There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

System Identification I

https://people.kth.se/~crro/pubs/rojas_welsh_goodwin_feuer2007.pdf

Robust optimal experiment design for system identification

In this article, we analyze the SPICE method developed in , and establish its connections with other standard sparse estimation methods such as the Lasso and the LAD-Lasso. This result positions SPICE as a computationally efficient technique for the calculation of Lasso-type estimators. Conversely, this connection is very useful for establishing the asymptotic properties of SPICE under several problem scenarios and for suggesting suitable modifications in cases where the naive version of SPICE would not work.

/pdf/a-note-on-the-spice-method-4juqvw6spo.pdf

A Note on the SPICE Method

This paper aims to develop a new data-driven H-infinity norm estimation algorithm for model-error modeling of multivariable systems. An iterative approach is presented that requires significantly a ...

http://www.dct.tue.nl/toomen/files/OomenMaaRojHja2014preprint.pdf

Iterative Data-Driven H-infinity Norm Estimation of Multivariable Systems With Application to Robust Active Vibration Isolation

Model predictive control has become an increasingly popular control strategy thanks to the ability to handle constrained systems. Obtaining the required models through system identification is often a time consuming and costly process. Applications oriented experiment design is a means of reducing this effort but is often formulated in terms of the input's spectral properties. Therefore, time domain constraints are difficult to enforce. In this contribution we combine MPC with experiment design to formulate a control problem where excitation constraints are included. The benefits are that time domain constraints are respected while the experiment design criteria are fulfilled. The method is evaluated on a numerical example.

/pdf/model-predictive-control-with-integrated-experiment-design-wticujj116.pdf

Model predictive control with integrated experiment design for output error systems

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to changes in these model parameters. This change point detection and estimation problem is also referred to as total variation denoising or l1 -mean filtering and has many important applications in most fields of science and engineering. We establish the (approximate) sparse consistency properties, including rate of convergence, of the so-called fused lasso signal approximator (FLSA). We show that this only holds if the sign of the corresponding consecutive changes are all different, and that this estimator is otherwise incapable of correctly detecting the underlying sparsity pattern. The key idea is to notice that the optimality conditions for this problem can be analyzed using techniques related to brownian bridge theory.

Cristian R. Rojas

Papers

Robust optimal experiment design for system identification

A Note on the SPICE Method

Iterative Data-Driven H-infinity Norm Estimation of Multivariable Systems With Application to Robust Active Vibration Isolation

Model predictive control with integrated experiment design for output error systems

On change point detection using the fused lasso method