Nonparametric Regression for Exploring Data

This paper presents the adaptation of the Cross Ambiguity Function Mapping (CAF- Mapping) algorithm for use in acoustics. The CAF-Mapping algorithm provides a useful means of generating a geographic visualization of acoustic data. Modifications of the algorithm for use in acoustics are explained, including use of acoustic modeling to generate propagation time differences, nonlinear grid spacing for frequency differences, location seeding using either three sensors or two sensors and two data samples, and frequency normalization. The algorithm allows discrimination between multiple acoustic signals with spatial or velocity vector variance. The presentation compares simulation results for several different types of data, then provides results that track a likely group of pygmy blue whale (Balaenoptera musculus brevicauda) using data from the Comprehensive Test Ban Treaty (CTBT) sensors off the coast of Australia. The author's affiliation with The MITRE Corporation is provided for identification purposes only and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions, or viewpoints expressed by the author. [Approved for Public Release; Distribution Unlimited Case 19-1301. Copyright 2019, The MITRE Corporation.]This paper presents the adaptation of the Cross Ambiguity Function Mapping (CAF- Mapping) algorithm for use in acoustics. The CAF-Mapping algorithm provides a useful means of generating a geographic visualization of acoustic data. Modifications of the algorithm for use in acoustics are explained, including use of acoustic modeling to generate propagation time differences, nonlinear grid spacing for frequency differences, location seeding using either three sensors or two sensors and two data samples, and frequency normalization. The algorithm allows discrimination between multiple acoustic signals with spatial or velocity vector variance. The presentation compares simulation results for several different types of data, then provides results that track a likely group of pygmy blue whale (Balaenoptera musculus brevicauda) using data from the Comprehensive Test Ban Treaty (CTBT) sensors off the coast of Australia. The author's affiliation with The MITRE Corporation is provided for identification purposes onl...

Linear systems are good approximations of the input-output relationship for many real systems. In practice, ensembles of nominally identical systems can seldom be adequately represented by a single linear system. Some accommodation needs to be made for representing inherent ensemble randomness. One approach would be to use a parameterized model of the system, with the random nature captured in discrete parameters of the parameterized model. Another approach is to use data measured from each system in the ensemble to represent the random nature of the ensemble in a non-parametric form. This is the approach described in this paper. There are several different types of data that could be collected from each system in the ensemble, each type capable of capturing the input-output behavior of the linear system: input-output time domain data, perhaps with specific excitation sequences; Markov parameters; and Frequency Response Functions (FRFs) to name a few. We choose to work with FRF data because many system attributes can be easily interpreted by inspection of the FRF. FRF data can also be used directly for control design. This paper develops a Karhunen-Loeve expansion representation for linear system behavior based on FRF data to develop a compact representation of the uncertainty inherent in an ensemble of systems. This non-parametric, compact, representation of the distribution of linear systems can then be used to characterize the performance and stability of a given feedback control law, as well as for control law design.

A prototype of a computerized patient record

Biomedical questions are often complex and address multiple topics simultaneously. Answering them requires the comprehensive evaluation of several different types of data. They are often available, but in distributed and heterogeneous data sources; this hampers their global evaluation. We developed a software architecture to create and maintain updated a Genomic and Proteomic Data Warehouse (GPDW), which integrates several of the main of such dispersed data. It uses a modular and multi-level global data schema based on abstraction and generalization of integrated data features. Such a schema eases integration of data sources evolving in data content, structure and number, and assures provenance tracking of all the integrated data. Thanks to the developed software architecture and adopted data schema, the GPDW has been kept updated easily and progressively extended with additional data types and sources; it is publicly usable at http://www.bioinformatics.dei.polimi.it/GPKB/.

Understanding how ensembles of neurons collectively interact will be a key step in developing a mechanistic theory of cognitive processes. Recent progress in multineuron recording and analysis techniques has generated tremendous excitement over the physiology of living neural networks. One of the key developments driving this interest is a new class of models based on the principle of maximum entropy. Maximum entropy models have been reported to account for spatial correlation structure in ensembles of neurons recorded from several different types of data. Importantly, these models require only information about the firing rates of individual neurons and their pairwise correlations. If this approach is generally applicable, it would drastically simplify the problem of understanding how neural networks behave. Given the interest in this method, several groups now have worked to extend maximum entropy models to account for temporal correlations. Here, we review how maximum entropy models have been applied to neuronal ensemble data to account for spatial and temporal correlations. We also discuss criticisms of the maximum entropy approach that argue that it is not generally applicable to larger ensembles of neurons. We conclude that future maximum entropy models will need to address three issues: temporal correlations, higher-order correlations, and larger ensemble sizes. Finally, we provide a brief list of topics for future research.

