Deep-learning improves 6x6-mm OCTA angiograms by reducing noise and artifacts.
problem Reduced scan quality in 6x6-mm OCTA angiograms due to undersampling.
method Deep-learning-based high-resolution angiogram reconstruction network (HARNet) trained on 3x3-mm and 6x6-mm angiogram data.
result Reconstructed 6x6-mm angiograms have lower noise and better vascular connectivity.
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.
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…
Kernel density estimators enhance Markov models with hidden states for complex data.
problem Modeling complex, non-Markovian processes with short-term dependencies.
method Kernel Density Estimation (KDE) for conditional distributions, hidden states for long-term dependencies.
result KDE-HMMs outperform traditional models on held-out data.
Paper explores MM strategies that can refuse to quote or provide single-sided quotes.
problem Overcoming risks in market making due to changing market conditions.
method Adversarial reinforcement learning with new MM agent designs.
result Refusal to quote or providing single-sided quotes can improve MM performance.
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.
NS-GAN mode collapse due to sample weighting inversion, solved with MM-nsat.
problem Mode collapse in GANs due to sample weighting inversion.
method Preserves MM-GAN sample weighting while avoiding saturation by rescaling gradients.
result MM-nsat improves mode coverage, stability, and FID on MNIST and CIFAR-10.
Paper accelerates MM algorithm for faster inference of ranking scores from comparison data.
problem Inference of Bradley-Terry model parameters from comparison data.
method Developed and analyzed MM algorithm for maximum likelihood and Bayesian estimation, proposed an accelerated version.
result Accelerated MM algorithm achieves faster convergence rates compared to classical MM algorithm.
The MM algorithm improves robust penalized estimation for outlier-contaminated data.
problem Outliers in data affect the reliability of penalized estimation.
method Innovative MM algorithm for both convex and nonconvex loss functions.
result Established convergence theory for MM algorithm with various loss functions.
IMM uses imitation learning and predictive representation learning to improve market making strategies.
problem Challenges in training RL agents for multi-price level market making strategies.
method IMM combines RL and imitation learning, introducing effective state and action representations and a representation learning unit.
result IMM outperforms existing RL-based market making strategies in financial criteria.
The purpose of this paper is the study of the roots in the mapping class groups. Let Σ be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the interior of Σ, and let $\MM (Σ, \PP)$ denote the mapping class group of $(Σ, \PP)$. We prove that, if Σ is of genus 0, then ea…
Let $(\MM ,{\tilde g})$ be an N-dimensional smooth compact Riemannian manifold. We consider the singularly perturbed Allen-Cahn equation $$ ε^2Δ_{ {\tilde g}} {u}\,+\, (1 - {u}^2)u \,=\,0\quad \mbox{in } \MM, $$ where ε is a small parameter. Let $\KK\subset \MM$ be an (N−1)-dimensional smooth minimal submanifold …
New method clusters time-evolving networks using exponential-family models.
problem Detecting community structure in time-evolving networks.
method Model-based clustering using temporal Exponential-Family Random Graph Models (ERGMs).
result Efficient variational EM algorithm for large-scale networks.
The paper classifies Poincaré complexes as topological manifolds.
problem Classifying Poincaré complexes as topological manifolds.
method Using spherical fibrations and CW-complexes, the paper proves stability and homotopy equivalence.
result A sufficient condition for Poincaré complexes to be homotopy types of topological manifolds.
This paper proposes MM-DAGs for analyzing traffic congestion, learning multiple DAGs jointly.
problem Analyzing multi-modal traffic data with overlapping and distinct variables.
method Developed MM-DAGs for multi-task, multi-modal DAG learning, using multi-modal regression and CD measure.
result Proved the effectiveness of MM-DAGs in traffic congestion analysis.
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.
A novel MM algorithm optimizes DCOV for SDR and SVS.
problem Dimension reduction and variable selection in nonparametric settings.
method Formulated as a DC program, MM algorithm solves quadratic subproblems on the Stiefel manifold.
result Improves computation efficiency and robustness across various settings.
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.
A new method estimates expectations from subtractive mixture models without sampling.
problem Estimating expectations from multimodal distributions using SMMs.
method Difference representation of SMMs to create unbiased IS estimator (ΔextEx). result Demonstrates that ΔextEx can achieve comparable estimation quality to auto-regressive sampling but is faster. Proposes MM-KTD for efficient RL learning with reduced sample size.
problem High sensitivity to parameter selection and overfitting in DNN-based RL methods.
method Adapts Kalman filter parameters using observed states and rewards, enhances sampling efficiency through active learning.
result Significantly reduced number of samples needed to learn optimal policy.
A new method accelerates deep neural network training using minimal margin score.
problem Training deep neural networks is computationally expensive.
method Introduces minimal margin score (MMS) for selecting samples.
result Significant acceleration in training deep neural networks.
The measure concentration property of an mm-space X is roughly described as that any 1-Lipschitz map on X to a metric space Y is almost close to a constant map. The target space Y is called the screen. The case of Y=R is widely studied in many literature (see \cite{gromov}, \cite{ledoux}, \cite{mil2}…
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.
MM-DREX adapts LLM experts for financial trading via dynamic routing.
problem Challenges of non-stationary financial markets and static expert designs.
method MM-DREX uses a VLM-powered dynamic router to allocate expert weights and designs heterogeneous trading experts.
result Significantly outperforms 15 baselines across key metrics.
