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*Least* *Squares* *Regression*

"... A drawback of many voice conversion algorithms is that they rely on linear models and/or require a lot of tuning. In addition, many of them ignore the inherent time-dependency between speech features. To address these issues, we propose to use dynamic kernel partial least squares (DKPLS) technique t ..."

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to model nonlinearities as well as to capture the dynamics in the

*data*. The method is based on a kernel transformation of the source features to allow non-linear modeling and concatenation of previous and next frames to model the dynamics. Partial*least**squares**regression*is used to find a conversion###
An Introduction to Partial *Least* *Squares* *Regression*

"... Partial least squares is a popular method for Soft ..."

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AN *ALGORITHM* FOR NONLINEAR *LEAST* *SQUARES*

"... Optimization Toolbox of MATLAB represents very mighty apparatus for solution of wide set of optimization problems. Also basic MATLAB provides means for optimization purposes, e.g. backslash operator for solving set of linear equations or the function fminsearch for nonlinear problems. Should the set ..."

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the set of equations be nonlinear, an application of fminsearch for finding the

*least**squares*solution would be inefficient. The paper describes a better*algorithm*for the given task. 1 Principles of Levenberg-Marquardt-Fletcher*algorithm*Let us have a general overdetermined system of nonlinear algebraic###
20 The Geometry of *Least* *Squares*

"... seem to have introduced, and then reintroduced, it to econometricians. The theorem is much more general, and much more generally useful, than a casual reading of those papers might suggest, however. Among other things, it almost totally eliminates the need to invert partitioned matrices when one is ..."

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is deriving many standard results about ordinary (and nonlinear)

*least**squares*. The FWL Theorem applies to any*regression*where there are two or more regressors, and these can logically be broken up into two groups. The*regression*can thus be written as y = X1β1 + X2β2 + residuals, (1.18) where X1 is n×k1###
Some Sharp Performance Bounds for *Least* *Squares* *Regression* with

"... We derive sharp performance bounds for least squares regression with L1 regularization, from parameter estimation accuracy and feature selection quality perspectives. The main result proved for L1 regularization extends a similar result in [4] for the Dantzig selector. It gives an affirmative answer ..."

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We derive sharp performance bounds for

*least**squares**regression*with L1 regularization, from parameter estimation accuracy and feature selection quality perspectives. The main result proved for L1 regularization extends a similar result in [4] for the Dantzig selector. It gives an affirmative###
52 Nonlinear *Regression* Models and Nonlinear *Least* *Squares*

"... with the values of certain variables. They may be the only variables about which we have information or the only ones that we are interested in for a particular purpose. If we had more information about potential explanatory variables, we might very well specify xt(β) differently so as to make use o ..."

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with the values of certain variables. They may be the only variables about which we have information or the only ones that we are interested in for a particular purpose. If we had more information about potential explanatory variables, we might very well specify xt(β) differently so as to make use of that additional information. It is sometimes desirable to make explicit the fact that xt(β) represents the conditional mean of yt, that is, the mean of yt conditional on the values of a number of other variables. The set of variables on which yt is conditioned is often referred to as an information set. If Ωt denotes the information set on which the expectation of yt is to be conditioned, one could define xt(β) formally as E(yt | Ωt). There may be more than one such information set. Thus we might well have both x1t(β1) ≡ E(yt | Ω1t) and x2t(β2) ≡ E(yt | Ω2t), where Ω1t and Ω2t denote two different information sets. The functions x1t(β1) and x2t(β2) might well be quite different, and we might want to

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52 Nonlinear *Regression* Models and Nonlinear *Least* *Squares*

"... with the values of certain variables. They may be the only variables about which we have information or the only ones that we are interested in for a particular purpose. If we had more information about potential explanatory variables, we might very well specify xt(β) differently so as to make use o ..."

Abstract
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with the values of certain variables. They may be the only variables about which we have information or the only ones that we are interested in for a particular purpose. If we had more information about potential explanatory variables, we might very well specify xt(β) differently so as to make use of that additional information. It is sometimes desirable to make explicit the fact that xt(β) represents the conditional mean of yt, that is, the mean of yt conditional on the values of a number of other variables. The set of variables on which yt is conditioned is often referred to as an information set. If Ωt denotes the information set on which the expectation of yt is to be conditioned, one could define xt(β) formally as E(yt | Ωt). There may be more than one such information set. Thus we might well have both x1t(β1) ≡ E(yt | Ω1t) and x2t(β2) ≡ E(yt | Ω2t), where Ω1t and Ω2t denote two different information sets. The functions x1t(β1) and x2t(β2) might well be quite different, and we might want to