Many classification problems are naturally multi-view in the sense their data are described through multiple heterogeneous descriptions. For such tasks, dissimilarity strategies are effective ways to make the different descriptions comparable and to easily merge them, by (i) building intermediate dissimilarity representations for each view and (ii) fusing these representations by averaging the dissimilarities over the views. In this work, we show that the Random Forest proximity measure can be used to build the dissimilarity representations, since this measure reflects similarities between features but also class membership. We then propose a Dynamic View Selection method to better combine the view-specific dissimilarity representations. This allows to take a decision, on each instance to predict, with only the most relevant views for that instance. Experiments are conducted on several real-world multi-view datasets, and show that the Dynamic View Selection offers a significant improvement in performance compared to the simple average combination and two state-of-the-art static view combinations.

We expand the family of tensors that can be efficiently decomposed and apply our new algorithmic ideas to blind deconvolution and Gaussian mixture models. Our basic contribution is an efficient algorithm to decompose certain symmetric overcomplete order-3 tensors, that is, three dimensional arrays of the form $T = \sum_{i=1}^n a_i \otimes a_i \otimes a_i$ where the $a_i$s are not linearly independent. Our second contribution builds on top of our tensor decomposition algorithm to expand the family of Gaussian mixture models whose parameters can be estimated efficiently. These ideas are also presented in a much more general framework of blind deconvolution that makes them applicable to mixture models of identical but very general distributions, including all centrally symmetric distributions with finite 6th moment.

Motivated by practical needs such as large-scale learning, we study the impact of adaptivity constraints to linear contextual bandits, a central problem in online active learning. We consider two popular limited adaptivity models in literature: batch learning and rare policy switches. We show that, when the context vectors are adversarially chosen in $d$-dimensional linear contextual bandits, the learner needs $O(d \log d \log T)$ policy switches to achieve the minimax-optimal regret, and this is optimal up to $\mathrm{poly}(\log d, \log \log T)$ factors; for stochastic context vectors, even in the more restricted batch learning model, only $O(\log \log T)$ batches are needed to achieve the optimal regret. Together with the known results in literature, our results present a complete picture about the adaptivity constraints in linear contextual bandits. Along the way, we propose the distributional optimal design, a natural extension of the optimal experiment design, and provide a both statistically and computationally efficient learning algorithm for the problem, which may be of independent interest.

Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to $\infty$ with fixed ratio $\alpha=n/p$. This family covers a broad range of commonly used classifiers including support vector machine, distance weighted discrimination, and penalized logistic regression. Our result can be used to establish the phase transition boundary for the separability of two classes. We assume that the data are generated from a single multivariate Gaussian distribution with arbitrary covariance structure. We explore two special choices for the covariance matrix: spiked population model and two layer neural networks with random first layer weights. The method we used for deriving the closed-form expression is from statistical physics known as the replica method. Our asymptotic results match simulations already when $n,p$ are of the order of a few hundreds. For two layer neural networks, we reproduce the recently developed `double descent' phenomenology for several classification models. We also discuss some statistical insights that can be drawn from these analysis.

Dimension reduction and visualization of high-dimensional data have become very important research topics in many scientific fields because of the rapid growth of data sets with large sample size and/or dimensions. In the literature of dimension reduction and information visualization, linear methods such as principal component analysis (PCA) [7] and classical scaling [17] mainly focus on preserving the most significant structure or maximum variance in data; nonlinear methods such as multidimensional scaling [2], isomap [16], and curvilinear component analysis (CCA) [5] mainly focus on preserving the long or short distances in the high-dimensional space. They generally perform well in preserving the global structure of data but can fail to preserve the local structure. In recent years, the manifold learning methods, such as SNE [6], Laplacian eigenmap [1], LINE [15], LARGEVIS [14], t-SNE [19] [18], and UMAP [10], have gained popularity because of their ability to preserve both the local and some aspects of the global structure of data. These methods generally assume that data lie on a low-dimensional manifold of the high-dimensional input space. They seek to find the manifold that preserves the intrinsic structure of the high-dimensional data. Many of the manifold learning methods suffer from something called the "crowding problem" while preserving local distance of high-dimensional data in low-dimensional space. This means that, if you want to describe small distances in high-dimensional space faithfully, the points with moderate or large distances between them in high-dimensional space are placed too far away from each other in low-dimensional space.

