| 61. |
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| 62. |
- Judisky, Anatoli, et al.
(författare)
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Minimax Confidence Intervals for Pointwise Nonparametric Regression Estimation
- 2009
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Ingår i: Proceedings of the 15th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press.
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We address a problem of estimation of an unknown regression function f at a given point x0 from noisy observations yi = f(xi)+ ei, ;i =1, ..., n. Here xi in ε Rk are observable regressors and (e_i) are normal i.i.d. (unobservable) disturbances. The problem is analyzed in the minimax framework, namely, we suppose that f belongs to some functional class F, such that its finite-dimensional cut Fn = {f(xi), f ε F, i =0, ..., n, } is a convex compact set. For an arbitrary fixed regression plan Xn =(x1;...;xn) we study minimax on Fn confidence intervals of affine estimators and construct an estimator which attains the minimax performance on the class of arbitrary estimators when the confidence level approaches 1.
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| 63. |
- Lindgren, David, et al.
(författare)
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Clustered Regression Analysis
- 2002
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Ingår i: Proceedings of the 41st IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780375165 ; , s. 1838-1844 vol.2
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Konferensbidrag (refereegranskat)abstract
- Cluster structure in (multicollinear) data can be utilized by pattern recognition methods in order to find adequate subspaces for nonlinear regression. When regressing a particular severely nonlinear function, it is demonstrated that this approach is superior to polynomial PLS. It is also demonstrated that for nonlinear functions, the choice of regressing explained variables onto the explaining variables, or vice-versa, is not arbitrary. Numerical experiments indicate that the classical statistical model is more powerful than the inverse regression approach.
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| 64. |
- Lindgren, David, et al.
(författare)
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Nonlinear Dynamics Isolated by Delaunay Triangulation Criteria
- 2004
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Ingår i: Proceedings of the 43rd IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780386825 ; , s. 3862-3867 Vol.4
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Inspired by an idea by Q. Zhang, we show that Delaunay triangulation of data points sampled from a system with an additive nonlinearity gives a criterion by which a linear projection can be found that isolates the nonlinear dependence, leaving out the linear one. This isolation means the nonlinear modeling can be confined to a regressor space of lower dimensionality, which in turn means over-parameterization can be avoided. Monte Carlo simulations indicate that a particular criterion built on triangle asymmetries has a minimum that coincides with the sampled system nonlinear part. The criterion is however complex to compute and non-convex, which makes it difficult to optimize globally.
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| 65. |
- Lindskog, Peter, 1965-, et al.
(författare)
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Ensuring Certain Physical Properties in Black Box Models by Applying Fuzzy Techniques
- 1997
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Ingår i: Proceedings of the 11th IFAC Symposium on System Identification. - Linköping : Linköping University Electronic Press. - 0080425925 ; , s. 721-727
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We consider the situation where a nonlinear physical system is identified from input-output data. In case no specific physical structural knowledge about the system is available, parameterized grey box models cannot be used. Identification in black-box-type of model structures is then the only alternative, and general approaches like neural nets, neuro-fuzzy models, etc., have to be applied.However, certain non-structural knowledge about the system is sometimes available. It could be known, e.g., that the step response is monotonic, or that the steady-state gain curve is monotonic. The question is then how to utilize and maintain such knowledge in a black box framework.In this paper we show how to incorporate this type of prios information in an otherwise black box environment, by applying a specific fuzzy model structure, with strict parametric constraints. The usefulness of the apporach is illustrated by experiments on real-world data.
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| 66. |
- Lindsten, Fredrik, et al.
(författare)
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Clustering using Sum-of-Norms Regularization : With Application to Particle Filter Output Computation
- 2011
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Ingår i: Proceedings of the 2011 IEEE Statistical Signal Processing Workshop. - Linköping : Linköping University Electronic Press. - 9781457705694 ; , s. 201-204
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Konferensbidrag (refereegranskat)abstract
- We present a novel clustering method, formulated as a convex optimization problem. The method is based on over-parameterization and uses a sum-of-norms (SON) regularization to control the trade-off between the model fit and the number of clusters. Hence, the number of clusters can be automatically adapted to best describe the data, and need not to be specified a priori. We apply SON clustering to cluster the particles in a particle filter, an application where the number of clusters is often unknown and time varying, making SON clustering an attractive alternative.
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| 67. |
- Ljung, Lennart, 1946-, et al.
(författare)
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A Comment on Leakage in Adaptive Algorithms
- 1992
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Ingår i: Proceedings of the 4th IFAC International Symposium on Adaptive Systems in Control and Signal Processing. - Linköping : Linköping University. - 9780080425962 ; , s. 377-382
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Konferensbidrag (refereegranskat)abstract
- By "leakage" in adaptive control and adaptive signal processing algorithm is understood that a pull term towards a given parameter value is introduced. Leakage has been introduced both as trick to be able to prove certain convergence results as an ad hoc means for obtaining less drifting parameters. Leakage is the same as regularization and we explain what benefits - from an estimation point of view - this gives.
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| 68. |
- Ljung, Lennart, et al.
(författare)
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A Least Squares Interpretation of Sub-Space Methods for System Identification
- 1996
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Ingår i: Proceedings of the 35th IEEE Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780335902 ; , s. 335-342 vol.1
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- So called subspace methods for direct identification of linear models in state space form have drawn considerable interest. The algorithms consist of series of quite complex projections, and it is not so easy to intuitively understand how they work. They have also defied, so far, complete asymptotic analysis of their stochastic properties. This contribution describes an interpretation of how they work. It specifically deals with how consistent estimates of the dynamics can be achieved, even though correct predictors are not used. We stress how the basic idea is to focus on the estimation of the state-variable candidates-the k-step ahead output predictors.
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| 69. |
- Ljung, Lennart, 1946-, et al.
(författare)
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A Result of the Mean Square Error Obtained using General Tracking Algorithms
- 1991
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Ingår i: International journal of adaptive control and signal processing (Print). - Linköping : Wiley-Blackwell. - 0890-6327 .- 1099-1115. ; 5:4, s. 231-348
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Tracking time-varying properties is of crucial importance in all adaptive algorithms. In this contribution we study a fairly general algorithm for tracking properties of model parameters that can be described in a linear regression form (including AR models and the like). An explicit expression for the mean square error between the estimated and the true (time-varying) parameter is established. For slow adaptation this expression can be arbitrarily well approximated by a much simpler expression. The treatment differs from other related studies using weak convergence theory, averaging, etc. in that the results are not asymptotic in nature and are applicable also to the transient phase as well as over unbounded time intervals.
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| 70. |
- Ljung, Lennart, 1946-
(författare)
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A Simple Start-Up Procedure for Canonical form State Space Identification, based on Subspace Approximation
- 1991
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Ingår i: Proceedings of the 30th IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780304500 ; , s. 1333-1336 vol.2
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Konferensbidrag (refereegranskat)abstract
- The authors describe a procedure for estimating parameters in multivariable linear systems, parameterized in pseudo-observability state-space canonical forms. The procedure is based on a standard four-stage instrumental variable method and subsequent operations in the Hankel matrix of estimated impulse responses. The main use of the procedure is for initialization of maximum likelihood/prediction error estimation methods.
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