The typical approach for learned DBMS components is to capture the behavior by running a representative set of queries and use the observations to train a machine learning model. This workload-driven approach, however, has two major downsides. First, collecting the training data can be very expensive, since all queries need to be executed on potentially large databases. Second, training data has to be recollected when the workload or the database changes. To overcome these limitations, we take a different route and propose a new data-driven approach for learned DBMS components which directly supports changes of the workload and data without the need of retraining. Indeed, one may now expect that this comes at a price of lower accuracy since workload-driven approaches can make use of more information. However, this is not the case. The results of our empirical evaluation demonstrate that our data-driven approach not only provides better accuracy than state-ofthe- art learned components but also generalizes better to unseen queries.

Abstract Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact and approximative feature maps for widely used graph kernels based on the kernel trick. We analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive approximative, explicit feature maps for state-of-the-art kernels supporting real-valued attributes including the GraphHopper and graph invariant kernels. In extensive experiments we show that our approaches often achieve a classification accuracy close to the exact methods based on the kernel trick, but require only a fraction of their running time. Moreover, we propose and analyze algorithms for computing random walk, shortest-path and subgraph matching kernels by explicit and implicit feature maps. Our theoretical results are confirmed experimentally by observing a phase transition when comparing running time with respect to label diversity, walk lengths and subgraph size, respectively.

Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take global graph properties into account may not scale well to large graph databases. Here we propose to start exploring the space between local and global graph kernels, so called glocalized graph kernels, striking the balance between both worlds. Specifically, we introduce a novel graph kernel based on the k-dimensional Weisfeiler-Lehman algorithm. Unfortunately, the k-dimensional Weisfeiler-Lehman algorithm scales exponentially in k. Consequently, we devise a stochastic version of the kernel with provable approximation guarantees using conditional Rademacher averages. On bounded-degree graphs, it can even be computed in constant time. We support our theoretical results with experiments on several graph classification benchmarks, showing that our kernels often outperform the state-of-the-art in terms of classification accuracies.

While state-of-the-art kernels for graphs with discrete labels scale well to graphs with thousands of nodes, the few existing kernels for graphs with continuous attributes, unfortunately, do not scale well. To overcome this limitation, we present hash graph kernels, a general framework to derive kernels for graphs with continuous attributes from discrete ones. The idea is to iteratively turn continuous attributes into discrete labels using randomized hash functions. We illustrate hash graph kernels for the Weisfeiler-Lehman subtree kernel and for the shortest-path kernel. The resulting novel graph kernels are shown to be, both, able to handle graphs with continuous attributes and scalable to large graphs and data sets. This is supported by our theoretical analysis and demonstrated by an extensive experimental evaluation.

Over the past decade, exploiting relations and symmetries within probabilistic models has been proven to be surprisingly effective at solving large scale data mining problems. One of the key operations inside these lifted approaches is counting - be it for parameter/structure learning or for efficient inference. Typically, however, they just count exploiting the logical structure using adhoc operators. This paper investigates whether ‘Compilation to Graph Databases’ could be a practical technique for scaling lifted probabilistic inference and learning methods. We demonstrate that the proposed approach achieves reasonable speed-ups for both inference and learning, without sacrificing performance.

Transfer learning is typically performed between problem instances within the same domain. We consider the problem of transferring across domains. To this effect, we adopt a probabilistic logic approach. First, our approach automatically identifies predicates in the target domain that are similar in their relational structure to predicates in the source domain. Second, it transfers the logic rules and learns the parameters of the transferred rules using target data. Finally, it refines the rules as necessary using theory refinement. Our experimental evidence supports that this transfer method finds models as good or better than those found with state-of-the-art methods, with and without transfer, and in a fraction of the time.

As many real-world data can elegantly be represented as graphs, various graph kernels and methods for computing them have been proposed. Surprisingly, many of the recent graph kernels do not employ the kernel trick anymore but rather compute an explicit feature map and report higher efficiency. So, is there really no benefit of the kernel trick when it comes to graphs? Triggered by this question, we investigate under which conditions it is possible to compute a graph kernel explicitly and for which graph properties this computation is actually more efficient. We give a sufficient condition for R-convolution kernels that enables kernel computation by explicit mapping. We theoretically and experimentally analyze efficiency and flexibility of implicit kernel functions and dot products of explicitly computed feature maps for widely used graph kernels such as random walk kernels, sub graph matching kernels, and shortest-path kernels. For walk kernels we observe a phase transition when comparing runtime with respect to label diversity and walk lengths leading to the conclusion that explicit computations are only favourable for smaller label sets and walk lengths whereas implicit computation is superior for longer walk lengths and data sets with larger label diversity.

