Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables. We present a thorough theoretical analysis of REMBO. Empirical results confirm that REMBO can effectively solve problems with billions of dimensions, provided the intrinsic dimensionality is low. They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.

Immunoglobulin is known to be an immunomodulator. It can induce protein mediators from mononuclear cells, particularly monocytes in vitro. Intravenous immunoglobulin (IVIg) has been used as a therapy in several clinical situations. In this study, the influence of IVIg infusion on the plasma levels of two protein mediators, interferon-gamma (IFN-gamma) and interleukin-6 (IL-6), was assessed in patients with secondary generalized epilepsy. Compared to preinfusion levels, plasma interferon-gamma was increased in 18 of 18 patients 20 min after the 6- to 8-hr infusion of IVIg. Plasma interferon-gamma levels reached their peak at various times from 20 min to 3 days post IVIg infusion, dependent upon the individual patient. Plasma IL-6 levels also increased after IVIg infusion. Generally, IL-6 reached its peak level after IFN-gamma. No activated T cells or B cells were observed as determined by the expression of surface CD25, CD23, and HLA-DR 20 min following the infusion when the IFN-gamma and IL-6 levels were assessed. The expression of the high-affinity receptor for IgG, CD64, on monocytes was significantly enhanced after IVIg infusion, while the low-affinity receptor for IgG, CD32, was only slightly increased. Cytoplasmic staining of PBMC indicates that both CD16-positive and CD16-negative cells may contribute to the increase seen in plasma IFN-gamma. These data raise the possibility that the therapeutic effects of intravenous immunoglobulin may be related, at least in part, to the immunomodulatory activity as demonstrated by the changes in plasma levels of IFN-gamma and IL-6.

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