Monocular depth estimation, which plays a crucial role in understanding 3D scene geometry, is an ill-posed problem. Recent methods have gained significant improvement by exploring image-level information and hierarchical features from deep convolutional neural networks (DCNNs). These methods model depth estimation as a regression problem and train the regression networks by minimizing mean squared error, which suffers from slow convergence and unsatisfactory local solutions. Besides, existing depth estimation networks employ repeated spatial pooling operations, resulting in undesirable low-resolution feature maps. To obtain high-resolution depth maps, skip-connections or multilayer deconvolution networks are required, which complicates network training and consumes much more computations. To eliminate or at least largely reduce these problems, we introduce a spacing-increasing discretization (SID) strategy to discretize depth and recast depth network learning as an ordinal regression problem. By training the network using an ordinary regression loss, our method achieves much higher accuracy and faster convergence in synch. Furthermore, we adopt a multi-scale network structure which avoids unnecessary spatial pooling and captures multi-scale information in parallel. The proposed deep ordinal regression network (DORN) achieves state-of-the-art results on three challenging benchmarks, i.e., KITTI [16], Make3D [49], and NYU Depth v2 [41], and outperforms existing methods by a large margin.
To address the non-stationary property of aging patterns, age estimation can be cast as an ordinal regression problem. However, the processes of extracting features and learning a regression model are often separated and optimized independently in previous work. In this paper, we propose an End-to-End learning approach to address ordinal regression problems using deep Convolutional Neural Network, which could simultaneously conduct feature learning and regression modeling. In particular, an ordinal regression problem is transformed into a series of binary classification sub-problems. And we propose a multiple output CNN learning algorithm to collectively solve these classification sub-problems, so that the correlation between these tasks could be explored. In addition, we publish an Asian Face Age Dataset (AFAD) containing more than 160K facial images with precise age ground-truths, which is the largest public age dataset to date. To the best of our knowledge, this is the first work to address ordinal regression problems by using CNN, and achieves the state-of-the-art performance on both the MORPH and AFAD datasets.  We investigate the problem of predicting variables of ordinal scale. This task is referred to as ordinal regression and is complementary to the standard machine learning tasks of classification and metric regression. In contrast to statistical models we present a distribution independent formulation of the problem together with uniform bounds of the risk functional. The approach presented is based on a mapping from objects to scalar utility values. Similar to support vector methods we derive a new learning algorithm for the task of ordinal regression based on large margin rank boundaries. We give experimental results for an information retrieval task: learning the order of documents with respect to an initial query. Experimental results indicate that the presented algorithm outperforms more naive approaches to ordinal regression such as support vector classification and support vector regression in the case of more than two ranks. We discuss the problem of ranking k instances with the use of a "large margin" principle. We introduce two main approaches: the first is the "fixed margin" policy in which the margin of the closest neighboring classes is being maximized — which turns out to be a direct generalization of SVM to ranking learning. The second approach allows for k - 1 different margins where the sum of margins is maximized. This approach is shown to reduce to v-SVM when the number of classes k - 2. Both approaches are optimal in size of 2l where l is the total number of training examples. Experiments performed on visual classification and "collaborative filtering" show that both approaches outperform existing ordinal regression algorithms applied for ranking and multi-class SVM applied to general multi-class classification. We discuss the problem of ranking instances. In our framework each instance is associated with a rank or a rating, which is an integer from 1 to k. Our goal is to find a rank-predict ion rule that assigns each instance a rank which is as close as possible to the instance's true rank. We describe a simple and efficient online algorithm, analyze its performance in the mistake bound model, and prove its correctness. We describe two sets of experiments, with synthetic data and with the EachMovie dataset for collaborative filtering. In the experiments we performed, our algorithm outperforms online algorithms for regression and classification applied to ranking. Machine learning methods for classification problems commonly assume that the class values are unordered. However, in many practical applications the class values do exhibit a natural order--for example, when learning how to grade. The standard approach to ordinal classification converts the class value into a numeric quantity and applies a regression learner to the transformed data, translating the output back into a discrete class value in a post-processing step. A disadvantage of this method is that it can only be applied in conjunction with a regression scheme. In this paper we present a simple method that enables standard classification algorithms to make use of ordering information in class attributes. By applying it in conjunction with a decision tree learner we show that it outperforms the naive approach, which treats the class values as an unordered set. Compared to special-purpose algorithms for ordinal classification our method has the advantage that it can be applied without any modification to the underlying learning scheme.