We consider the problem of learning probabilistic models from relational data. One of the key issues with relational data is class imbalance where the number of negative examples far outnumbers the number of positive examples. The common approach for dealing with this problem is the use of sub-sampling of negative examples. We, on the other hand, consider a soft margin approach that explicitly trades off between the false positives and false negatives. We apply this approach to the recently successful formalism of relational functional gradient boosting. Specifically, we modify the objective function of the learning problem to explicitly include the trade-off between false positives and negatives. We show empirically that this approach is more successful in handling the class imbalance problem than the original framework that weighed all the examples equally.

Spectral hashing (SH) seeks compact binary codes of data points so that Hamming distances between codes correlate with data similarity. Quickly learning such codes typically boils down to principle component analysis (PCA). However, this is only justified for normally distributed data. For proportional data (normalized histograms), this is not the case. Due to the sum-to-unity constraint, features that are as independent as possible will not all be uncorrelated. In this paper, we show that a linear-time transformation efficiently copes with sum-to-unity constraints: first, we select a small number K of diverse data points by maximizing the volume of the simplex spanned by these prototypes; second, we represent each data point by means of its cosine similarities to the K selected prototypes. This maximum volume hashing is sensible since each dimension in the transformed space is likely to follow a von Mises (vM) distribution, and, in very high dimensions, the vM distribution closely resembles a Gaussian distribution. This justifies to employ PCA on the transformed data. Our extensive experiments validate this: maximum volume hashing outperforms spectral hashing and other state of the art techniques.

Early stress recognition is of great relevance in precision plant protection. Pre-symptomatic water stress detection is of particular interest, ultimately helping to meet the challenge of “How to feed a hungry world?”. Due to the climate change, this is of considerable political and public interest. Due to its large-scale and temporal nature, e.g., when monitoring plants using hyper-spectral imaging, and the demand of physical meaning of the results, it presents unique computational problems in scale and interpretability. However, big data matrices over time also arise in several other real-life applications such as stock market monitoring where a business sector is characterized by the ups and downs of each of its companies per year or topic monitoring of document collections. Therefore, we consider the general problem of embedding data matrices into Euclidean space over time without making any assumption on the generating distribution of each matrix. To do so, we represent all data samples by means of convex combinations of only few extreme ones computable in linear time. On the simplex spanned by the extremes, there are then natural candidates for distributions inducing distances between and in turn embeddings of the data matrices. We evaluate our method across several domains, including synthetic, text, and financial data as well as a large-scale dataset on water stress detection in plants with more than 3 billion matrix entries. The results demonstrate that the embeddings are meaningful and fast to compute. The stress detection results were validated by a domain expert and conform to existing plant physiological knowledge.

Low-rank approximations which are computed from selected rows and columns of a given data matrix have attracted considerable attention lately. They have been proposed as an alternative to the SVD because they naturally lead to interpretable decompositions which was shown to be successful in application such as fraud detection, fMRI segmentation, and collaborative filtering. The CUR decomposition of large matrices, for example, samples rows and columns according to a probability distribution that depends on the Euclidean norm of rows or columns or on other measures of statistical leverage. At the same time, there are various deterministic approaches that do not resort to sampling and were found to often yield factorization of superior quality with respect to reconstruction accuracy. However, these are hardly applicable to large matrices as they typically suffer from high computational costs. Consequently, many practitioners in the field of data mining have abandon deterministic approaches in favor of randomized ones when dealing with today's large-scale data sets. In this paper, we empirically disprove this prejudice. We do so by introducing a novel, linear-time, deterministic CUR approach that adopts the recently introduced Simplex Volume Maximization approach for column selection. The latter has already been proven to be successful for NMF-like decompositions of matrices of billions of entries. Our exhaustive empirical study on more than 30 synthetic and real-world data sets demonstrates that it is also beneficial for CUR-like decompositions. Compared to other deterministic CUR-like methods, it provides comparable reconstruction quality but operates much faster so that it easily scales to matrices of billions of elements. Compared to sampling-based methods, it provides competitive reconstruction quality while staying in the same run-time complexity class.

