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Distributed dataflow systems like Apache Flink and Apache Spark simplify processing large amounts of data on clusters in a data-parallel manner. However, choosing suitable cluster resources for distributed dataflow jobs in both type and number is difficult, especially for users who do not have access to previous performance metrics. One approach to overcoming this issue is to have users share runtime metrics to train context-aware performance models that help find a suitable configuration for the job at hand. A problem when sharing runtime data instead of trained models or model parameters is that the data size can grow substantially over time. This paper examines several clustering techniques to minimize training data size while keeping the associated performance models accurate. Our results indicate that efficiency gains in data transfer, storage, and model training can be achieved through training data reduction. In the evaluation of our solution on a dataset of runtime data from 930 unique distributed dataflow jobs, we observed that, on average, a 75% data reduction only increases prediction errors by one percentage point.

Many real-world phenomena are naturally bivariate. This includes blood pressure, which comprises systolic and diastolic levels. Here, we develop a Bayesian hierarchical model that estimates these values and their interactions simultaneously, using sparse data that vary substantially between countries and over time. A key element of the model is a two-dimensional second-order Intrinsic Gaussian Markov Random Field, which captures non-linear trends in the variables and their interactions. The model is fitted using Markov chain Monte Carlo methods, with a block Metropolis-Hastings algorithm providing efficient updates. Performance is demonstrated using simulated and real data.

Developing speech technologies is a challenge for low-resource languages for which both annotated and raw speech data is sparse. Maltese is one such language. Recent years have seen an increased interest in the computational processing of Maltese, including speech technologies, but resources for the latter remain sparse. In this paper, we consider data augmentation techniques for improving speech recognition for such languages, focusing on Maltese as a test case. We consider three different types of data augmentation: unsupervised training, multilingual training and the use of synthesized speech as training data. The goal is to determine which of these techniques, or combination of them, is the most effective to improve speech recognition for languages where the starting point is a small corpus of approximately 7 hours of transcribed speech. Our results show that combining the three data augmentation techniques studied here lead us to an absolute WER improvement of 15% without the use of a language model.

Treatment effects on asymmetric and heavy tailed distributions are better reflected at extreme tails rather than at averages or intermediate quantiles. In such distributions, standard methods for estimating quantile treatment effects can provide misleading inference due to the high variability of the estimators at the extremes. In this work, we propose a novel method which incorporates a heavy tailed component in the outcome distribution to estimate the extreme tails and simultaneously employs quantile regression to model the remainder of the distribution. The threshold between the bulk of the distribution and the extreme tails is estimated by utilising a state of the art technique. Simulation results show the superiority of the proposed method over existing estimators for quantile causal effects at extremes in the case of heavy tailed distributions. The method is applied to analyse a real dataset on the London transport network. In this application, the methodology proposed can assist in effective decision making to improve network performance, where causal inference in the extremes for heavy tailed distributions is often a key aim.

We analyze the performance of a reduced-order simulation of geometric meta-materials based on zigzag patterns using a simplified representation. As geometric meta-materials we denote planar cellular structures which can be fabricated in 2d and bent elastically such that they approximate doubly-curved 2-manifold surfaces in 3d space. They obtain their elasticity attributes mainly from the geometry of their cellular elements and their connections. In this paper we focus on cells build from so-called zigzag springs. The physical properties of the base material (i.e., the physical substance) influence the behavior as well, but we essentially factor them out by keeping them constant. The simulation of such complex geometric structures comes with a high computational cost, thus we propose an approach to reduce it by abstracting the zigzag cells by a simpler model and by learning the properties of their elastic deformation behavior. In particular, we analyze the influence of the sampling of the full parameter space and the expressiveness of the reduced model compared to the full model. Based on these observations, we draw conclusions on how to simulate such complex meso-structures with simpler models.

