We study the expressivity of deep neural networks. Measuring a network's complexity by its number of connections or by its number of neurons, we consider the class of functions for which the error of best approximation with networks of a given complexity decays at a certain rate when increasing the complexity budget. Using results from classical approximation theory, we show that this class can be endowed with a (quasi)-norm that makes it a linear function space, called approximation space. We establish that allowing the networks to have certain types of "skip connections" does not change the resulting approximation spaces. We also discuss the role of the network's nonlinearity (also known as activation function) on the resulting spaces, as well as the role of depth. For the popular ReLU nonlinearity and its powers, we relate the newly constructed spaces to classical Besov spaces. The established embeddings highlight that some functions of very low Besov smoothness can nevertheless be well approximated by neural networks, if these networks are sufficiently deep.

We consider the problem of learning the weighted edges of a mixture of two graphs from epidemic cascades. This is a natural setting in the context of social networks, where a post created by one user will not spread on the same graph if it is about basketball or if it is about politics. However, very little is known about whether this problem is solvable. To the best of our knowledge, we establish the first conditions under which this problem can be solved, and provide conditions under which the problem is provably not solvable. When the conditions are met, i.e. when the graphs are connected, with distinct edges, and have at least three edges, we give an efficient algorithm for learning the weights of both graphs with almost optimal sample complexity (up to log factors). We extend the results to the setting in which the priors of the mixture are unknown and obtain similar guarantees.

ABSTRACT This paper aims to propose a novel deep learning-integrated framework for deriving reliable simulation input models through incorporating multi-source information. The framework sources and extracts multisource data generated from construction operations, which provides rich information for input modeling. The framework implements Bayesian deep neural networks to facilitate the purpose of incorporating richer information in input modeling. A case study on road paving operation is performed to test the feasibility and applicability of the proposed framework. Overall, this research enhances input modeling by deriving detailed input models, thereby, augmenting the decision-making processes in construction operations.

In this paper we consider the problem of maximizing the Area under the ROC curve (AUC) which is a widely used performance metric in imbalanced classification and anomaly detection. Due to the pairwise nonlinearity of the objective function, classical SGD algorithms do not apply to the task of AUC maximization. We propose a novel stochastic proximal algorithm for AUC maximization which is scalable to large scale streaming data. Our algorithm can accommodate general penalty terms and is easy to implement with favorable $O(d)$ space and per-iteration time complexities. We establish a high-probability convergence rate $O(1/\sqrt{T})$ for the general convex setting, and improve it to a fast convergence rate $O(1/T)$ for the cases of strongly convex regularizers and no regularization term (without strong convexity). Our proof does not need the uniform boundedness assumption on the loss function or the iterates which is more fidelity to the practice. Finally, we perform extensive experiments over various benchmark data sets from real-world application domains which show the superior performance of our algorithm over the existing AUC maximization algorithms.

Those discussions have focused on data collection, experimental design, and interventions in modeling. But we argue that we ought to first understand the frameworks of ethics that are being used to evaluate the fairness and justice of algorithmic systems. Here, we begin that discussion by outlining deontological ethics, and envision a research agenda prioritized by it. Due to the sheer global reach of machine learning and NLP applications, they are empowered to impact societies (Hovy and Spruit, 2016) - potentially for the worse. Potential harms include exclusion of communities due to demographic bias, overgeneralization of model predictions to amplify bias or prejudice, and overstepping privacy concerns in the pursuit of data and quantification (Mieskes, 2017).

We propose a Gradient Boosting algorithm for learning an ensemble of kernel functions adapted to the task at hand. Unlike state-of-the-art Multiple Kernel Learning techniques that make use of a pre-computed dictionary of kernel functions to select from, at each iteration we fit a kernel by approximating it as a weighted sum of Random Fourier Features (RFF) and by optimizing their barycenter. This allows us to obtain a more versatile method, easier to setup and likely to have better performance. Our study builds on a recent result showing one can learn a kernel from RFF by computing the minimum of a PAC-Bayesian bound on the kernel alignment generalization loss, which is obtained efficiently from a closed-form solution. We conduct an experimental analysis to highlight the advantages of our method w.r.t. both Boosting-based and kernel-learning state-of-the-art methods.

