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Partial least squares methods are applied to statistical problems where data result from discretized functions rather than individual predictors. We apply the discrete wavelet transform by preconditioning the normal equations to solve the problem on the wavelet domain. The relative importance of the wavelet coefficients is then assessed by adaptively rescaling the solution in the transformed coordinates. The final solution is finally expressed in original terms by means of the inverse wavelet transform. The proposed method is well adapted for large scale problems. It is especially suited for data resulting from discretized functions related to modern instrumentation. The computational ease of the wavelet transform combined with the adaptive rescaling of the final solution allows obtaining sparse solutions in a computationally fast and efficient manner.
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Reduced Risk Products ("RRPs”) is the term we use to refer to products that present, are likely to present, or have the potential to present less risk of harm to smokers who switch to these products versus continuing smoking. PMI has a range of RRPs in various stages of development, scientific assessment and commercialization. All of our RRPs are smoke-free products that deliver nicotine with far lower quantities of harmful and potentially harmful constituents than found in cigarette smoke.