The analysis of GPS trajectories is a well-studied problem in Urban Computing and has been used to track people. Analyzing people mobility and identifying the transportation mode used by them is essential for cities that want to reduce traffic jams and travel time between their points, thus helping to improve the quality of life of citizens. The trajectory data of a moving object is represented by a discrete collection of points through time, i.e., a time series. Regarding its interdisciplinary and broad scope of real-world applications, it is evident the need of extracting knowledge from time series data. Mining this type of data, however, faces several complexities due to its unique properties. Different representations of data may overcome this. In this work, we propose the use of a feature retained from the Ordinal Pattern Transition Graph, called the probability of self-transition for transportation mode classification. The proposed feature presents better accuracy results than Permutation Entropy and Statistical Complexity, even when these two are combined. This is the first work, to the best of our knowledge, that uses Information Theory quantifiers to transportation mode classification, showing that it is a feasible approach to this kind of problem.

Recently, there has been an increasing interest in (supervised) learning with graph data, especially using graph neural networks. However, the development of meaningful benchmark datasets and standardized evaluation procedures is lagging, consequently hindering advancements in this area. To address this, we introduce the TUDataset for graph classification and regression. The collection consists of over 120 datasets of varying sizes from a wide range of applications. We provide Python-based data loaders, kernel and graph neural network baseline implementations, and evaluation tools. Here, we give an overview of the datasets, standardized evaluation procedures, and provide baseline experiments. All datasets are available at www.graphlearning.io. The experiments are fully reproducible from the code available at www.github.com/chrsmrrs/tudataset.

Stochastic block models (SBM) are widely used in network science due to their interpretable structure that allows inference on groups of nodes having common connectivity patterns. Although providing a well established model-based approach for community detection, such formulations are still the object of intense research to address the key problem of inferring the unknown number of communities. This has motivated the development of several probabilistic mechanisms to characterize the node partition process, covering solutions with fixed, random and infinite number of communities. In this article we provide a unified view of all these formulations within a single extended stochastic block model (ESBM), that relies on Gibbs-type processes and encompasses most existing representations as special cases. Connections with Bayesian nonparametric literature open up new avenues that allow the natural inclusion of several unexplored options to model the nodes partition process and to incorporate node attributes in a principled manner. Among these new alternatives, we focus on the Gnedin process as an example of a probabilistic mechanism with desirable theoretical properties and nice empirical performance. A collapsed Gibbs sampler that can be applied to the whole ESBM class is proposed, and refined methods for estimation, uncertainty quantification and model assessment are outlined. The performance of ESBM is assessed in simulations and an application to bill co-sponsorship networks in the Italian parliament, where we find key hidden block structures and core-periphery patterns.

We obtain a robust and computationally efficient estimator for Linear Regression that achieves statistically optimal convergence rate under mild distributional assumptions. Concretely, we assume our data is drawn from a $k$-hypercontractive distribution and an $\epsilon$-fraction is adversarially corrupted. We then describe an estimator that converges to the optimal least-squares minimizer for the true distribution at a rate proportional to $\epsilon^{2-2/k}$, when the noise is independent of the covariates. We note that no such estimator was known prior to our work, even with access to unbounded computation. The rate we achieve is information-theoretically optimal and thus we resolve the main open question in Klivans, Kothari and Meka [COLT'18]. Our key insight is to identify an analytic condition relating the distribution over the noise and covariates that completely characterizes the rate of convergence, regardless of the noise model. In particular, we show that when the moments of the noise and covariates are negatively-correlated, we obtain the same rate as independent noise. Further, when the condition is not satisfied, we obtain a rate proportional to $\epsilon^{2-4/k}$, and again match the information-theoretic lower bound. Our central technical contribution is to algorithmically exploit independence of random variables in the "sum-of-squares" framework by formulating it as a polynomial identity.

There has been increased interest in missing sensor data imputation, which is ubiquitous in the field of structural health monitoring (SHM) due to discontinuous sensing caused by sensor malfunction. To address this fundamental issue, this paper presents an incremental Bayesian tensor learning method for reconstruction of spatiotemporal missing data in SHM and forecasting of structural response. In particular, a spatiotemporal tensor is first constructed followed by Bayesian tensor factorization that extracts latent features for missing data imputation. To enable structural response forecasting based on incomplete sensing data, the tensor decomposition is further integrated with vector autoregression in an incremental learning scheme. The performance of the proposed approach is validated on continuous field-sensing data (including strain and temperature records) of a concrete bridge, based on the assumption that strain time histories are highly correlated to temperature recordings. The results indicate that the proposed probabilistic tensor learning approach is accurate and robust even in the presence of large rates of random missing, structured missing and their combination. The effect of rank selection on the imputation and prediction performance is also investigated. The results show that a better estimation accuracy can be achieved with a higher rank for random missing whereas a lower rank for structured missing.