2 research outputs found
Stochastic First-Order Learning for Large-Scale Flexibly Tied Gaussian Mixture Model
Gaussian Mixture Models (GMM) are one of the most potent parametric density
estimators based on the kernel model that finds application in many scientific
domains. In recent years, with the dramatic enlargement of data sources,
typical machine learning algorithms, e.g. Expectation Maximization (EM),
encounters difficulty with high-dimensional and streaming data. Moreover,
complicated densities often demand a large number of Gaussian components. This
paper proposes a fast online parameter estimation algorithm for GMM by using
first-order stochastic optimization. This approach provides a framework to cope
with the challenges of GMM when faced with high-dimensional streaming data and
complex densities by leveraging the flexibly-tied factorization of the
covariance matrix. A new stochastic Manifold optimization algorithm that
preserves the orthogonality is introduced and used along with the well-known
Euclidean space numerical optimization. Numerous empirical results on both
synthetic and real datasets justify the effectiveness of our proposed
stochastic method over EM-based methods in the sense of better-converged
maximum for likelihood function, fewer number of needed epochs for convergence,
and less time consumption per epoch
Bayesian Dynamic DAG Learning: Application in Discovering Dynamic Effective Connectome of Brain
Understanding the complex mechanisms of the brain can be unraveled by
extracting the Dynamic Effective Connectome (DEC). Recently, score-based
Directed Acyclic Graph (DAG) discovery methods have shown significant
improvements in extracting the causal structure and inferring effective
connectivity. However, learning DEC through these methods still faces two main
challenges: one with the fundamental impotence of high-dimensional dynamic DAG
discovery methods and the other with the low quality of fMRI data. In this
paper, we introduce Bayesian Dynamic DAG learning with M-matrices Acyclicity
characterization \textbf{(BDyMA)} method to address the challenges in
discovering DEC. The presented dynamic causal model enables us to discover
bidirected edges as well. Leveraging an unconstrained framework in the BDyMA
method leads to more accurate results in detecting high-dimensional networks,
achieving sparser outcomes, making it particularly suitable for extracting DEC.
Additionally, the score function of the BDyMA method allows the incorporation
of prior knowledge into the process of dynamic causal discovery which further
enhances the accuracy of results. Comprehensive simulations on synthetic data
and experiments on Human Connectome Project (HCP) data demonstrate that our
method can handle both of the two main challenges, yielding more accurate and
reliable DEC compared to state-of-the-art and baseline methods. Additionally,
we investigate the trustworthiness of DTI data as prior knowledge for DEC
discovery and show the improvements in DEC discovery when the DTI data is
incorporated into the process