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Peters Jonas - One of the best experts on this subject based on the ideXlab platform.

  • A Causal framework for distribution generalization
    2020
    Co-Authors: Christiansen Rune, Pfister Niklas, Jakobsen, Martin Emil, Gnecco Nicola, Peters Jonas
    Abstract:

    We consider the problem of predicting a response from a set of covariates when the test distribution may differ from the training distribution. Motivated by the idea that such differences may have Causal explanations, we consider a class of test distributions that emerge from interventions in a structural Causal model, and focus on minimizing the worst-case risk over this class. Causal regression models, which regress the response variable on all of its direct parents, remain valid under arbitrary interventions on any subset of covariates, but they are not always optimal in the above sense. For example, in linear models, for a set of interventions with bounded strength, alternative solutions have been shown to be minimax prediction optimal. We introduce the formal framework of distribution generalization that allows us to analyze the above problem in partially observed nonlinear models for both direct and indirect interventions on the covariates. It takes into account that, in practice, minimax solutions need to be identified from observational data. Our framework allows us to characterize under which class of interventions the Causal Function is minimax optimal. We prove several sufficient conditions for distribution generalization and present corresponding impossibility results. We propose a practical method, called NILE, that achieves distribution generalization in a nonlinear instrumental variables setting with linear extrapolation. We prove consistency and present empirical results.Comment: 49 pages, 6 figures, 2 table

P P Vaidyanatha - One of the best experts on this subject based on the ideXlab platform.

  • a state space approach to the design of globally optimal fir energy compaction filters
    IEEE Transactions on Signal Processing, 2000
    Co-Authors: J Tuqa, P P Vaidyanatha
    Abstract:

    We introduce a new approach for the least squared optimization of a weighted FIR filter of arbitrary order N under the constraint that its magnitude squared response be Nyquist(M). Although the new formulation is general enough to cover a wide variety of applications, the focus of the paper is on optimal energy compaction filters. The optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks (PCFBs). The newly proposed method finds the optimum product filter F/sub opt/(z)=H/sub opt/(Z)H/sub opt/(z/sup -1/) corresponding to the compaction filter H/sub opt/(z). By expressing F(z) in the form D(z)+D(z/sup -1/), we show that the compaction problem can be completely parameterized in terms of the state-space realization of the Causal Function D(z). For a given input power spectrum, the resulting filter F/sub opt/(z) is guaranteed to be a global optimum solution due to the convexity of the new formulation. The new algorithm is universal in the sense that it works for any M, arbitrary filter length N, and any given input power spectrum. Furthermore, additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem. Finally, obtaining H/sub opt/(z) from F/sub opt/(z) does not require an additional spectral factorization step. The minimum-phase spectral factor H/sub min/(z) can be obtained automatically by relating the state space realization of D/sub opt/(z) to that of H/sub opt/(z).

Christiansen Rune - One of the best experts on this subject based on the ideXlab platform.

  • A Causal framework for distribution generalization
    2020
    Co-Authors: Christiansen Rune, Pfister Niklas, Jakobsen, Martin Emil, Gnecco Nicola, Peters Jonas
    Abstract:

    We consider the problem of predicting a response from a set of covariates when the test distribution may differ from the training distribution. Motivated by the idea that such differences may have Causal explanations, we consider a class of test distributions that emerge from interventions in a structural Causal model, and focus on minimizing the worst-case risk over this class. Causal regression models, which regress the response variable on all of its direct parents, remain valid under arbitrary interventions on any subset of covariates, but they are not always optimal in the above sense. For example, in linear models, for a set of interventions with bounded strength, alternative solutions have been shown to be minimax prediction optimal. We introduce the formal framework of distribution generalization that allows us to analyze the above problem in partially observed nonlinear models for both direct and indirect interventions on the covariates. It takes into account that, in practice, minimax solutions need to be identified from observational data. Our framework allows us to characterize under which class of interventions the Causal Function is minimax optimal. We prove several sufficient conditions for distribution generalization and present corresponding impossibility results. We propose a practical method, called NILE, that achieves distribution generalization in a nonlinear instrumental variables setting with linear extrapolation. We prove consistency and present empirical results.Comment: 49 pages, 6 figures, 2 table

J Tuqa - One of the best experts on this subject based on the ideXlab platform.

  • a state space approach to the design of globally optimal fir energy compaction filters
    IEEE Transactions on Signal Processing, 2000
    Co-Authors: J Tuqa, P P Vaidyanatha
    Abstract:

    We introduce a new approach for the least squared optimization of a weighted FIR filter of arbitrary order N under the constraint that its magnitude squared response be Nyquist(M). Although the new formulation is general enough to cover a wide variety of applications, the focus of the paper is on optimal energy compaction filters. The optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks (PCFBs). The newly proposed method finds the optimum product filter F/sub opt/(z)=H/sub opt/(Z)H/sub opt/(z/sup -1/) corresponding to the compaction filter H/sub opt/(z). By expressing F(z) in the form D(z)+D(z/sup -1/), we show that the compaction problem can be completely parameterized in terms of the state-space realization of the Causal Function D(z). For a given input power spectrum, the resulting filter F/sub opt/(z) is guaranteed to be a global optimum solution due to the convexity of the new formulation. The new algorithm is universal in the sense that it works for any M, arbitrary filter length N, and any given input power spectrum. Furthermore, additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem. Finally, obtaining H/sub opt/(z) from F/sub opt/(z) does not require an additional spectral factorization step. The minimum-phase spectral factor H/sub min/(z) can be obtained automatically by relating the state space realization of D/sub opt/(z) to that of H/sub opt/(z).

Pfister Niklas - One of the best experts on this subject based on the ideXlab platform.

  • A Causal framework for distribution generalization
    2020
    Co-Authors: Christiansen Rune, Pfister Niklas, Jakobsen, Martin Emil, Gnecco Nicola, Peters Jonas
    Abstract:

    We consider the problem of predicting a response from a set of covariates when the test distribution may differ from the training distribution. Motivated by the idea that such differences may have Causal explanations, we consider a class of test distributions that emerge from interventions in a structural Causal model, and focus on minimizing the worst-case risk over this class. Causal regression models, which regress the response variable on all of its direct parents, remain valid under arbitrary interventions on any subset of covariates, but they are not always optimal in the above sense. For example, in linear models, for a set of interventions with bounded strength, alternative solutions have been shown to be minimax prediction optimal. We introduce the formal framework of distribution generalization that allows us to analyze the above problem in partially observed nonlinear models for both direct and indirect interventions on the covariates. It takes into account that, in practice, minimax solutions need to be identified from observational data. Our framework allows us to characterize under which class of interventions the Causal Function is minimax optimal. We prove several sufficient conditions for distribution generalization and present corresponding impossibility results. We propose a practical method, called NILE, that achieves distribution generalization in a nonlinear instrumental variables setting with linear extrapolation. We prove consistency and present empirical results.Comment: 49 pages, 6 figures, 2 table