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Bennett White
Bennett White

Linear Models With R Faraway Pdf 31



When more than one independent variable is used in the regression, it is referred to as multiple linear regression. In regression models, the response (or dependent) variable must always be continuous. The predictor (or independent) variable(s) can be continuous or categorical. In order to use linear regression or any linear model, the errors (i.e. residuals) must be normally distributed. Most environmental data are skewed and require transformations to the response variable (such as square root or log) for use in linear models. Normality can be assessed using a QQ plot or histogram of the residuals.




linear models with r faraway pdf 31



Modeling is an iterative process that cycles between fitting and evaluating alternative models. Compared to tree and forest models, linear and generalized models typically less automated. Automated model selection procedures are available, but should not be taken at face value because they may result in complex and unstable models. This is in part due to correlation amongist the predictive variables that can confuse the model. Also, the order in which the variables are included or excluded from the model effects the significance of the other variables, and thus several weak predictors might mask the effect of one strong predictor. Regardless of the approach used, variable selection is probably the most controversial aspect of linear modeling.


A tremendous interest in deep learning has emerged in recent years [1]. The most established algorithm among various deep learning models is convolutional neural network (CNN), a class of artificial neural networks that has been a dominant method in computer vision tasks since the astonishing results were shared on the object recognition competition known as the ImageNet Large Scale Visual Recognition Competition (ILSVRC) in 2012 [2, 3]. Medical research is no exception, as CNN has achieved expert-level performances in various fields. Gulshan et al. [4], Esteva et al. [5], and Ehteshami Bejnordi et al. [6] demonstrated the potential of deep learning for diabetic retinopathy screening, skin lesion classification, and lymph node metastasis detection, respectively. Needless to say, there has been a surge of interest in the potential of CNN among radiology researchers, and several studies have already been published in areas such as lesion detection [7], classification [8], segmentation [9], image reconstruction [10, 11], and natural language processing [12]. Familiarity with this state-of-the-art methodology would help not only researchers who apply CNN to their tasks in radiology and medical imaging, but also clinical radiologists, as deep learning may influence their practice in the near future. This article focuses on the basic concepts of CNN and their application to various radiology tasks, and discusses its challenges and future directions. Other deep learning models, such as recurrent neural networks for sequence models, are beyond the scope of this article.


Transfer learning is a common and effective strategy to train a network on a small dataset, where a network is pretrained on an extremely large dataset, such as ImageNet, which contains 1.4 million images with 1000 classes, then reused and applied to the given task of interest. The underlying assumption of transfer learning is that generic features learned on a large enough dataset can be shared among seemingly disparate datasets. This portability of learned generic features is a unique advantage of deep learning that makes itself useful in various domain tasks with small datasets. At present, many models pretrained on the ImageNet challenge dataset are open to the public and readily accessible, along with their learned kernels and weights, such as AlexNet [3], VGG [30], ResNet [31], Inception [32], and DenseNet [33]. In practice, there are two ways to utilize a pretrained network: fixed feature extraction and fine-tuning (Fig. 10).


Although there are several methods that facilitate learning on smaller datasets as described above, well-annotated large medical datasets are still needed since most of the notable accomplishments of deep learning are typically based on very large amounts of data. Unfortunately, building such datasets in medicine is costly and demands an enormous workload by experts, and may also possess ethical and privacy issues. The goal of large medical datasets is the potential to enhance generalizability and minimize overfitting, as discussed previously. In addition, dedicated medical pretrained networks can probably be proposed once such datasets become available, which may foster deep learning research on medical imaging, though whether transfer learning with such networks improves the performance in the medical field compared to that with ImageNet pretrained models is not clear and remains an area of further investigation.


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