Deep Neural Networks (DNNs) excel on many complex perceptual tasks but it has proven notoriously difficult to understand how they reach their decisions. We here introduce a high-performance DNN architecture on ImageNet whose decisions are considerably easier to explain. Our model, a simple variant of the ResNet-50 architecture called BagNet, classifies an image based on the occurrences of small local image features without taking into account their spatial ordering. This strategy is closely related to the bag-of-feature (BoF) models popular before the onset of deep learning and reaches a surprisingly high accuracy on ImageNet (87.6% top-5 for 33 x 33 px features and Alexnet performance for 17 x 17 px features). The constraint on local features makes it straight-forward to analyse how exactly each part of the image influences the classification. Furthermore, the BagNets behave similar to state-of-the art deep neural networks such as VGG-16, ResNet-152 or DenseNet-169 in terms of feature sensitivity, error distribution and interactions between image parts. This suggests that the improvements of DNNs over previous bag-of-feature classifiers in the last few years is mostly achieved by better fine-tuning rather than by qualitatively different decision strategies.

Time series forecasting is a crucial component of many important applications, ranging from predicting thebehavior of financial markets [5], to accurate energy load prediction [13]. Even though the large amount of data that can be nowadays collected from these domains provide an unprecedented opportunity for applying powerful deep learning (DL) methods [23, 41, 24], the high-dimensionality, velocity and variety of such data also pose significant and unique challenges that must be carefully addressed for each application. To this end, many methods have been proposed to analyze and forecast time series data. For example, traditional approaches employ adaptive distance metrics, such as Dynamic Time Wrapping [4], to tackle these kind of tasks. However, with the advent of DL the interest is gradually shifting toward using neural network-based methods, including recurrent and convolutional architectures [25, 7], that seem to be more effective for handling such kind of data. It is worth noting that other approaches for time series analysis also exist, such as using the Bag-of-Features model (BoF) [35]. The BoF model was recently adapted toward efficiently processing large amounts of complex and high-dimensional time series [2, 1, 32], due its ability to analyze objects that consist of a varying number of features, as well as withstanding distribution shifts better than competitive methods [29]. The Bag-of-Features model (BoF) involves the following pipeline [35]: a) Several feature vectors are extracted from each input object, e.g., an image or time series. This step is called feature extraction and allows for forming the feature space, where each object is represented as a set of feature vectors.