Regression analysis is one method in statistics that used to know the pattern of functional relationships between response variables and predictor variables. Combination of parametric and nonparametric regression is semi parametric regression. The most popular estimator for nonparametric or semi parametric regression is spline truncated estimator. Problems in everyday life often using regression modeling with longitudinal data. Longitudinal data is a combination of cross-section data and time-series data. In longitudinal data, between subjects are independent of each other but between observations in the subject are dependent. One of the most important parts of statistical inference is interval estimation. Interval estimation aims to determine predictor variables that have a significant effect on the response variable. This study aims to obtain the form of interval estimation for parameters of semi parametric regression models using spline truncated estimator in longitudinal data. To solve this problem, the Weighted Least Square method and a pivotal quantity method were used for unknown population variance cases. The result of the theoretical study was that pivotal quantity distributed student-t. The shortest parameter interval estimation of semi parametric spline truncated regression model was obtained through the optimization process using the method of Lagrange.Regression analysis is one method in statistics that used to know the pattern of functional relationships between response variables and predictor variables. Combination of parametric and nonparametric regression is semi parametric regression. The most popular estimator for nonparametric or semi parametric regression is spline truncated estimator. Problems in everyday life often using regression modeling with longitudinal data. Longitudinal data is a combination of cross-section data and time-series data. In longitudinal data, between subjects are independent of each other but between observations in the subject are dependent. One of the most important parts of statistical inference is interval estimation. Interval estimation aims to determine predictor variables that have a significant effect on the response variable. This study aims to obtain the form of interval estimation for parameters of semi parametric regression models using spline truncated estimator in longitudinal data. To solve this problem, t...

Indonesia Composite Index (IHSG) is an indicator of stock price changes in Indonesia Stock Exchange. IHSG is time series data that can be modeled with parametric models. But there are some assumptions for parametric model, while the fluctuated IHSG data usually doesn’t occupy these assumptions. Another alternative for this study is nonparametric regression. Penalized spline regression is one of nonparametric regression method that can be used. The optimal penalized spline models depends on the determination of the optimal smoothing parameter λ and the optimal number of knots, that has a minimum value of Generalized Cross Validation (GCV). The best model in this study is penalized spline degree 1 (linear) with 1 knot, that is 5120,625, smoothing parameter λ value is 41590, and GCV value is 1567,203. R 2 value for in sample data is 83,2694% and R 2 value for out sample data is 96,4976% show that the model have a very good performance. MAPE values for in sample data is 0,5983% and MAPE values for out sample data is 0,4974%. Because the value of MAPE in sample and out sample is less than 10%, it means that the performance of the model and forecasting are very accurate. Keywords: Indonesia Composite Index, Nonparametric Regression, Penalized Spline Regression, GCV, MAPE

For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the non parametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach mayreadily be extended to handle partial linear, and linear autoregressive models.

Spatial linear mixed-models, consisting of a linear covariate effect and a Gaussian process (GP) distributed spatial random effect, are widely used for analyses of geospatial data. We consider the setting where the covariate effect is nonlinear. Random forests (RF) are popular for estimating nonlinear functions but applications of RF for spatial data have often ignored the spatial correlation. We show that this impacts the performance of RF adversely. We propose RF-GLS, a novel and well-principled extension of RF, for estimating nonlinear covariate effects in spatial mixed models where the spatial correlation is modeled using GP. RF-GLS extends RF in the same way generalized least squares (GLS) fundamentally extends ordinary least squares (OLS) to accommodate for dependence in linear models. RF becomes a special case of RF-GLS, and is substantially outperformed by RF-GLS for both estimation and prediction across extensive numerical experiments with spatially correlated data. RF-GLS can be used for functional estimation in other types of dependent data like time series. We prove consistency of RF-GLS for β-mixing dependent error processes that include the popular spatial Matérn GP. As a byproduct, we also establish, to our knowledge, the first consistency result for RF under dependence. We establish results of independent importance, including a general consistency result of GLS optimizers of data-driven function classes, and a uniform law of large number under β-mixing dependence with weaker assumptions. These new tools can be potentially useful for asymptotic analysis of other GLS-style estimators in nonparametric regression with dependent data.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