There have recently been considerable advances in fast inference for (online) latent Dirichlet allocation (LDA). While it is widely recognized that the scheduling of documents in stochastic optimization and in turn in LDA may have significant consequences, this issue remains largely unexplored. Instead, practitioners schedule documents essentially uniformly at random, due perhaps to ease of implementation, and to the lack of clear guidelines on scheduling the documents.

Traffic and mobility mining are fascinating and fast growing areas of data mining and geographical information systems that impact the lives of billions of people every day. Another well-known scientific field that impacts lives of billions is biological sequence analysis. It has experienced an incredible evolution in the recent decade, especially since the Human Genome project. Although, a very first link between both fields has been established already in the early 90ies, many recent papers on mobility mining seem to be unaware of it. We therefore revisit the link and show that many unexplored and novel mobility mining methods fall naturally out of it. Specifically, using advanced discretization techniques for stay-point detection and map matching, we turn traffic sequences into a "biological" ones. Then, we introduce a novel distance function that enables us to directly apply the rich toolbox for biological sequence analysis to it. For instance, by just looking at complex traffic data through the biological glasses of sequence logos we get a novel, easy-to-grasp visualization of data, called "Traffic Logos". For clustering and prediction tasks, our empirical evaluation on three real-world data sets demonstrates that revisiting the link can yield performance as good as state-of-the-art data mining techniques.

Recent years have seen a surge of interest in Statistical Relational Learning (SRL) models that combine logic with probabilities. One prominent example is Markov Logic Networks (MLNs). While MLNs are indeed highly expressive, this expressiveness comes at a cost. Learning MLNs is a hard problem and therefore has attracted much interest in the SRL community. Current methods for learning MLNs follow a two-step approach: first, perform a search through the space of possible clauses and then learn appropriate weights for these clauses. We propose to take a different approach, namely to learn both the weights and the structure of the MLN simultaneously. Our approach is based on functional gradient boosting where the problem of learning MLNs is turned into a series of relational functional approximation problems. We use two kinds of representations for the gradients: clause-based and tree-based. Our experimental evaluation on several benchmark data sets demonstrates that our new approach can learn MLNs as good or better than those found with state-of-the-art methods, but often in a fraction of the time.

Multi-task and relational learning with Gaussian processes are two active but also orthogonal areas of research. So far, there has been few attempt at exploring relational information within multi-task Gaussian processes. While existing relational Gaussian process methods have focused on relations among entities and in turn could be employed within an individual task, we develop a class of Gaussian process models which incorporates relational information across multiple tasks. As we will show, inference and learning within the resulting class of models, called relational multi-task Gaussian processes, can be realized via a variational EM algorithm. Experimental results on synthetic and real-world datasets verify the usefulness of this approach: The observed relational knowledge at the level of tasks can indeed reveal additional pair wise correlations between tasks of interest and, in turn, improve prediction performance.

Matrix factorization methods are among the most common techniques for detecting latent components in data. Popular examples include the Singular Value Decomposition or Non-negative Matrix Factorization. Unfortunately, most methods suffer from high computational complexity and therefore do not scale to massive data. In this paper, we present a linear time algorithm for the factorization of gigantic matrices that iteratively yields latent components. We consider a constrained matrix factorization s.t.~the latent components form a simplex that encloses most of the remaining data. The algorithm maximizes the volume of that simplex and thereby reduces the displacement of data from the space spanned by the latent components. Hence, it also lowers the Frobenius norm, a common criterion for matrix factorization quality. Our algorithm is efficient, well-grounded in distance geometry, and easily applicable to matrices with billions of entries. In addition, the resulting factors allow for an intuitive interpretation of data: every data point can now be expressed as a convex combination of the most extreme and thereby often most descriptive instances in a collection of data. Extensive experimental validations on web-scale data, including 80 million images and 1.5 million twitter tweets, demonstrate superior performance compared to related factorization or clustering techniques.

