Hidden bias

Systematic Operating Errors Fifth, systematic operating errors may be unknown at the time of measurements. Wriile not intended as part of daily operations, leaky or open valves frequently result in bypasses, leaks, and alternative feeds that will add hidden bias. Consequently, constraints assumed to hold and used to reconcile the data, identify systematic errors, estimate parameters, and build models are in error. The constraint bias propagates to the resultant models. 

Gotzsche PC (1989). Methodology and overt and hidden bias in reports of 196 doubleblind trials of nonsteroidal antiinflammatory drugs in rheumatoid arthritis. Control in Clinical Trials 10 31-56 Gruppo ItaUano per lo Studio della Streptochinasi nell Infarto Miocardico (GISSI) (1986). Effectiveness of intravenous thrombolytic treatment in acute myocardial infarction. Lancet 1 397-402 Gurwitz JH, Col NF, Avorn J (1992). The exclusion of elderly and women from clinical trials in acute myocardial infarction. Journal of the American Medical Association 268 1417-1422... 

Every hexapeptide in the database was selected in turn as a query peptide and its fold type predicted from sets of related peptides in the database, excluding the protein containing the query peptide. For over 90% of all hexapeptides at least one related peptide in another protein structure could be found in the database. With the highest cumulative score as fold type predictor, a sobering 40% of all predictions turn out to be correct, as is evident from Table 17.3. From the data shown in Table 17.3 a, a hidden bias towards prediction of helical and non-classified folds is apparent, whereas extended conformations and turns are underestimated. This was compensated for by modifying the pattern weights in the database by factors of 0.82, 1.06,... 

This paradox highlights the hidden bias of circuit representations with dipolar devices. They need to be accompanied by the convention chosen for stating which is the across variable and which one is the through variable. 

Figure 9-16. ArtiFicial neural network architecture with a two-layer design, compri ing Input units, a so-called hidden layer, and an output layer. The squares Inclosing the ones depict the bias which Is an extra weight (see Ref, [10 for further details),...

Figure 6 Schematic of a typical neural network training process. I-input layer H-hidden layer 0-output layer B-bias neuron.

Just as in the perceptron-Iike networks, an additional column of ones is added to the X matrix to accommodate for the offset or bias. This is sometimes explicitly depicted in the structure (see Fig. 44.9b). Notice that an offset term is also provided between the hidden layer and the output layer. 

The threshold values 6> of the neuron are considered by using an additional neuron in the hidden layer ( on neuron y bias neuron) the output of which is always +1. 

Fig. 6.22. Structure of a RBF net with one hidden layer with bias neuron and one output unit as used for single component calibration (according to Fischbacher et al. [1997] Jagemann [1998])...

This type of network is composed of an input layer, an output layer and one or more hidden layers (figure 1). Bias term in each layer is analogous to the constant term of any polynomial. The number of neurons in the input and the output layer depends on the respective number of input and output parameters taken into consideration. However, the hidden layer may contain zero or more neurons. All the layers are interconnected as shown in the figure and the strength of these interconnections is determined by the weights associated with them. The output from a neuron in the hidden layer is the transformation of the weighted sum of output from the input layers and is given as (1)... 

I is the number of input variables, J is the number of nodes in the hidden layer to be optimized. The model output S was set to 1 for the cubic MCM-48 structure, 2 for the MCM-41 hexagonal form and 3 for the lamellar form. The input variables Ui and U2 were the normalized weight fractions of CTAB and TMAOH, respectively. Hj+i and U1+1 are the bias constants set equal to 1, and coj and coy are the fitting parameters. The NNFit software... 

The processing elements are typically arranged in layers one of the most commonly used arrangements is known as a back propagation, feed forward network as shown in Figure 7.8. In this network there is a layer of neurons for the input, one unit for each physicochemical descriptor. These neurons do no processing, but simply act as distributors of their inputs (the values of the variables for each compound) to the neurons in the next layer, the hidden layer. The input layer also includes a bias neuron that has a constant output of 1 and serves as a scaling device to ensure... 

A multilayer perception with two hidden units is shown in Figure 3.7, with the actual weights and bias terms included, after training. This network can solve the nonlinear depression classification problem, presented in Figure 3.4. 

Figure 5.13 Layers of units and connection links in an artificial neuronal network. Ij-ij.- input neurons, h-hj hidden neurons, b, b exit and output bias neurons, w,2hi weight of transmission, ij-h, x.-Xji input process variables and y output...

Figure 18 A neural network, comprising an input layer (I), a hidden layer (H), and an output layer (O). This is capable of correctly classifying the analytical data from Table 1. The required weighting coefficients are shown on each connection and the bias values for a sigmoidal threshold function are shown above each neuron...

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