Multi-omics data, that is, datasets containing different types of high-dimensional molecular variables (often in addition to classical clinical variables), are increasingly generated for the investigation of various diseases. Nevertheless, questions remain regarding the usefulness of multi-omics data for the prediction of disease outcomes such as survival time. It is also unclear which methods are most appropriate to derive such prediction models. We aim to give some answers to these questions by means of a large-scale benchmark study using real data. Different prediction methods from machine learning and statistics were applied on 18 multi-omics cancer datasets from the database "The Cancer Genome Atlas", containing from 35 to 1,000 observations and from 60,000 to 100,000 variables. The considered outcome was the (censored) survival time. Twelve methods based on boosting, penalized regression and random forest were compared, comprising both methods that do and that do not take the group structure of the omics variables into account. The Kaplan-Meier estimate and a Cox model using only clinical variables were used as reference methods. The methods were compared using several repetitions of 5-fold cross-validation. Uno's C-index and the integrated Brier-score served as performance metrics. The results show that, although multi-omics data can improve the prediction performance, this is not generally the case. Only the method block forest slightly outperformed the Cox model on average over all datasets. Taking into account the multi-omics structure improves the predictive performance and protects variables in low-dimensional groups - especially clinical variables - from not being included in the model. All analyses are reproducible using freely available R code.

We investigate online nonlinear regression with continually running recurrent neural network networks (RNNs), i.e., RNN-based online learning. For RNN-based online learning, we introduce an efficient first-order training algorithm that theoretically guarantees to converge to the optimum network parameters. Our algorithm is truly online such that it does not make any assumption on the learning environment to guarantee convergence. Through numerical simulations, we verify our theoretical results and illustrate significant performance improvements achieved by our algorithm with respect to the state-of-the-art RNN training methods.

When we enforce differential privacy in machine learning, the utility-privacy trade-off is different w.r.t. each group. Gradient clipping and random noise addition disproportionately affect underrepresented and complex classes and subgroups, which results in inequality in utility loss. In this work, we analyze the inequality in utility loss by differential privacy and propose a modified differentially private stochastic gradient descent (DPSGD), called DPSGD-F, to remove the potential disparate impact of differential privacy on the protected group. DPSGD-F adjusts the contribution of samples in a group depending on the group clipping bias such that differential privacy has no disparate impact on group utility. Our experimental evaluation shows how group sample size and group clipping bias affect the impact of differential privacy in DPSGD, and how adaptive clipping for each group helps to mitigate the disparate impact caused by differential privacy in DPSGD-F.

Many real-world classification problems come with costs which can vary for different types of misclassification. It is thus important to develop cost-sensitive classifiers which minimize the total misclassification cost. Although binary cost-sensitive classifiers have been well-studied, solving multicategory classification problems is still challenging. A popular approach to address this issue is to construct K classification functions for a K-class problem and remove the redundancy by imposing a sum-to-zero constraint. However, such method usually results in higher computational complexity and inefficient algorithms. In this paper, we propose a novel angle-based cost-sensitive classification framework for multicategory classification without the sum-to-zero constraint. Loss functions that included in the angle-based cost-sensitive classification framework are further justified to be Fisher consistent. To show the usefulness of the framework, two cost-sensitive multicategory boosting algorithms are derived as concrete instances. Numerical experiments demonstrate that proposed boosting algorithms yield competitive classification performances against other existing boosting approaches.

This paper proposes inverse feature learning as a novel supervised feature learning technique that learns a set of high-level features for classification based on an error representation approach. The key contribution of this method is to learn the representation of error as high-level features, while current representation learning methods interpret error by loss functions which are obtained as a function of differences between the true labels and the predicted ones. One advantage of such learning method is that the learned features for each class are independent of learned features for other classes; therefore, this method can learn simultaneously meaning that it can learn new classes without retraining. Error representation learning can also help with generalization and reduce the chance of over-fitting by adding a set of impactful features to the original data set which capture the relationships between each instance and different classes through an error generation and analysis process. This method can be particularly effective in data sets, where the instances of each class have diverse feature representations or the ones with imbalanced classes. The experimental results show that the proposed method results in significantly better performance compared to the state-of-the-art classification techniques for several popular data sets. We hope this paper can open a new path to utilize the proposed perspective of error representation learning in different feature learning domains.