Study uses logistic regression and association rules to identify early symptoms of malignant mesothelioma.
problem Difficult diagnosis of malignant mesothelioma leading to late-stage detection and poor patient survival.
method Implemented logistic regression and developed association rules to identify early symptoms.
result Categorical logistic regression improved training accuracy from 72.30% to 81.40%.
Let Ef be the energy of some knot τ for any f from certain class of functions. The problem is to find knots with extremal values of energy. We discuss the notion of the locally perturbed knot. The knot circle minimizes some energies Ef and maximizes some others. So, is there any energy such that the circle ne…
DGMM improves Gaussian mixture modeling efficiency and stability.
problem Efficiently estimating Gaussian mixtures in high dimensions.
method Diagonally-weighted generalized method of moments (DGMM).
result DGMM achieves smaller estimation errors with shorter runtime.
Introduces screening rules for non-convex Lasso problems.
problem Efficiently solving non-convex Lasso problems with theoretical guarantees.
method Iterative majorization-minimization strategy with screening rule.
result Significant computational gain compared to classical methods.
Models interactions among market participants in a financial asset's order book.
problem Understanding dynamic interactions among market participants in a financial asset's order book.
method Derives variational partial differential equations for MM and HFT strategies, and explains almost optimal control.
result Illustrates interactions between market participants through simulations of an order book.
New methods for parameter estimation in mechanistic models using data-consistent inversion.
problem Parameter estimation bias in Bayesian analysis for mechanistic models.
method Data-consistent inversion methods based on rejection sampling, MCMC, GANs, and constrained optimization.
result Improved parameter estimation without bias from uninformative priors.
This paper uses deep RL to optimize market quotes from LOB data.
problem Optimizing quotes for market making from complex LOB data.
method Attn-LOB neural network with convolutional filters and attention mechanism for feature extraction; hybrid reward function for continuous action space.
result The RL agent outperforms traditional methods in market making tasks.
PNNs improve personalized healthcare policies using mixed integer programming.
problem Learning treatment policies for patients with limited data.
method Prescriptive networks (PNNs) trained with mixed integer programming.
result PNNs outperform existing methods in reducing peak blood pressure.
A new method trains physics-constrained neural networks more efficiently.
problem Training machine learning tools with limited data and physical constraints.
method Dual-Dimer method for searching saddle points in nonconvex-nonconcave functions.
result The Dual-Dimer method improves training efficiency and convergence speed.
Proposes a new method for estimating sparse precision matrices in GMRF-MM models.
problem Difficulty in learning GMMs with large parameters and limited data.
method Restricts GMM to GMRF-MM, proposes efficient optimization for sparse precision matrices, and debiases the estimates.
result Debiasing approach outperforms GLASSO in single-GMRF and GMRF-MM cases.
The article explains how to use Mixture-of-Experts models for complex data.
problem Modeling complex data generating processes (DGPs).
method Constructing Mixture-of-Experts (MoE) models using maximum quasi-likelihood (MQL) estimators and blockwise-MM algorithms.
result MQL estimators are consistent and asymptotically normal under certain conditions.
New algorithm speeds up NMF with β-divergence.
problem Efficiently factorize nonnegative matrices with β-divergence. method Joint majorization-minimization with multiplicative updates.
result Significant reduction in computation time for NMF.
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.
Paper introduces new copulas from shock models, improving on maxmin copulas.
problem Improving on maxmin copulas for better characteristics.
method Developed RMM copulas with dependent endogenous shocks and proved convergence of iteration procedures.
result RMM copulas exhibit better characteristics than maxmin copulas, including convergence properties.
Proposes a new metric for comparing shapes in different spaces.
problem Comparing shapes in different metric spaces with unequal mass.
method Developed a Partial Gromov-Wasserstein (PGW) metric and algorithms to solve it.
result PGW is a well-defined metric between metric measure spaces.
Study models illiquid stock prices and finds low correlation due to constant prices.
problem Modeling illiquid stock prices and measuring correlation accurately.
method Combined Markov model with Ornstein Uhlenbeck and geometric Brownian motion.
result Low correlation in USE stocks due to constant prices and illiquidity.
Develops RL for optimal market-making in non-Markov processes.
problem Optimal market-making in non-Markov price processes.
method Deep reinforcement learning with Soft Actor-Critic (SAC) algorithm.
result Optimal strategy for market-making in semi-Markov and Hawkes Jump-Diffusion dynamics.
Bayesian optimization for function-valued responses, addressing worst case deviations.
problem Optimizing expensive functions with functional responses, focusing on worst case performance.
method Min-Max Functional Bayesian Optimization (MM-FBO) using Gaussian process surrogates and functional principal component analysis.
result MM-FBO consistently outperforms existing methods in synthetic and real-world applications.
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.
Some aspects of the multidimensional soliton geometry are considered. The relation between soliton equations in 2+1 dimensions and the Self-Dual Yang-Mills and Bogomolny equations are discussed.
NDI enables high-quality QSM without parameter tuning.
problem Quantitative Susceptibility Mapping (QSM) with regularization tuning issues.
method Nonlinear Dipole Inversion (NDI) using a physics-based forward model and a Variational Network (VN).
result NDI achieves high-quality QSM from as few as 2-direction data.
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.
New method uses subtractive mixture models for approximate inference.
problem How to effectively use subtractive mixture models for approximate inference.
method Design expectation estimators for IS and learning schemes for VI with SMMs.
result Empirical evaluation shows SMMs can approximate distributions effectively.
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's metho…