Influence diagnostics in Gaussian spatial linear models

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

Preliminary Experience in Treatment of Papillary and Macular Retinoblastoma: Evaluation of Local Control and Local Complications After Treatment with Linear Accelerator-Based Stereotactic Radiotherapy with Micromultileaf Collimator as Second-Line or Salvage Treatment after chemotherapy

To determine the local control and complication rates for children with papillary and/or macular retinoblastoma progressing after chemotherapy and undergoing stereotactic radiotherapy (SRT) with a micromultileaf collimator.

Distributed static linear Gaussian models using consensus

Algorithms for distributed agreement are a powerful means for formulating distributed versions of existing centralized algorithms. We present a toolkit for this task and show how it can be used systematically to design fully distributed algorithms for static linear Gaussian models, including principal component analysis, factor analysis, and probabilistic principal component analysis. These algorithms do not rely on a fusion center, require only low-volume local (1-hop neighborhood) communications, and are thus efficient, scalable, and robust. We show how they are also guaranteed to asymptotically converge to the same solution as the corresponding existing centralized algorithms. Finally, we illustrate the functioning of our algorithms on two examples, and examine the inherent cost-performance tradeoff.

A unified framework for linear function approximation of value functions in stochastic control

This paper contributes with a unified formulation that merges previ- ous analysis on the prediction of the performance ( value function ) of certain sequence of actions ( policy ) when an agent operates a Markov decision process with large state-space. When the states are represented by features and the value function is linearly approxi- mated, our analysis reveals a new relationship between two common cost functions used to obtain the optimal approximation. In addition, this analysis allows us to propose an efficient adaptive algorithm that provides an unbiased linear estimate. The performance of the pro- posed algorithm is illustrated by simulation, showing competitive results when compared with the state-of-the-art solutions.

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

Specification and data presentation in linear control systems; [final report,

"EE 61-4. Research project PRF 30. Contract no. AF 29(600)-1933."

Economics of Douglas-fir tussock moth control : an analysis using the combined stand prognosis/Douglas-fir tussock moth outbreak model and the FORPLAN linear programming model on the Clearwater and Malheur National Forests /

"March 1984."

Comparison of linear optics quantum-computation control-sign gates with ancilla inefficiency and an improvement to functionality under these conditions

We compare three proposals for nondeterministic control-sign gates implemented using linear optics and conditional measurements with nonideal ancilla mode production and detection. The simplified Knill-Laflamme-Milburn gate [Ralph , Phys. Rev. A 65, 012314 (2001)] appears to be the most resilient under these conditions. We also find that the operation of this gate can be improved by adjusting the beam splitter ratios to compensate to some extent for the effects of the imperfect ancilla.

Gaussian regression and optimal finite dimensional linear models

The problem of regression under Gaussian assumptions is treated generally. The relationship between Bayesian prediction, regularization and smoothing is elucidated. The ideal regression is the posterior mean and its computation scales as O(n³), where n is the sample size. We show that the optimal m-dimensional linear model under a given prior is spanned by the first m eigenfunctions of a covariance operator, which is a trace-class operator. This is an infinite dimensional analogue of principal component analysis. The importance of Hilbert space methods to practical statistics is also discussed.

Neural network enhanced self tuning adaptive control application for non-linear control of dynamic systems

The main theme of research of this project concerns the study of neutral networks to control uncertain and non-linear control systems. This involves the control of continuous time, discrete time, hybrid and stochastic systems with input, state or output constraints by ensuring good performances. A great part of this project is devoted to the opening of frontiers between several mathematical and engineering approaches in order to tackle complex but very common non-linear control problems. The objectives are: 1. Design and develop procedures for neutral network enhanced self-tuning adaptive non-linear control systems; 2. To design, as a general procedure, neural network generalised minimum variance self-tuning controller for non-linear dynamic plants (Integration of neural network mapping with generalised minimum variance self-tuning controller strategies); 3. To develop a software package to evaluate control system performances using Matlab, Simulink and Neural Network toolbox. An adaptive control algorithm utilising a recurrent network as a model of a partial unknown non-linear plant with unmeasurable state is proposed. Appropriately, it appears that structured recurrent neural networks can provide conveniently parameterised dynamic models for many non-linear systems for use in adaptive control. Properties of static neural networks, which enabled successful design of stable adaptive control in the state feedback case, are also identified. A survey of the existing results is presented which puts them in a systematic framework showing their relation to classical self-tuning adaptive control application of neural control to a SISO/MIMO control. Simulation results demonstrate that the self-tuning design methods may be practically applicable to a reasonably large class of unknown linear and non-linear dynamic control systems.