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Found 21 papers, 15 papers with code
On the Complexity of First-Order Methods in Stochastic Bilevel Optimization
We study the complexity of finding stationary points with such an $y^*$-aware oracle: we propose a simple first-order method that converges to an $\epsilon$ stationary point using $O(\epsilon^{-6}), O(\epsilon^{-4})$ access to first-order $y^*$-aware oracles.
Stochastic optimization with arbitrary recurrent data sampling
For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency.
Convergence and complexity of block majorization-minimization for constrained block-Riemannian optimization
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are held fixed.
Interpretable Online Network Dictionary Learning for Inferring Long-Range Chromatin Interactions
First, we demonstrate that online cvxNDL retains the accuracy of classical DL methods while simultaneously ensuring unique interpretability and scalability.
A latent linear model for nonlinear coupled oscillators on graphs
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph.
Exponentially Convergent Algorithms for Supervised Matrix Factorization
Supervised matrix factorization (SMF) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives.
Supervised low-rank semi-nonnegative matrix factorization with frequency regularization for forecasting spatio-temporal data
We propose a novel methodology for forecasting spatio-temporal data using supervised semi-nonnegative matrix factorization (SSNMF) with frequency regularization.
Complexity of Block Coordinate Descent with Proximal Regularization and Applications to Wasserstein CP-dictionary Learning
We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical applications.
Supervised Dictionary Learning with Auxiliary Covariates
Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives.
Convergence of First-Order Methods for Constrained Nonconvex Optimization with Dependent Data
As an application, we obtain first online nonnegative matrix factorization algorithms for dependent data based on stochastic projected gradient methods with adaptive step sizes and optimal rate of convergence.
Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogates
The surrogates are required to be strongly convex and convergence rate analysis for the general non-convex setting was not available.
Learning low-rank latent mesoscale structures in networks
It is common to use networks to encode the architecture of interactions between entities in complex systems in the physical, biological, social, and information sciences.
Learning to predict synchronization of coupled oscillators on randomly generated graphs
However, in the problem setting where these graph statistics cannot distinguish the two classes very well (e. g., when the graphs are generated from the same random graph model), we find that pairing a few iterations of the initial dynamics along with the graph statistics as the input to our classification algorithms can lead to significant improvement in accuracy; far exceeding what is known by the classical oscillator theory.
Block majorization-minimization with diminishing radius for constrained nonconvex optimization
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex constrained optimization that sequentially minimizes majorizing surrogates of the objective function in each block coordinate while the other coordinates are held fixed.
Applications of Online Nonnegative Matrix Factorization to Image and Time-Series Data
Online nonnegative matrix factorization (ONMF) is a matrix factorization technique in the online setting where data are acquired in a streaming fashion and the matrix factors are updated each time.
Sparseness-constrained Nonnegative Tensor Factorization for Detecting Topics at Different Time Scales
Further, we propose quantitative ways to measure the topic length and demonstrate the ability of S-NCPD (as well as its online variant) to discover short and long-lasting temporal topics in a controlled manner in semi-synthetic and real-world data including news headlines.
Online nonnegative CP-dictionary learning for Markovian data
We prove that our algorithm converges almost surely to the set of stationary points of the objective function under the hypothesis that the sequence of data tensors is generated by an underlying Markov chain.
COVID-19 Time-series Prediction by Joint Dictionary Learning and Online NMF
One of the main sources of difficulty is that a very limited amount of daily COVID-19 case data is available, and with few exceptions, the majority of countries are currently in the "exponential spread stage," and thus there is scarce information available which would enable one to predict the phase transition between spread and containment.
Topic-aware chatbot using Recurrent Neural Networks and Nonnegative Matrix Factorization
We propose a novel model for a topic-aware chatbot by combining the traditional Recurrent Neural Network (RNN) encoder-decoder model with a topic attention layer based on Nonnegative Matrix Factorization (NMF).
Online matrix factorization for Markovian data and applications to Network Dictionary Learning
As the main application, by combining online non-negative matrix factorization and a recent MCMC algorithm for sampling motifs from networks, we propose a novel framework of Network Dictionary Learning, which extracts ``network dictionary patches' from a given network in an online manner that encodes main features of the network.
Sampling random graph homomorphisms and applications to network data analysis
We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages.
