1,721,049 research outputs found

    Measuring and managing financial risk

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    Partitioned least squares

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    Linear least squares is one of the most widely used regression methods in many fields. The simplicity of the model allows this method to be used when data is scarce and allows practitioners to gather some insight into the problem by inspecting the values of the learnt parameters. In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. We show that the new formulation is not convex and provide two alternative methods to deal with the problem: one non-exact method based on an alternating least squares approach; and one exact method based on a reformulation of the problem. We show the correctness of the exact method and compare the two solutions showing that the exact solution provides better results in a fraction of the time required by the alternating least squares solution (when the number of partitions is small). We also provide a branch and bound algorithm that can be used in place of the exact method when the number of partitions is too large as well as a proof of NP-completeness of the optimization problem

    Partitioned Least Squares

    No full text
    Linear least squares is one of the most widely used regression methods among scientists in many fields. The simplicity of the model allows this method to be used when data is scarce and it is usually appealing to practitioners that need to gather some insight into the problem by inspecting the values of the learnt parameters. In this paper we propose a variant of the linear least squares model that allows practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. We formally show that the new formulation is not convex and provide two alternative methods to deal with the problem: one non-exact method based on an alternating least squares approach; and one exact method based on a reformulation of the problem using an exponential number of sub-problems whose minimum is guaranteed to be the optimal solution. We formally show the correctness of the exact method and also compare the two solutions showing that the exact solution provides better results in a fraction of the time required by the alternating least squares solution (assuming that the number of partitions is small)

    Going Beyond Counting First Authors in Author Co-citation Analysis

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    The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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