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…
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48 results for “MM framework”
MM (majorization--minimization) algorithms are an increasingly popular tool for solving optimization problems in machine learning and statistical estimation. This article introduces the MM algorithm framework in general and via three popular example applications: Gaussian mixture regressions, multinomial logistic regre…
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.
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.
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 for Penalized Estimationstat.CO
Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The majorization-minimization (MM) algorithm is a computational scheme for stability and simplicity, and …
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.
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.
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.
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.
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.
The purpose of this paper is the study of the roots in the mapping class groups. Let be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the interior of , and let $\MM (Σ, \PP)$ denote the mapping class group of $(Σ, \PP)$. We prove that, if is of genus 0, then ea…
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.
Interface Foliation Near Minimal Submanifolds in Riemannian Manifolds with Positive Ricci Curvaturemath.AP
Let $(\MM ,{\tilde g})$ be an -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 is a small parameter. Let $\KK\subset \MM$ be an -dimensional smooth minimal submanifold …
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.
In this paper, we study a popular method for inference of the Bradley-Terry model parameters, namely the MM algorithm, for maximum likelihood estimation and maximum a posteriori probability estimation. This class of models includes the Bradley-Terry model of paired comparisons, the Rao-Kupper model of paired comparison…
We present a selective sampling method designed to accelerate the training of deep neural networks. To this end, we introduce a novel measurement, the minimal margin score (MMS), which measures the minimal amount of displacement an input should take until its predicted classification is switched. For multi-class linear…
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.
Identification of Cancer -- Mesothelioma Disease Using Logistic Regression and Association Rulecs.CY
Malignant Pleural Mesothelioma (MPM) or malignant mesothelioma (MM) is an atypical, aggressive tumor that matures into cancer in the pleura, a stratum of tissue bordering the lungs. Diagnosis of MPM is difficult and it accounts for about seventy-five percent of all mesothelioma diagnosed yearly in the United States of …
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.
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Alg…
The measure concentration property of an mm-space is roughly described as that any 1-Lipschitz map on to a metric space is almost close to a constant map. The target space is called the screen. The case of 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.
Let be the energy of some knot for any 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 and maximizes some others. So, is there any energy such that the circle ne…
Mixture-of-experts (MoE) models are a powerful paradigm for modeling of data arising from complex data generating processes (DGPs). In this article, we demonstrate how different MoE models can be constructed to approximate the underlying DGPs of arbitrary types of data. Due to the probabilistic nature of MoE models, we…
We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [14,…
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.
Sufficient dimension reduction (SDR) using distance covariance (DCOV) was recently proposed as an approach to dimension-reduction problems. Compared with other SDR methods, it is model-free without estimating link function and does not require any particular distributions on predictors (see Sheng and Yin, 2013, 2016). …
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.
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking the prior structure information into account in the estimation procedure is benef…
In this paper we introduce some new copulas emerging from shock models. It was shown earlier that reflected maxmin copulas (RMM for short) are not just some specific singular copulas; they contain many important absolutely continuous copulas including the negative quadrant dependent part of the Eyraud-Farlie-Gumbel-Mor…
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.
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.
We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov models (KDE-MMs) we discuss are nonlinear, nonparametric, fully probabilistic repr…
RLMM extends psychometric models to larger tasks.
problem Sequential process data from interactive assessments are not well handled by conventional models.
method RLMM decouples person-level choice sensitivity from task-level value representation through a shared parametric action-value function.
result RLMM achieves higher estimation accuracy and lower runtime than MDP-MM in peg-solitaire simulations and AQUALAB gameplay logs.
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.
A Stochastic Model for Illiquid Stock Prices and its Conclusion about Correlation Measurementq-fin.ST
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.
Unified NMF models for various noise distributions, improving feature extraction.
problem Inadequate assumptions for NMF under complex data distributions.
method Unified framework using MM-algorithms for traditional and convex NMF under Tweedie and Negative Binomial models.
result Unified multiplicative update rules for all models, including novel updates for convex NMF.
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.
Deformation estimation of elastic object assuming an internal organ is important for the computer navigation of surgery. The aim of this study is to estimate the deformation of an entire three-dimensional elastic object using displacement information of very few observation points. A learning approach with a neural net…
Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.
problem Lasso's sensitivity to outliers and heavy-tailed noise in high-dimensional statistics.
method Integrates an exponential-type loss function into the Lasso framework.
result Achieves strong statistical convergence rates robust to heavy-tailed contamination.
We revisit and demonstrate the Epps effect using two well-known non-parametric covariance estimators; the Malliavin and Mancino (MM), and Hayashi and Yoshida (HY) estimators. We show the existence of the Epps effect in the top 10 stocks from the Johannesburg Stock Exchange (JSE) by various methods of aggregating Trade …
Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been prop…
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.
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.
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.