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Ulf Brefeld

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11 papers
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11

NeurIPS Conference 2022 Conference Paper

Semi-Supervised Generative Models for Multiagent Trajectories

  • Dennis Fassmeyer
  • Pascal Fassmeyer
  • Ulf Brefeld

Analyzing the spatiotemporal behavior of multiple agents is of great interest to many communities. Existing probabilistic models in this realm are formalized either in an unsupervised framework, where the latent space is described by discrete or continuous variables, or in a supervised framework, where weakly preserved labels add explicit information to continuous latent representations. To overcome inherent limitations, we propose a novel objective function for processing multi-agent trajectories based on semi-supervised variational autoencoders, where equivariance and interaction of agents are captured via customized graph networks. The resulting architecture disentangles discrete and continuous latent effects and provides a natural solution for injecting expensive domain knowledge into interactive sequential systems. Empirically, our model not only outperforms various state-of-the-art baselines in trajectory forecasting, but also learns to effectively leverage unsupervised multi-agent sequences for classification tasks on interactive real-world sports datasets.

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NeurIPS Conference 2019 Conference Paper

Coresets for Archetypal Analysis

  • Sebastian Mair
  • Ulf Brefeld

Archetypal analysis represents instances as linear mixtures of prototypes (the archetypes) that lie on the boundary of the convex hull of the data. Archetypes are thus often better interpretable than factors computed by other matrix factorization techniques. However, the interpretability comes with high computational cost due to additional convexity-preserving constraints. In this paper, we propose efficient coresets for archetypal analysis. Theoretical guarantees are derived by showing that quantization errors of k-means upper bound archetypal analysis; the computation of a provable absolute-coreset can be performed in only two passes over the data. Empirically, we show that the coresets lead to improved performance on several data sets.

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ICML Conference 2017 Conference Paper

Frame-based Data Factorizations

  • Sebastian Mair 0001
  • Ahcène Boubekki
  • Ulf Brefeld

Archetypal Analysis is the method of choice to compute interpretable matrix factorizations. Every data point is represented as a convex combination of factors, i. e. , points on the boundary of the convex hull of the data. This renders computation inefficient. In this paper, we show that the set of vertices of a convex hull, the so-called frame, can be efficiently computed by a quadratic program. We provide theoretical and empirical results for our proposed approach and make use of the frame to accelerate Archetypal Analysis. The novel method yields similar reconstruction errors as baseline competitors but is much faster to compute.

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JMLR Journal 2011 Journal Article

l p -Norm Multiple Kernel Learning

  • Marius Kloft
  • Ulf Brefeld
  • Sören Sonnenburg
  • Alexander Zien

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and scalability. Unfortunately, this l 1 -norm MKL is rarely observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures that generalize well, we extend MKL to arbitrary norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary norms, that is l p -norms with p ≥ 1. This interleaved optimization is much faster than the commonly used wrapper approaches, as demonstrated on several data sets. A theoretical analysis and an experiment on controlled artificial data shed light on the appropriateness of sparse, non-sparse and l ∞ -norm MKL in various scenarios. Importantly, empirical applications of l p -norm MKL to three real-world problems from computational biology show that non-sparse MKL achieves accuracies that surpass the state-of-the-art. Data sets, source code to reproduce the experiments, implementations of the algorithms, and further information are available at http://doc.ml.tu-berlin.de/nonsparse_mkl/. [abs] [ pdf ][ bib ] &copy JMLR 2011. ( edit, beta )

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JMLR Journal 2010 Journal Article

Approximate Tree Kernels

  • Konrad Rieck
  • Tammo Krueger
  • Ulf Brefeld
  • Klaus-Robert Müller

Convolution kernels for trees provide simple means for learning with tree-structured data. The computation time of tree kernels is quadratic in the size of the trees, since all pairs of nodes need to be compared. Thus, large parse trees, obtained from HTML documents or structured network data, render convolution kernels inapplicable. In this article, we propose an effective approximation technique for parse tree kernels. The approximate tree kernels (ATKs) limit kernel computation to a sparse subset of relevant subtrees and discard redundant structures, such that training and testing of kernel-based learning methods are significantly accelerated. We devise linear programming approaches for identifying such subsets for supervised and unsupervised learning tasks, respectively. Empirically, the approximate tree kernels attain run-time improvements up to three orders of magnitude while preserving the predictive accuracy of regular tree kernels. For unsupervised tasks, the approximate tree kernels even lead to more accurate predictions by identifying relevant dimensions in feature space. [abs] [ pdf ][ bib ] &copy JMLR 2010. ( edit, beta )

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NeurIPS Conference 2009 Conference Paper

Efficient and Accurate Lp-Norm Multiple Kernel Learning

  • Marius Kloft
  • Ulf Brefeld
  • Pavel Laskov
  • Klaus-Robert Müller
  • Alexander Zien
  • Sören Sonnenburg

Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations and hence support interpretability. Unfortunately, L1-norm MKL is hardly observed to outperform trivial baselines in practical applications. To allow for robust kernel mixtures, we generalize MKL to arbitrary Lp-norms. We devise new insights on the connection between several existing MKL formulations and develop two efficient interleaved optimization strategies for arbitrary p>1. Empirically, we demonstrate that the interleaved optimization strategies are much faster compared to the traditionally used wrapper approaches. Finally, we apply Lp-norm MKL to real-world problems from computational biology, showing that non-sparse MKL achieves accuracies that go beyond the state-of-the-art.

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ICML Conference 2006 Conference Paper

Efficient co-regularised least squares regression

  • Ulf Brefeld
  • Thomas Gärtner 0001
  • Tobias Scheffer
  • Stefan Wrobel

In many applications, unlabelled examples are inexpensive and easy to obtain. Semi-supervised approaches try to utilise such examples to reduce the predictive error. In this paper, we investigate a semi-supervised least squares regression algorithm based on the co-learning approach. Similar to other semi-supervised algorithms, our base algorithm has cubic runtime complexity in the number of unlabelled examples. To be able to handle larger sets of unlabelled examples, we devise a semi-parametric variant that scales linearly in the number of unlabelled examples. Experiments show a significant error reduction by co-regularisation and a large runtime improvement for the semi-parametric approximation. Last but not least, we propose a distributed procedure that can be applied without collecting all data at a single site.

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