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The survey data are used to compute an annual percentage rate (APR) for the 30- and 15-year fixed-rate products. For the two variable-rate products, a weekly estimate of the fully-indexed rate (the sum of the index and margin) is calculated as the margin (collected in the applicable survey) plus the current one-year Treasury rate, which is estimated as the average of the close-of-business, one-year Treasury rates for Monday, Tuesday, and Wednesday of the survey week. If Treasury rate data are available for fewer than three days, only yields for the available days are used for the average. Survey data on the initial interest rate and points, and the estimated fully indexed rate, are used to compute a composite APR for the one- and five-year variable-rate mortgage products. See Regulation Z official commentary, 12 CFR part 1026, Supp. I, comment 17(c)(1)-10 (creditors to compute a composite APR where initial rate on variable-rate transaction not determined by reference to index and margin).
In computing the APR for the four products, a fully amortizing loan is assumed, with monthly compounding. A two-percentage-point cap on the annual interest rate adjustments is assumed for the variable-rate products. For the four products, the APR is calculated using the actuarial method, pursuant to appendix J to Regulation Z. A payment schedule is used that assumes equal monthly payments (even if this entails fractions of cents), assumes each payment due date to be the 1st of the month regardless of the calendar day on which it falls, treats all months as having 30 days, and ignores the occurrence of leap years. See 12 CFR 1026.17(c)(3). The APR calculation also assumes no irregular first period or per diem interest collected.
Thus estimated, the initial rates, margins, and points are used to calculate a fully-indexed rate and ultimately an APR for the two-, three-, seven-, and ten-year variable-rate products. To estimate APRs for one-, two-, three-, five-, seven-, and ten-year fixed-rate loans, respectively, the Bureau uses the initial interest rates and points, but not the fully-indexed rates, of the one-, two-, three-, five-, seven-, and ten-year variable-rate loan products calculated above.
Because both variable-rate products in the survey data use the same margin, the fully-indexed rate for the five-year variable-rate mortgage is the same number: 2.07+2.75=4.82 (since each adjusts to the 1-year treasury).
Mortgage rates inched down again, with the 30-year fixed-rate down nearly a full point from November, when it peaked at just over seven percent. According to Freddie Mac research, this one percentage point reduction in rates can allow as many as three million more mortgage-ready consumers to qualify and afford a $400,000 loan, which is the median home price.
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Convolutional neural network (CNN), a class of artificial neural networks that has become dominant in various computer vision tasks, is attracting interest across a variety of domains, including radiology. CNN is designed to automatically and adaptively learn spatial hierarchies of features through backpropagation by using multiple building blocks, such as convolution layers, pooling layers, and fully connected layers. This review article offers a perspective on the basic concepts of CNN and its application to various radiological tasks, and discusses its challenges and future directions in the field of radiology. Two challenges in applying CNN to radiological tasks, small dataset and overfitting, will also be covered in this article, as well as techniques to minimize them. Being familiar with the concepts and advantages, as well as limitations, of CNN is essential to leverage its potential in diagnostic radiology, with the goal of augmenting the performance of radiologists and improving patient care.
The key feature of a convolution operation is weight sharing: kernels are shared across all the image positions. Weight sharing creates the following characteristics of convolution operations: (1) letting the local feature patterns extracted by kernels translation b invariant as kernels travel across all the image positions and detect learned local patterns, (2) learning spatial hierarchies of feature patterns by downsampling in conjunction with a pooling operation, resulting in capturing an increasingly larger field of view, and (3) increasing model efficiency by reducing the number of parameters to learn in comparison with fully connected neural networks.
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, then reused and applied to the given task of interest. A fixed feature extraction method is a process to remove FC layers from a pretrained network and while maintaining the remaining network, which consists of a series of convolution and pooling layers, referred to as the convolutional base, as a fixed feature extractor. In this scenario, any machine learning classifier, such as random forests and support vector machines, as well as the usual FC layers, can be added on top of the fixed feature extractor, resulting in training limited to the added classifier on a given dataset of interest. A fine-tuning method, which is more often applied to radiology research, is to not only replace FC layers of the pretrained model with a new set of FC layers to retrain them on a given dataset, but to fine-tune all or part of the kernels in the pretrained convolutional base by means of backpropagation. FC, fully connected
A fine-tuning method, which is more often applied to radiology research, is to not only replace fully connected layers of the pretrained model with a new set of fully connected layers to retrain on a given dataset, but to fine-tune all or part of the kernels in the pretrained convolutional base by means of backpropagation. All the layers in the convolutional base can be fine-tuned or, alternatively, some earlier layers can be fixed while fine-tuning the rest of the deeper layers. This is motivated by the observation that the early-layer features appear more generic, including features such as edges applicable to a variety of datasets and tasks, whereas later features progressively become more specific to a particular dataset or task [34, 35].
One drawback of transfer learning is its constraints on input dimensions. The input image has to be 2D with three channels relevant to RGB because the ImageNet dataset consists of 2D color images that have three channels (RGB: red, green, and blue), whereas medical grayscale images have only one channel (levels of gray). On the other hand, the height and width of an input image can be arbitrary, but not too small, by adding a global pooling layer between the convolutional base and added fully connected layers.
Because 2D images are frequently utilized in computer vision, deep learning networks developed for the 2D images (2D-CNN) are not directly applied to 3D images obtained in radiology [thin-slice CT or 3D-magnetic resonance imaging (MRI) images]. To apply deep learning to 3D radiological images, different approaches such as custom architectures are used. For example, Setio et al.  used a multistream CNN to classify nodule candidates of chest CT images between nodules or non-nodules in the databases of the Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) , ANODE09 , and the Danish Lung Cancer Screening Trial . They extracted differently oriented 2D image patches based on multiplanar reconstruction from one nodule candidate (one or nine patches per candidate), and these patches were used in separate streams and merged in the fully connected layers to obtain the final classification output. One previous study used 3D-CNN for fully capturing the spatial 3D context information of lung nodules . Their 3D-CNN performed binary classification (benign or malignant nodules) and ternary classification (benign lung nodule, and malignant primary and secondary lung cancers) using the LIDC-IDRI database. They used a multiview strategy in 3D-CNN, whose inputs were obtained by cropping three 3D patches of a lung nodule in different sizes and then resizing them into the same size. They also used the 3D Inception model in their 3D-CNN, where the network path was divided into multiple branches with different convolution and pooling operators.
Deep learning is considered as a black box, as it does not leave an audit trail to explain its decisions. Researchers have proposed several techniques in response to this problem that give insight into what features are identified in the feature maps, called feature visualization, and what part of an input is responsible for the corresponding prediction, called attribution. For feature visualization, Zeiler and Fergus  described a way to visualize the feature maps, where the first layers identify small local patterns, such as edges or circles, and subsequent layers progressively combine them into more meaningful structures. For attribution, Zhou et al. proposed a way to produce coarse localization maps, called class activation maps (CAMs), that localize the important regions in an input use