Map matching is a fundamental operation in many applications such as traffic analysis and location-aware services, the killer apps for ubiquitous computing. In past, several map matching approaches have been proposed. Roughly, they can be categorized into four groups: geometric, topological, probabilistic, and other advanced techniques. Surprisingly, kernel methods have not received attention yet although they are very popular in the machine learning community due to their solid mathematical foundation, tendency toward easy geometric interpretation, and strong empirical performance in a wide variety of domains. In this paper, we show how to employ kernels for map matching. Specifically, ignoring map constraints, we first maximize the consistency between the similarity measures captured by the kernel matrices of the trajectory and relevant part of the street map. The resulting relaxed assignment is then "rounded" into a hard assignment fulfilling the map constraints. On synthetic and real-world trajectories, we show that kernels methods can be used for map matching and perform well compared to probabilistic methods such as HMMs.

Triggered by a market relevant application that involves making joint predictions of pedestrian and public transit flows in urban areas, we address the question of how to utilize hidden common cause relations among variables of interest in order to improve performance in the two related regression tasks. Specifically, we propose stacked Gaussian process learning, a meta-learning scheme in which a base Gaussian process is enhanced by adding the posterior covariance functions of other related tasks to its covariance function in a stage-wise optimization. The idea is that the stacked posterior covariances encode the hidden common causes among variables of interest that are shared across the related regression tasks. Stacked Gaussian process learning is efficient, capable of capturing shared common causes, and can be implemented with any kind of standard Gaussian process regression model such as sparse approximations and relational variants. Our experimental results on real-world data from the market relevant application show that stacked Gaussian processes learning can significantly improve prediction performance of a standard Gaussian process.

Quantile regression refers to the process of estimating the quantiles of a conditional distribution and has many important applications within econometrics and data mining, among other domains. In this paper, we show how to estimate these conditional quantile functions within a Bayes risk minimization framework using a Gaussian process prior. The resulting non-parametric probabilistic model is easy to implement and allows non-crossing quantile functions to be enforced. Moreover, it can directly be used in combination with tools and extensions of standard Gaussian processes such as principled hyperparameter estimation, sparsification, and quantile regression with input-dependent noise rates. No existing approach enjoys all of these desirable properties. Experiments on benchmark datasets show that our method is competitive with state-of-the-art approaches.

Non-negative matrix factorization (NMF) has recently received a lot of attention in data mining, information retrieval, and computer vision. It factorizes a non-negative input matrix V into two non-negative matrix factors V = WH such that W describes "clusters" of the datasets. Analyzing genotypes, social networks, or images, it can be beneficial to ensure V to contain meaningful "cluster centroids", i.e., to restrict W to be convex combinations of data points. But how can we run this convex NMF in the wild, i.e., given millions of data points? Triggered by the simple observation that each data point is a convex combination of vertices of the data convex hull, we propose to restrict W further to be vertices of the convex hull. The benefits of this convex-hull NMF approach are twofold. First, the expected size of the convex hull of, for example, n random Gaussian points in the plane is ¿(¿log n), i.e., the candidate set typically grows much slower than the data set. Second, distance preserving low-dimensional embeddings allow one to compute candidate vertices efficiently. Our extensive experimental evaluation shows that convex-hull NMF compares favorably to convex NMF for large data sets both in terms of speed and reconstruction quality. Moreover, we show that our method can easily be applied to large-scale, real-world data sets, in our case consisting of 1.6 million images respectively 150 million votes on World of Warcraft ® guilds.

The task of aligning sequences arises in many applications. Classical dynamic programming approaches require the explicit state enumeration in the reward model. This is often impractical: the number of states grows very quickly with the number of domain objects and relations among these objects. Relational sequence alignment aims at exploiting symbolic structure to avoid the full enumeration. This comes at the expense of a more complex reward model selection problem: virtually infinitely many abstraction levels have to be explored. In this paper, we apply gradient-based boosting to leverage this problem. Specifically, we show how to reduce the learning problem to a series of relational regressions problems. The main benefit of this is that interactions between states variables are introduced only as needed, so that the potentially infinite search space is not explicitly considered. As our experimental results show, this boosting approach can significantly improve upon established results in challenging applications.