Forecasting electricity prices is an important task in an energy utility and needed not only for proprietary trading but also for the optimisation of power plant production schedules and other technical issues. A promising approach in power price forecasting is based on a recalculation of the order book using forecasts on market fundamentals like demand or renewable infeed. However, this approach requires extensive statistical analysis of market data. In this paper, we examine if and how this statistical work can be reduced using machine learning. Our paper focuses on two research questions: - How can order books from electricity markets be included in machine learning algorithms? - How can order-book-based spot price forecasts be improved using machine learning? We consider the German/Austrian EPEX spot market for electricity. There is a daily auction for electricity with delivery the next day. All 24 hours of the day are traded as separate products.

In personalised decision making, evidence is required to determine suitable actions for individuals. Such evidence can be obtained by identifying treatment effect heterogeneity in different subgroups of the population. In this paper, we design a new type of pattern, treatment effect pattern to represent and discover treatment effect heterogeneity from data for determining whether a treatment will work for an individual or not. Our purpose is to use the computational power to find the most specific and relevant conditions for individuals with respect to a treatment or an action to assist with personalised decision making. Most existing work on identifying treatment effect heterogeneity takes a top-down or partitioning based approach to search for subgroups with heterogeneous treatment effects. We propose a bottom-up generalisation algorithm to obtain the most specific patterns that fit individual circumstances the best for personalised decision making. For the generalisation, we follow a consistency driven strategy to maintain inner-group homogeneity and inter-group heterogeneity of treatment effects. We also employ graphical causal modelling technique to identify adjustment variables for reliable treatment effect pattern discovery. Our method can find the treatment effect patterns reliably as validated by the experiments. The method is faster than the two existing machine learning methods for heterogeneous treatment effect identification and it produces subgroups with higher inner-group treatment effect homogeneity.

Training disentangled representations with generative adversarial networks (GANs) remains challenging, with leading implementations failing to achieve comparable performance to Variational Autoencoder (VAE)-based methods. After $\beta$-VAE and FactorVAE discovered that regularizing the total correlation of the latent vectors promotes disentanglement, numerous VAE-based methods emerged. Such a discovery has yet to be made for GANs, and reported disentanglement scores of GAN-based methods are significantly inferior to VAE-based methods on benchmark datasets. To this end, we propose a novel regularizer that achieves higher disentanglement scores than state-of-the-art VAE- and GAN-based approaches. The proposed contrastive regularizer is inspired by a natural notion of disentanglement: latent traversal. Latent traversal refers to generating images by varying one latent code while fixing the rest. We turn this intuition into a regularizer by adding a discriminator that detects how the latent codes are coupled together, in paired examples. Numerical experiments show that this approach improves upon competing state-of-the-art approaches on benchmark datasets.

The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network. This paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DNN. This paper utilizes knowledge distillation through teacher-student paradigm (Hinton et al., 2015) in a novel setting that exploits the feature extraction capability of DNNs for higher-accuracy quantization. As such, our algorithm logically divides a pretrained full-precision DNN to multiple sections, each of which exposes intermediate features to train a team of students independently in the quantized domain. This divide and conquer strategy, in fact, makes the training of each student section possible in isolation while all these independently trained sections are later stitched together to form the equivalent fully quantized network. Experiments on various DNNs (LeNet, ResNet-20, SVHN and VGG-11) show that, on average, this approach - called DCQ (Divide and Conquer Quantization) - achieves on average 9.7% accuracy improvement to a state-of-the-art quantized training technique, DoReFa (Zhou et al., 2016) for binary and ternary networks.