**Discrete Choice**

In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods (e.g. first-order conditions) can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis. On the other hand, discrete choice analysis examines situations in which the potential outcomes are discrete, such that the optimum is not characterized by standard first-order conditions. Thus, instead of examining ‘how much’ as in problems with continuous choice variables, discrete choice analysis examines ‘which one.’ However, discrete choice analysis can also be used to examine the chosen quantity when only a few distinct quantities must be chosen from, such as the number of vehicles a household chooses to own [1] and the number of minutes of telecommunications service a customer decides to purchase.[2] Techniques such as logistic regression and probit regression can be used for empirical analysis of discrete choice.

… **Random Erasing**

In this paper, we introduce Random Erasing, a simple yet effective data augmentation techniques for training the convolutional neural network (CNN). In training phase, Random Erasing randomly selects a rectangle region in an image, and erases its pixels with random values. In this process, training images with various levels of occlusion are generated, which reduce the risk of network overfitting and make the model robust to occlusion. Random Erasing is parameter learning free, easy to implement, and can be integrated into most of the CNN-based recognition models. Albeit simple, Random Erasing yields consistent improvement in image classification, object detection and person re-identification (re-ID). For image classification, our method improves WRN-28-10: top-1 error rate from 3.72% to 3.08% on CIFAR10, and from 18.68% to 17.65% on CIFAR100. For object detection on PASCAL VOC 2007, Random Erasing improves Fast-RCNN from 74.8% to 76.2% in mAP. For person re-ID, when using Random Erasing in recent deep models, we achieve the state-of-the-art accuracy: the rank-1 accuracy is 89.13% for Market-1501, 84.02% for DukeMTMC-reID, and 63.93% for CUHK03 under the new evaluation protocol. … **k-SVRG**

In recent years, many variance reduced algorithms for empirical risk minimization have been introduced. In contrast to vanilla SGD, these methods converge linearly on strong convex problems. To obtain the variance reduction, current methods either require frequent passes over the full data to recompute gradients—without making any progress during this time (like in SVRG), or they require memory of the same size as the input problem (like SAGA). In this work, we propose k-SVRG, an algorithm that interpolates between those two extremes: it makes best use of the available memory and in turn does avoid full passes over the data without making progress. We prove linear convergence of k-SVRG on strongly convex problems and convergence to stationary points on non-convex problems. Numerical experiments show the effectiveness of our method. …

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