To present an application of optimal controller design to a block-ice production process using dynamic programming. First, we develop mathematical models for such a process by employing system identification techniques. In particular, we build two parametric models, namely, linear model and neural network model. Linear models are built with Auto-Regressive model with exogenous inputs (linear ARX model). Feedforward neural networks (NNARX model) are constructed using the information provided by the linear ARX models. In addition, the Optimal Brain Surgeon (OBS) method is employed to prune the neural network models. Comparing the experimental results obtained from these models, it indicates that linear ARX models yield reasonably good performance in terms of the model fit. Then, using the obtained models, we investigate the energy consumption and operation cost of an ice factory when using time of use (TOU) tariff and time of day (TOD) tariff. Specifically, we develop an optimal control design for block-ice production process. The optimal strategy aims to minimize the electricity cost over a finite-time horizon and is subjected to constraints involving the control input of compressors, the brine temperature, and the number of block-ices ready for sales. Moreover, various factors in the design criteria have been analyzed with respect to the energy consumption and the operation cost. We compare the performance of the optimal controllers and the conventional control strategy. The simulation reveals that the proposed optimal control design has better performance than that of the conventional control. Furthermore, the optimal control using TOU tariff can reduce the operation cost when comparing to the one using TOD tariff.

The nonparametric binary logistic model assumes that the logit function is a linear function in the parameter, where the parameter depends on arbitrary fixed point. This study discusses the estimation of a nonparametric binary logistic regression model using the local likelihood logit estimation method. This method assumes that the log likelihood logit function depends on the multivariate kernel weighting. The parameter estimation of a nonparametric binary logistic regression model is obtained by maximizing the log likelihood logit function. The parameter estimation result are implicit, so to estimate it started with determining the optimal bandwidth value based on the maximum Cross Validation value. Furthermore, the optimal bandwidth value is used to estimate parameters using the multivariate Newton-Raphson algorithm until converging iterations are obtained. The parameter estimation process is done by creating a program in OSS-R software. This study also discusses the application of parametric and nonparametric binary logistic regression models in the case study of Type II Diabetes Mellitus patients at the Surabaya Hajj General Hospital. The modeling results show that the classification accuracy value of the parametric and nonparametric binary logistic regression models is 80.2% and 100% for the cut of value of 0.5.

We study the exact anomaly model of a simple two-level GCM. Linear predictions made from the initial state and a posteriori forcings are described. From the initial state alone, a linear barotropic model is superior to dependent persistence forecasts. Even greater dependent and independent skill is obtained from a linear baroclinic model, especially at short time scales. Inclusion of an empirical linear prediction for surface temperature provides only a marginal improvement, despite the significant effect that the surface temperature field has a posteriori on the atmospheric anomalies. This marginal improvement is related to the skill of the linear model in predicting the surface temperature which is the same as for predicting the atmospheric anomalies. Inclusion of an empirical parameterization for the transient eddies provides a significant improvement to the linear models. This parameterization method is also used to parameterize the baroclinic forcings in a barotropic model. The heavily parameterized barotropic model shows a significant improvement, and is comparable to the parameterized linear baroclinic model, especially for long term forecasts. DOI: 10.1034/j.1600-0870.1991.t01-1-00001.x

ABSTRACTThe Dirichlet process has been used extensively in Bayesian non parametric modeling, and has proven to be very useful. In particular, mixed models with Dirichlet process random effects have been used in modeling many types of data and can often outperform their normal random effect counterparts. Here we examine the linear mixed model with Dirichlet process random effects from a classical view, and derive the best linear unbiased estimator (BLUE) of the fixed effects. We are also able to calculate the resulting covariance matrix and find that the covariance is directly related to the precision parameter of the Dirichlet process, giving a new interpretation of this parameter. We also characterize the relationship between the BLUE and the ordinary least-squares (OLS) estimator and show how confidence intervals can be approximated.

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.