BCD-Net improves low-dose CT image reconstruction.
problem Challenges in obtaining accurate low-dose CT images.
method Modified iterative regression CNN, BCD-Net, with faster numerical solvers.
result BCD-Net achieves better image quality and generalization than state-of-the-art methods.
BCD-prox improves robustness and accuracy in filtering and parameter estimation.
problem Simultaneous filtering and parameter estimation of complex ODE models.
method Block coordinate descent proximal algorithm (BCD-prox) for ODE systems.
result BCD-prox outperforms state-of-the-art methods in robustness, accuracy, and training time.
BCD-Net uses identical CNN structures for image recovery in undersampled imaging.
problem Challenges in obtaining accurate images from undersampled or noisy measurements.
method Incorporates image mapping CNN into BCD signal recovery method using alternating direction method of multipliers.
result Significantly more accurate image recovery compared to existing methods.
BCD algorithm finds global minima in neural networks.
problem Training deep neural networks to find global minima.
method Block coordinate descent with skip connections and non-negative projection.
result Proves convergence to global minima for strictly monotonic and ReLU activations.
Improved DNN training with BCD converging faster than SGD.
problem Training deep neural networks efficiently and accurately.
method Developed a smooth multi-convex formulation and BCD algorithm for training Tikhonov regularized DNNs.
result BCD algorithm converges globally to a stationary point with R-linear rate.
This paper introduces a new method for optimizing large-scale problems using Markov chain block updates.
problem Optimizing large-scale problems with efficient and natural block selection.
method Markov chain block coordinate descent (BCD) for optimization.
result The method converges for minimizing Lipschitz differentiable functions, with sublinear and linear convergence rates for convex and strongly convex functions, respectively.
BCD-Net improves PET image reconstruction in low-count scenarios.
problem Low-count PET imaging challenges due to high random fractions and low SNR.
method Modified BCD-Net architecture for iterative neural network-based PET image reconstruction.
result BCD-Net significantly improves CNR and RMSE of reconstructed images compared to traditional methods.
BCD Nets use variational inference to estimate DAGs with uncertainty.
problem Uncertainty in inferring causal graphs from limited data.
method Variational inference framework for Bayesian DAG estimation.
result BCD Nets outperform maximum-likelihood methods in low data regimes.
BCD methods provide provable convergence guarantees for deep learning models.
problem Theoretical convergence guarantees for BCD methods in deep learning.
method Established global convergence rate of O(1/k) for DNN training models.
result Global convergence to a critical point at a rate of O(1/k) for most DNN training models.
Paper proposes a framework and algorithm for model compression in neural networks.
problem Training neural networks with model compression techniques suffers from accuracy loss and convergence issues.
method Holistic framework based on nonconvex optimization, using NN-BCD algorithm with closed-form iteration scheme.
result The proposed algorithm globally converges to a critical point at a rate of O(1/k).
A new algorithm for training deep neural networks efficiently.
problem Efficient training of deep neural networks due to nonconvex optimization.
method Proximal block coordinate descent (BCD) algorithm based on the Kurdyka-Lojasiewicz (KL) property.
result Global convergence results and competitive efficiency compared to standard optimizers.
The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions, or solve a stochastic optimization problem, to a moderate accuracy. The block coordinate descent/update (BCD) method, on the other hand, handles problems with multiple blocks of variables by up…
A new algorithm for optimizing huge-scale black-box problems with reduced memory usage.
problem Optimizing huge-scale black-box problems with limited vector operations.
method ZO-BCD algorithm for zeroth-order optimization with reduced memory footprint.
result ZO-BCD achieves state-of-the-art adversarial attack success rate of 97.9%.
For the root systems of type Bl,Cl and Dl, we generalize the result of \cite{DZ1998} by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in \cite{DZ1998}. It also …
In this paper we consider sparse approximation problems, that is, general l0 minimization problems with the l0-"norm" of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) me…
Study shows unique sharp local minimum in ℓ1-minimization for dictionary learning.
problem Global recovery of a dictionary from random linear combinations of atoms.
method Norm condition, explicit bound, perturbation-based test, Block Coordinate Descent algorithm.
result Reference dictionary is the unique sharp local minimum of the ℓ1 objective function. A novel algorithm converges for solving a specific matrix decomposition problem.
problem Nonlinear matrix decomposition with ReLU function for sparse data.
method Introduced a reparametrization of the Latent-RMD model and developed eBCD for convergence proof.
result eBCD converges and outperforms state-of-the-art methods on various data sets.
A model learns causal representations from high-dimensional data.
problem Challenges in learning causal representations from high-dimensional data.
method Formulated a latent variable decoder model, Decoder BCD, for Bayesian causal discovery.
result Shows that using known intervention targets as labels helps in unsupervised Bayesian inference over structure and parameters.
The problem of outlier detection is extremely challenging in many domains such as text, in which the attribute values are typically non-negative, and most values are zero. In such cases, it often becomes difficult to separate the outliers from the natural variations in the patterns in the underlying data. In this paper…
We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the alternating direction method of multipliers (ADMM): each matrix factor is updated in tur…
CAKD framework optimizes knowledge transfer by focusing on influential components of distillation.
problem Balancing and optimizing knowledge transfer in distillation models.
method Decouple KL divergence into BCD, SCD, and WCD; prioritize influential components.
result CAKD framework consistently outperforms baseline across diverse models and datasets.
Study tackles nonlinear factor models with unknown monotone links from incomplete and noisy data.
problem Learning nonlinear factor models with unknown monotone links from incomplete and noisy data.
method Formulated as joint recovery of low-rank factors, loadings, and nonlinear link function; proposed BCD algorithm with regularization.
result Established convergence guarantees and sublinear regret bounds for link-function updates.
We present a hybrid method for latent information discovery on the data sets containing both text content and connection structure based on constrained low rank approximation. The new method jointly optimizes the Nonnegative Matrix Factorization (NMF) objective function for text clustering and the Symmetric NMF (SymNMF…
Paper optimizes UAV-assisted mobile edge computing for energy efficiency.
problem Minimizing energy consumption in UAV-assisted mobile edge computing.
method Proposes CAT and RAT algorithms combining convex optimization and deep reinforcement learning.
result RAT achieves similar performance and outperforms traditional algorithms.
SON-NMF estimates nonnegative rank on-the-fly for NMF.
problem Estimating the nonnegative rank of data in NMF.
method Sum-of-norms (SON) regularization to reduce rank, combined with a first-order BCD algorithm.
result SON-NMF can automatically estimate the rank from data without prior knowledge.
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this relatively low degree of popularity is the lack of a well developed system of theory an…
GA optimizes EEG feature selection for BCI systems, improving classification accuracy.
problem Finding optimal EEG features for accurate classification in BCI systems.
method Genetic Algorithm (GA) for feature selection and classifier optimization.
result Katz fractal feature with LDA yields highest fitness value.