Dirichlet process mixture of Gaussians (DPMG) has been used in the literature for clustering and density estimation problems. However, many real-world data exhibit cluster distributions that cannot be captured by a single Gaussian. Modeling such data sets by DPMG creates several extraneous clusters even when clusters are relatively well-defined.

Dirichlet process mixture of Gaussians (DPMG) has been used in the literature for clustering and density estimation problems. However, many real-world data exhibit cluster distributions that cannot be captured by a single Gaussian. Modeling such data sets by DPMG creates several extraneous clusters even when clusters are relatively well-defined.

Dirichlet process mixture of Gaussians (DPMG) has been used in the literature for clustering and density estimation problems. However, many real-world data exhibit cluster distributions that cannot be captured by a single Gaussian. Modeling such data sets by DPMG creates several extraneous clusters even when clusters are relatively well-defined.

In this letter, we study the problem of accelerating reaching average consensus over connected graphs in a discrete-time communication setting. Literature has shown that consensus algorithms can be accelerated by increasing the graph connectivity or optimizing the weights agents place on the information received from their neighbors. Here, instead of altering the communication graph, we investigate two methods that use buffered states to accelerate reaching average consensus over a given graph. In the first method, we study how convergence rate of the well-known first-order Laplacian average consensus algorithm changes when agreement feedback is generated from buffered states. For this study, we obtain a sufficient condition on the ranges of buffered state that leads to faster convergence. In the second proposed method, we show how the average consensus problem can be cast as a convex optimization problem and solved by first-order accelerated optimization algorithms for strongly-convex cost functions. We construct an accelerated average consensus algorithm using the so-called Triple Momentum optimization algorithm. The first approach requires less global knowledge for choosing the step size, whereas the second one converges faster in our numerical results by using extra information from the graph topology. We demonstrate our results by implementing the proposed algorithms in a Gaussian Mixture Model (GMM) estimation problem used in sensor networks.

We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM) in an entirely automatic manner and simplifies an earlier supervised clustering approach [J. Chem. Theory Comput., 15, 6668 (2019)] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantage of accurately reproducing chemically intuitive groupings of frontier molecular orbitals and having improved performance with an increasing number of training examples. The resulting clusters from supervised or unsupervised clustering is further combined with scalable Gaussian process regression (GPR) or linear regression (LR) to learn molecular energies accurately by generating a local regression model in each cluster. Among all four combinations of regressors and clustering methods, GMM combined with scalable exact Gaussian process regression (GMM/GPR) is the most efficient training protocol for MOB-ML. The numerical tests of molecular energy learning on thermalized datasets of drug-like molecules demonstrate the improved accuracy, transferability, and learning efficiency of GMM/GPR over not only other training protocols for MOB-ML, i.e., supervised regression-clustering combined with GPR(RC/GPR) and GPR without clustering. GMM/GPR also provide the best molecular energy predictions compared with the ones from literature on the same benchmark datasets. With a lower scaling, GMM/GPR has a 10.4-fold speedup in wall-clock training time compared with scalable exact GPR with a training size of 6500 QM7b-T molecules.

We present an approach for efficiently training Gaussian Mixture Models (GMMs) with Stochastic Gradient Descent (SGD) on large amounts of high-dimensional data (e.g., images). In such a scenario, SGD is strongly superior in terms of execution time and memory usage, although it is conceptually more complex than the traditional Expectation-Maximization (EM) algorithm. For enabling SGD training, we propose three novel ideas: First, we show that minimizing an upper bound to the GMM log likelihood instead of the full one is feasible and numerically much more stable way in high-dimensional spaces. Secondly, we propose a new annealing procedure that prevents SGD from converging to pathological local minima. We also propose an SGD-compatible simplification to the full GMM model based on local principal directions, which avoids excessive memory use in high-dimensional spaces due to quadratic growth of covariance matrices. Experiments on several standard image datasets show the validity of our approach, and we provide a publicly available TensorFlow implementation.

A novel text-independent speaker identification (SI) method is proposed. This method uses the Mel-frequency Cepstral coefficients (MFCCs) and the dynamic information among adjacent frames as feature sets to capture speaker's characteristics. In order to utilize dynamic information, we design super-MFCCs features by cascading three neighboring MFCCs frames together. The probability density function (PDF) of these super-MFCCs features is estimated by the recently proposed histogram transform~(HT) method, which generates more training data by random transforms to realize the histogram PDF estimation and recedes the commonly occurred discontinuity problem in multivariate histograms computing. Compared to the conventional PDF estimation methods, such as Gaussian mixture models, the HT model shows promising improvement in the SI performance.

Dirichlet process mixture of Gaussians (DPMG) has been used in the literature for clustering and density estimation problems. However, many real-world data exhibit cluster distributions that cannot be captured by a single Gaussian. Modeling such data sets by DPMG creates several extraneous clusters even when clusters are relatively well-defined. Herein, we present the infinite mixture of infinite Gaussian mixtures (I2GMM) for more flexible modeling of data sets with skewed and multi-modal cluster distributions. Instead of using a single Gaussian for each cluster as in the standard DPMG model, the generative model of I2GMM uses a single DPMG for each cluster. The individual DPMGs are linked together through centering of their base distributions at the atoms of a higher level DP prior. Inference is performed by a collapsed Gibbs sampler that also enables partial parallelization. Experimental results on several artificial and real-world data sets suggest the proposed I2GMM model can predict clusters more accurately than existing variational Bayes and Gibbs sampler versions of DPMG.