Polynomial-based surrogate modeling of RF and microwave circuits in frequency domain exploiting the multinomial theorem

A general formulation to develop EM-based polynomial surrogate models in frequency domain utilizing the multinomial theorem is presented in this paper. Our approach is especially suitable when the number of learning samples is very limited and no physics-based coarse model is available. We compare our methodology against other four surrogate modeling techniques: response surface modeling, support vector machines, generalized regression neural networks, and Kriging. Results confirm that our modeling approach has the best performance among these techniques when using a very small amount of learning base points on relatively small modeling regions. We illustrate our technique by developing a surrogate model for an SIW interconnect with transitions to microstrip lines, a dual band T-slot PIFA handset antenna, and a high-speed package interconnect. Examples are simulated on a commercially available 3D FEM simulator

Bayesian nonlinear regression for large p small n problems

AbstractStatistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. This is known as large p small n problem. Furthermore, the problem is more complicated when we have multiple correlated responses. We develop multivariate nonlinear regression models in this setup for accurate prediction. In this paper, we introduce a full Bayesian support vector regression model with Vapnik’s ϵ-insensitive loss function, based on reproducing kernel Hilbert spaces (RKHS) under the multivariate correlated response setup. This provides a full probabilistic description of support vector machine (SVM) rather than an algorithm for fitting purposes. We have also introduced a multivariate version of the relevance vector machine (RVM). Instead of the original treatment of the RVM relying on the use of type II maximum likelihood estimates of the hyper-parameters, we put a prior on the hyper-parameters and use Markov chain Monte Carlo technique for computation. We have also proposed an empirical Bayes method for our RVM and SVM. Our methods are illustrated with a prediction problem in the near-infrared (NIR) spectroscopy. A simulation study is also undertaken to check the prediction accuracy of our models

High-Level Concepts for Affective Understanding of Images

This paper aims to bridge the affective gap between image content and the emotional response of the viewer it elicits by using High-Level Concepts (HLCs). In contrast to previous work that relied solely on low-level features or used convolutional neural network (CNN) as a black-box, we use HLCs generated by pretrained CNNs in an explicit way to investigate the relations/associations between these HLCs and a (small) set of Ekman's emotional classes. As a proof-of-concept, we first propose a linear admixture model for modeling these relations, and the resulting computational framework allows us to determine the associations between each emotion class and certain HLCs (objects and places). This linear model is further extended to a nonlinear model using support vector regression (SVR) that aims to predict the viewer's emotional response using both low-level image features and HLCs extracted from images. These class-specific regressors are then assembled into a regressor ensemble that provide a flexible and effective predictor for predicting viewer's emotional responses from images. Experimental results have demonstrated that our results are comparable to existing methods, with a clear view of the association between HLCs and emotional classes that is ostensibly missing in most existing work

Bacterial Growth Classification with Support Vector Machines: A Comparative Study

In this paper, we propose to use support vector machines for classification of bacterial growth and non growth database and modeling the probability= of growth. Unlike artificial neural networks paradigms, support vector machines use the kernel functions and support vectors with maximum margin, which allows a better performance. As a practical application of the new approach, support vector machines were investigated for their quality and accuracy in classifi-cation of growth/no-growth state of a pathogenic Escherichia coli R31 in response to temperature and water activity. A comparison with the most common used statistics, machine learning, and data mining schemes was carried out. The results shows that support vector machines classifier based on the Gaussian RBF Kernel was found to do better than most of logistic regression, K-nearest neighbor, probabilistic networks, and multilayer perceptron classifiers

Cost-efficient modeling of antenna structures using Gradient Enhanced Kriging

Reliable yet fast surrogate models are indispensable in the design of contemporary antenna structures. Data-driven models, e.g., based on Gaussian Processes or support-vector regression, offer sufficient flexibility and speed, however, their setup cost is large and grows very quickly with the dimensionality of the design space. In this paper, we propose cost-efficient modeling of antenna structures using Gradient-Enhanced Kriging. In our approach, the training data set contains, apart from the EM-simulation responses of the structure at hand, also derivative data at the respective training locations obtained at little extra cost using adjoint sensitivity techniques. We demonstrate that introduction of the derivative information into the model allows for considerable reduction of the model setup cost (in terms of the number of training points required) without compromising its predictive power. The Gradient-Enhanced Kriging technique is illustrated using a dielectric resonator antenna structure. Comparison with conventional Kriging interpolation is also provided

Variable-fidelity electromagnetic simulations and co-kriging for accurate modeling of antennas

Accurate and fast models are indispensable in contemporary antenna design. In this paper, we describe the low-cost antenna modeling methodology involving variable-fidelity electromagnetic (EM) simulations and co-Kriging. Our approach exploits sparsely sampled accurate (high-fidelity) EM data as well as densely sampled coarse-discretization (low-fidelity) EM simulations that are accommodated into one model using the co-Kriging technique. By using coarse-discretization simulations, the computational cost of creating the antenna model is greatly reduced compared to conventional approaches, where high-fidelity simulations are directly used to set up the model. At the same time, the modeling accuracy is not compromised. The proposed technique is demonstrated using three examples of antenna structures. Comparisons with conventional modeling based on high-fidelity data approximation, as well as applications for antenna design, are also discussed

Uplift Modeling with Multiple Treatments and General Response Types

Randomized experiments have been used to assist decision-making in many areas. They help people select the optimal treatment for the test population with certain statistical guarantee. However, subjects can show significant heterogeneity in response to treatments. The problem of customizing treatment assignment based on subject characteristics is known as uplift modeling, differential response analysis, or personalized treatment learning in literature. A key feature for uplift modeling is that the data is unlabeled. It is impossible to know whether the chosen treatment is optimal for an individual subject because response under alternative treatments is unobserved. This presents a challenge to both the training and the evaluation of uplift models. In this paper we describe how to obtain an unbiased estimate of the key performance metric of an uplift model, the expected response. We present a new uplift algorithm which creates a forest of randomized trees. The trees are built with a splitting criterion designed to directly optimize their uplift performance based on the proposed evaluation method. Both the evaluation method and the algorithm apply to arbitrary number of treatments and general response types. Experimental results on synthetic data and industry-provided data show that our algorithm leads to significant performance improvement over other applicable methods