Geometry and topology of decision regions are closely related with classification performance and robustness against adversarial attacks. In this paper, we use differential geometry and topology to explore theoretically the geometrical and topological properties of decision regions produced by deep neural networks (DNNs). The goals are to obtain some geometrical and topological properties of decision regions for given DNN models, and provide some principled guidances to designing and regularizing DNNs. At first, we give the curvatures of decision boundaries in terms of network weights. Based on the rotation index theorem and Gauss-Bonnet-Chern theorem, we then propose methods to identify the closeness and connectivity of given decision boundaries, and obtain the Euler characteristics of closed ones, all without the need to solve decision boundaries explicitly. Finally, we give necessary conditions on network architectures in order to produce closed decision boundaries, and sufficient conditions on network weights for producing zero curvature (flat or developable) decision boundaries.

We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In particular, we focus on spatio-temporal Hawkes processes that are commonly used due to their capability to capture excitations between event occurrences. We introduce a novel inference framework based on randomized transformations and gradient descent to learn the process. We replace the spatial kernel calculations by randomized Fourier feature-based transformations. The introduced randomization by this representation provides flexibility while modeling the spatial excitation between events. Moreover, the system described by the process is expressed within closed-form in terms of scalable matrix operations. During the optimization, we use maximum likelihood estimation approach and gradient descent while properly handling positivity and orthonormality constraints. The experiment results show the improvements achieved by the introduced method in terms of fitting capability in synthetic and real datasets with respect to the conventional inference methods in the spatio-temporal Hawkes process literature. We also analyze the triggering interactions between event types and how their dynamics change in space and time through the interpretation of learned parameters.

We study the spatio-temporal prediction problem, which has attracted attention of many researchers due to its critical real-life applications. In particular, we introduce a novel approach to this problem. Our approach is based on the Hawkes process, which is a non-stationary and self-exciting point process. We extend the formulations of a standard point process model that can represent time-series data to represent a spatio-temporal data. We model the data as nonstationary in time and space. Furthermore, we partition the spatial region we are working on into subregions via an adaptive decision tree and model the source statistics in each subregion with individual but mutually interacting point processes. We also provide a gradient based joint optimization algorithm for the point process and decision tree parameters. Thus, we introduce a model that can jointly infer the source statistics and an adaptive partitioning of the spatial region. Finally, we provide experimental results on a real-life data, which provides significant improvement due to space adaptation and joint optimization compared to standard well-known methods in the literature.

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a data-driven diffusion process. Unlike related diffusion methods, DSDs incorporate information across time scales, which allows for the intrinsic data structure to be inferred in a parameter-free manner. This article develops a theory for DSD based on the multitemporal emergence of mesoscopic equilibria in the underlying diffusion process. New algorithms for denoising and dimension reduction with DSD are also proposed and analyzed. These approaches are based on a weighted spectral decomposition of the underlying diffusion process, and experiments on synthetic datasets and real biological networks illustrate the efficacy of the proposed algorithms in terms of both speed and accuracy. Throughout, comparisons with related methods are made, in order to illustrate the distinct advantages of DSD for datasets exhibiting multiscale structure.

With the advancements in computing technology and web-based applications, data is increasingly generated in multi-dimensional form. This data is usually sparse due to the presence of a large number of users and fewer user interactions. To deal with this, the Nonnegative Tensor Factorization (NTF) based methods have been widely used. However existing factorization algorithms are not suitable to process in all three conditions of size, density, and rank of the tensor. Consequently, their applicability becomes limited. In this paper, we propose a novel fast and efficient NTF algorithm using the element selection approach. We calculate the element importance using Lipschitz continuity and propose a saturation point based element selection method that chooses a set of elements column-wise for updating to solve the optimization problem. Empirical analysis reveals that the proposed algorithm is scalable in terms of tensor size, density, and rank in comparison to the relevant state-of-the-art algorithms.