Regression modeling for digital test of ΣΔ modulators

The cost of Analogue and Mixed-Signal circuit testing is an important bottleneck in the industry, due to timeconsuming verification of specifications that require state-ofthe- art Automatic Test Equipment. In this paper, we apply the concept of Alternate Test to achieve digital testing of converters. By training an ensemble of regression models that maps simple digital defect-oriented signatures onto Signal to Noise and Distortion Ratio (SNDR), an average error of 1:7% is achieved. Beyond the inference of functional metrics, we show that the approach can provide interesting diagnosis information.Ministerio de Educación y Ciencia TEC2007-68072/MICJunta de Andalucía TIC 5386, CT 30

Regression games

The solution of a TU cooperative game can be a distribution of the value of the grand coalition, i.e. it can be a distribution of the payo (utility) all the players together achieve. In a regression model, the evaluation of the explanatory variables can be a distribution of the overall t, i.e. the t of the model every regressor variable is involved. Furthermore, we can take regression models as TU cooperative games where the explanatory (regressor) variables are the players. In this paper we introduce the class of regression games, characterize it and apply the Shapley value to evaluating the explanatory variables in regression models. In order to support our approach we consider Young (1985)'s axiomatization of the Shapley value, and conclude that the Shapley value is a reasonable tool to evaluate the explanatory variables of regression models

Branch and bound method for regression-based controlled variable selection

Self-optimizing control is a promising method for selection of controlled variables (CVs) from available measurements. Recently, Ye, Cao, Li, and Song (2012) have proposed a globally optimal method for selection of self-optimizing CVs by converting the CV selection problem into a regression problem. In this approach, the necessary conditions of optimality (NCO) are approximated by linear combinations of available measurements over the entire operation region. In practice, it is desired that a subset of available measurements be combined as CVs to obtain a good trade-off between the economic performance and the complexity of control system. The subset selection problem, however, is combinatorial in nature, which makes the application of the globally optimal CV selection method to large-scale processes difficult. In this work, an efficient branch and bound (BAB) algorithm is developed to handle the computational complexity associated with the selection of globally optimal CVs. The proposed BAB algorithm identifies the best measurement subset such that the regression error in approximating NCO is minimized and is also applicable to the general regression problem. Numerical tests using randomly generated matrices and a binary distillation column case study demonstrate the computational efficiency of the proposed BAB algorithm

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Tensor Regression Networks

Convolutional neural networks typically consist of many convolutional layers followed by one or more fully connected layers. While convolutional layers map between high-order activation tensors, the fully connected layers operate on flattened activation vectors. Despite empirical success, this approach has notable drawbacks. Flattening followed by fully connected layers discards multilinear structure in the activations and requires many parameters. We address these problems by incorporating tensor algebraic operations that preserve multilinear structure at every layer. First, we introduce Tensor Contraction Layers (TCLs) that reduce the dimensionality of their input while preserving their multilinear structure using tensor contraction. Next, we introduce Tensor Regression Layers (TRLs), which express outputs through a low-rank multilinear mapping from a high-order activation tensor to an output tensor of arbitrary order. We learn the contraction and regression factors end-to-end, and produce accurate nets with fewer parameters. Additionally, our layers regularize networks by imposing low-rank constraints on the activations (TCL) and regression weights (TRL). Experiments on ImageNet show that, applied to VGG and ResNet architectures, TCLs and TRLs reduce the number of parameters compared to fully connected layers by more than 65% while maintaining or increasing accuracy. In addition to the space savings, our approach's ability to leverage topological structure can be crucial for structured data such as MRI. In particular, we demonstrate significant performance improvements over comparable architectures on three tasks associated with the UK Biobank dataset

Nonparametric regression analysis

textNonparametric regression uses nonparametric and flexible methods in analyzing complex data with unknown regression relationships by imposing minimum assumptions on the regression function. The theory and applications of nonparametric regression methods with an emphasis on kernel regression, smoothing spines and Gaussian process regression are reviewed in this report. Two datasets are analyzed to demonstrate and compare the three nonparametric regression models in R.Statistic