Domain extrapolation

Applicability Domain for DT-Based Models We describe applicability domain for QSAR models as being determined by two parameters (1) prediction confidence, or the certainty of a prediction for an unknown chemical, and (2) domain extrapolation, or the prediction accuracy of an unknown chemical that lies beyond the chemical space of the training set [60]. Both parameters can be quantitatively estimated in the consensus tree approaches, where individual models are constructed as DTs. Taken together, prediction confidence and domain extrapolation assess the applicability domain of a model for each prediction. 

Defining the training domain is the prerequisite for assessing the domain extrapolation. Commonly in QSAR modeling, a training domain is viewed as an TV-dimensional space, where N is the number of descriptors in the model. We... 

Figure 6.10 DF prediction accuracy versus domains extrapolation for ER232 and ER1092 based on 2000 runs of 10-fold cross validation. Domain extrapolation (d) for a chemical is defined as a percentage away from the focused domain as illustrated in Figure 6.8, while the prediction accuracy for the domain d is calculated by dividing correct predictions by total number of chemicals in this domain.

The prediction confidence and domain extrapolation can be readily calculated and constitute the definition of the applicability domain for DF. 

Tong W, Xie Q, Hong H, Shi LM, Fang H, Perkins R. Assessment of prediction confidence and domain extrapolation of two structure-activity relationship models for predicting estrogen receptor binding activity. Environ Health Perspect 2004 112 1249-54. 

By the methods of Tasks B to D, minimalll and nonMinimalll are mutually exclusive over the domain of the induction parameter within (r). If the correct domain extrapolation hypothesis is taken by the method of Task D, then minimal/l and nonMinimal/l are also mutually exclusive over the entire intended domain of the induction parameter. ... 

This proof hinges on the fact that the correct domain extrapolation hypothesis must be taken by the method of Task D. We assume that such is the case. Of course, a reasonable implementation of this synthesis mechanism would include some interaction with the specifier so as to maximize the confidence that everything goes right. 

What are the structural forms Task D of Step 2 non-deterministically selects some domain extrapolation hypothesis and extracts the corresponding predefined forms from a typed database. 

Low and High frequency can be restored by use of a deconvolution algorithm that enhances the resolution. We operate an improvement of the spectral bandwidth by Papoulis deconvolution based essentially on a non-linear adaptive extrapolation of the Fourier domain. 

In the case of parallel reactions, the fastest reaction will set or control the overall change. In all rate determining cases, the relative speed of the reactions will change with the temperature. This is caused by different energies of activation among the steps in the sequence. This is just one more reason for limiting rate predictions from measurements within the studied domain to avoid extrapolation. 

Bridgman had strong views on the importance of empirical research, influenced as little as possible by theory, and this helped him test the influence of numerous variables that lesser mortals failed to heed. He kept clear of quantum mechanics and dislocation theory, for instance. He became deeply ensconced in the philosophy of physics research for instance, he published a famous book on dimensional analysis, and another on the logic of modern physics . When he sought to extrapolate his ideas into the domain of social science, he found himself embroiled in harsh disputes this has happened to a number of eminent scientists, for instance, J.D. Bernal. Walter s book goes into this aspect of Bridgman s life in detail. 

All predictions must be taken for what they are, namely, generalizations based on current knowledge and understanding. There is a temptation for a user to assume that a computer-generated answer must be correct. To determine whether this is in fact the case, a number of factors concerning the model must be addressed. The statistical evaluation of a model was addressed above. Another very important criterion is to ensure that a prediction is an interpolation within the model space, and not an extrapolation outside of it. To determine this, the concept of the applicability domain of a model has been introduced [106]. 

Because the FFT algorithm requires the number of data points to be a power of 2, it follows that the signal in the time domain has to be extrapolated (e.g. by zero filling) or cut off to meet that requirement. This has consequences for the resolution in the frequency domain as this virtually expands or shortens the measurement time. 

Fields of Application. In SAXS a calibration to absolute intensity is required if extrapolated or integrated numerical values must be compared on an absolute scale. Examples are the determination of density fluctuations or the density difference between matrix and domains as a function of materials composition. 

It is only natural to consider ways that would allow us to use our knowledge of the whole distribution P0(AU), rather than its lew-AU tail only. The simplest strategy is to represent the probability distribution as an analytical function or a power-series expansion. This would necessarily involve adjustable parameters that could be determined primarily from our knowledge of the function in the well-sampled region. Once these parameters are known, we can evaluate the function over the whole domain of interest. In a way, this approach to modeling P0(AU) constitutes an extrapolation strategy. 

Note that, for a material with an ionic conductivity that can be measured above and below T, extrapolated data for the aT term in the two domains should give an identical value when T approaches infinity ([Pg.93]

Extent of Extrapolation For a regression-like QSAR, a simple measure of a chemical being too far from the applicability domain of the model is its leverage, hi [36], which is defined as... 

The validity of a model is always limited to a certain domain in the parameter space. For example, if a quantitative structure-activity relationships (QSAR) model is specified for nonpolar organic chemicals in the log range from 2 to 6 and has a molecular weight below 700, then an application to substances outside this range is an improper extrapolation. Note that the parameter space may be difficult to discern for example, combinations of low values for one variable and high values for another could constitute an extrapolation if such combinations had been missing in the validation or specification of the model. Exceedence of model boundaries introduces additional uncertainty at best, but can also lead to completely incorrect outcomes. 

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