasticity and heterogeneity of benchmarks.
method Interpretable and scalable framework based on Item Response Theory (IRT) and majorization-minimization principle.
result Our method achieves superior scalability and interpretability compared to existing approaches.
New method improves tensor completion and robust PCA using non-convex tensor rank and sparsity measures.
problem Challenging tensor rank minimization in machine learning.
method Proposes a non-convex tensor rank surrogate function and sparsity measure, using concavity for optimization.
result Demonstrates improved accuracy and efficiency in tensor completion and robust PCA.
Efficient Hierarchical Bayesian Inference for Spatio-temporal Regression Models in Neuroimagingstat.ML
Novel Bayesian framework for spatio-temporal neuroimaging data.
problem Inference on multi-task sparse hierarchical regression models with complex spatio-temporal dynamics.
method Flexible hierarchical Bayesian framework with Kronecker product covariance structure, majorization-minimization optimization, and Riemannian geometry.
result Improved performance on synthetic and real M/EEG data.
New method identifies predictive biomarkers for subgroup analysis.
problem Identifying predictive biomarkers from large covariates.
method Generalized penalized regression with overlapped group penalties.
result Asymptotically consistent method for sparse, interpretable models.
Paper tackles low-rank matrix recovery with column -norm regularization.
problem Low-rank matrix recovery problems with column sparsity constraints.
method Developed alternating majorization-minimization (AMM) methods with extrapolation and hybrid AMM.
result Global convergence analysis and superior performance in matrix completion problems.
Paper improves robustness of SDP algorithms with nonconvex loss functions.
problem Improving robustness of SDP algorithms against outliers.
method Proposes nonconvex loss functions (e.g., -loss) and designs an efficient algorithm using ADMM.
result Empirically efficient and theoretically guaranteed to converge to a critical point.
WDL models density curves using Wasserstein distance and flexible mixture models.
problem Modeling entire distribution and non-negativity constraints.
method Wasserstein distance, Semi-parametric Conditional Gaussian Mixture Models (SCGMM), Majorization-Minimization optimization.
result WDL better characterizes nonlinear dependence of conditional densities.
Proposes a method for forecasting large-scale interval-valued time series.
problem Modeling and forecasting large-scale interval-valued time series.
method Feature extraction procedure involving auto-segmentation, clustering, and precision matrix estimation.
result The method enhances forecasting performance for large-scale interval-valued time series.
Paper proposes algorithms for sparse signal estimation with nonconvex regularization.
problem Sparse signal estimation with nonconvex regularization.
method Successive convex approximation framework combining majorization-minimization and line search.
result Flexibility, fast convergence, low complexity, guaranteed convergence to stationary point.
Optimal transport aggregation combines distributed MoE models efficiently.
problem Combining local MoE models trained on distributed datasets.
method Optimal transport for minimizing divergence between local and global estimators, with MM algorithm for optimization.
result Aggregated estimator achieves performance comparable to centralized training but with reduced computation time.
In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood principle we derive a criterion for learning the model. The resulting optimization…
The paper develops an algorithm to select a subset of training data for efficient regression models.
problem Designing an efficient algorithm for selecting a subset of training data to train regression models quickly without sacrificing accuracy.
method The paper tackles this problem by formulating it as a minimization of training loss with respect to both trainable parameters and subset of training data, subject to error bounds on the validation set. They use a novel problem formulation and represent it with simplified constraints using the dual of the original training problem. They then develop SELCON, an efficient majorization-minimization algorithm for data subset selection, which admits an approximation guarantee.
result The experiments show that SELCON trades off accuracy and efficiency more effectively than the current state-of-the-art.
PIANO speeds up multinomial logistic regression solving.
problem Handling large datasets and many classes in logistic regression.
method Parallel iterative algorithm based on Majorization Minimization.
result PIANO converges to a stationary point of Multinomial and Sparse Multinomial Logistic Regression.
Paper proposes SRA algorithm for online learning robustness and adaptivity.
problem Quantifying and evaluating tradeoff between robustness and adaptivity in online learning.
method SRA algorithm using biased stochastic approximation scheme with adaptive threshold.
result SRA algorithm provides superior performance in synthetic and real datasets.
Combines OT and PCA for DR, preserving clusters.
problem Analyzing high-dimensional data with global dependencies.
method Optimal transport (OT) for minimizing reconstruction error, combined with PCA.
result Effective preservation of high-dimensional clusters in embeddings.
Unified algorithm for tensor decomposition supports multiple loss functions and models.
problem Efficient tensor decomposition for various models and loss functions.
method Hierarchical combination of ADMM and MM for optimization.
result Wide-range applications can be solved by the proposed algorithm.
Proposes a robust method for estimating sparse VECM models.
problem Outliers and heavy-tailed data in traditional VECM models.
method Robust estimation using Cauchy distribution and sparse cointegration.
result Efficient algorithm for nonconvex problem solving.