To understand how deep learning works, it is crucial to understand the training dynamics of neural networks. Several interesting hypotheses about these dynamics have been made based on empirically observed phenomena, but there exists a limited theoretical understanding of when and why such phenomena occur. In this paper, we consider the training dynamics of gradient flow on kernel least-squares objectives, which is a limiting dynamics of SGD trained neural networks. Using precise high-dimensional asymptotics, we characterize the dynamics of the fitted model in two "worlds": in the Oracle World the model is trained on the population distribution and in the Empirical World the model is trained on a sampled dataset. We show that under mild conditions on the kernel and $L^2$ target regression function the training dynamics undergo three stages characterized by the behaviors of the models in the two worlds. Our theoretical results also mathematically formalize some interesting deep learning phenomena. Specifically, in our setting we show that SGD progressively learns more complex functions and that there is a "deep bootstrap" phenomenon: during the second stage, the test error of both worlds remain close despite the empirical training error being much smaller. Finally, we give a concrete example comparing the dynamics of two different kernels which shows that faster training is not necessary for better generalization.

One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions. While this paradigm has inspired significant research on the properties of large networks, relatively little work has been devoted to the fact that these networks are often used to model large complex datasets, which may themselves contain millions or even billions of constraints. In this work, we focus on this high-dimensional regime in which both the dataset size and the number of features tend to infinity. We analyze the performance of random feature regression with features $F=f(WX+B)$ for a random weight matrix $W$ and random bias vector $B$, obtaining exact formulae for the asymptotic training and test errors for data generated by a linear teacher model. The role of the bias can be understood as parameterizing a distribution over activation functions, and our analysis directly generalizes to such distributions, even those not expressible with a traditional additive bias. Intriguingly, we find that a mixture of nonlinearities can improve both the training and test errors over the best single nonlinearity, suggesting that mixtures of nonlinearities might be useful for approximate kernel methods or neural network architecture design.

We introduce a universal framework for characterizing the statistical efficiency of a statistical estimation problem with differential privacy guarantees. Our framework, which we call High-dimensional Propose-Test-Release (HPTR), builds upon three crucial components: the exponential mechanism, robust statistics, and the Propose-Test-Release mechanism. Gluing all these together is the concept of resilience, which is central to robust statistical estimation. Resilience guides the design of the algorithm, the sensitivity analysis, and the success probability analysis of the test step in Propose-Test-Release. The key insight is that if we design an exponential mechanism that accesses the data only via one-dimensional robust statistics, then the resulting local sensitivity can be dramatically reduced. Using resilience, we can provide tight local sensitivity bounds. These tight bounds readily translate into near-optimal utility guarantees in several cases. We give a general recipe for applying HPTR to a given instance of a statistical estimation problem and demonstrate it on canonical problems of mean estimation, linear regression, covariance estimation, and principal component analysis. We introduce a general utility analysis technique that proves that HPTR nearly achieves the optimal sample complexity under several scenarios studied in the literature.

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks). Yet, despite its long history, current approaches mostly focus on the optimization of graphs themselves, rather than on directly inferring learning strategies, such as detection, estimation, statistical and probabilistic inference, clustering and separation from signals and data acquired on graphs. To fill this void, we first revisit graph topologies from a Data Analytics point of view, and establish a taxonomy of graph networks through a linear algebraic formalism of graph topology (vertices, connections, directivity). This serves as a basis for spectral analysis of graphs, whereby the eigenvalues and eigenvectors of graph Laplacian and adjacency matrices are shown to convey physical meaning related to both graph topology and higher-order graph properties, such as cuts, walks, paths, and neighborhoods. Next, to illustrate estimation strategies performed on graph signals, spectral analysis of graphs is introduced through eigenanalysis of mathematical descriptors of graphs and in a generic way. Finally, a framework for vertex clustering and graph segmentation is established based on graph spectral representation (eigenanalysis) which illustrates the power of graphs in various data association tasks. The supporting examples demonstrate the promise of Graph Data Analytics in modeling structural and functional/semantic inferences. At the same time, Part I serves as a basis for Part II and Part III which deal with theory, methods and applications of processing Data on Graphs and Graph Topology Learning from data.