Learning variability

Table 6.2 Aspects of the sociahzation process and their impact on learning variability across new...

Socialization processes Potential learning variability across new employees... 

To address dynamic changes in how courses are structured and how students learn— variable math and reading preparation, less time for traditional studying, electronic media as part of lectures and homework, new challenges and options in career choices—the author and publisher consulted extensively with students and faculty. Based on their input, we developed the following ways to improve the text as a whole as well as the content of individual chapters. 

Multiple linear regression is strictly a parametric supervised learning technique. A parametric technique is one which assumes that the variables conform to some distribution (often the Gaussian distribution) the properties of the distribution are assumed in the underlying statistical method. A non-parametric technique does not rely upon the assumption of any particular distribution. A supervised learning method is one which uses information about the dependent variable to derive the model. An unsupervised learning method does not. Thus cluster analysis, principal components analysis and factor analysis are all examples of unsupervised learning techniques. 

Discriminant emalysis is a supervised learning technique which uses classified dependent data. Here, the dependent data (y values) are not on a continuous scale but are divided into distinct classes. There are often just two classes (e.g. active/inactive soluble/not soluble yes/no), but more than two is also possible (e.g. high/medium/low 1/2/3/4). The simplest situation involves two variables and two classes, and the aim is to find a straight line that best separates the data into its classes (Figure 12.37). With more than two variables, the line becomes a hyperplane in the multidimensional variable space. Discriminant analysis is characterised by a discriminant function, which in the particular case of hnear discriminant analysis (the most popular variant) is written as a linear combination of the independent variables ... 

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

This level of simplicity is not the usual case in the systems that are of interest to chemical engineers. The complexity we will encounter will be much higher and will involve more detailed issues on the right-hand side of the equations we work with. Instead of a constant or some explicit function of time, the function will be an explicit function of one or more key characterizing variables of the system and implicit in time. The reason for this is that of cause. Time in and of itself is never a physical or chemical cause—it is simply the independent variable. When we need to deal with the analysis of more complex systems the mechanism that causes the change we are modeling becomes all important. Therefore we look for descriptions that will be dependent on the mechanism of change. In fact, we can learn about the mechanism of... 

A very simple 2-4-1 neural network architecture with two input nodes, one hidden layer with four nodes, and one output node was used in each case. The two input variables were the number of methylene groups and the temperature. Although neural networks have the ability to learn all the differences, differentials, and other calculated inputs directly from the raw data, the training time for the network can be reduced considerably if these values are provided as inputs. The predicted variable was the density of the ester. The neural network model was trained for discrete numbers of methylene groups over the entire temperature range of 300-500 K. The... 

We proposed to study diet and health by combining bone chemistry and histomorphometry. Diet would be determined by analysis of stable isotopes of carbon and nitrogen in bone protein and some preserved hair. In addition, trace elements would be quantitatively analyzed in preserved bone mineral. Abonyi (1993) participated in the study by reconstructing the diet from historical sources and analyzing various foods. Having analyzed human tissues for stable isotopes and trace elements, and foods for the same variables, we hoped to learn more about 19th century diet in southern Ontario, and at the same time, learn more about paleodiet reconstruction. 

An examination of previous classical learning procedures reveals that they differ from each other only with respect to the choices of /, and S. All of them share the same basic format for and the corresponding solution space, S. Let s assume that each (x, y) pair in the problem statement (2) contains a total of M decision variables ... 

To benchmark our learning methodology with alternative conventional approaches, we used the same 500 (x, y) data records and followed the usual regression analysis steps (including stepwise variable selection, examination of residuals, and variable transformations) to find an approximate empirical model, / (x), with a coefficient of determination = 0.79. This model is given by... 

Both situations with categorical and continuous, real-valued performance metrics will be considered and analyzed. Since Taguchi loss functions provide quality cost models that allow the different objectives to be expressed on a commensurate basis, for continuous performance variables only minor modifications in the problem definition of the approach presented in Section V are needed. On the other hand, if categorical variables are chosen to characterize the system s multiple performance metrics, important modifications and additional components have to be incorporated into the basic learning methodology described in Section IV. 

To conclude this section on systems with multiple objectives, we will consider a specific plasma etching unit case study. This unit will be analyzed considering both categorical and continuous performance measurement variables. Provided that similar preference structures are expressed in both instances, we will see that the two approaches lead to similar final answers. Additional applications of the learning methodologies to multiobjective systems can be found in Saraiva and Stephanopoulos (1992b, c). 

In the bottom-up approach the initiative to start the learning process is taken by one of the infimal decision units. Since solutions found at this unit may include connection variables, the request for given values of these variables is propagated backward, to unit A + 1, through temporary loss functions. After successive backpropagation steps, the participation of several other fhe operators associated with them, a final decision... 

The learning process was initiated at the top-digester infimal decision unit, leading to a solution, Xjj, that involves local decision variables and a range of white liquor sulfidity (fraction of active reactants in the white... 

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