TY - CONF AB - High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most representation learning algorithms for time series data are difficult to interpret. This is due to non-intuitive mappings from data features to salient properties of the representation and non-smoothness over time. To address this problem, we propose a new representation learning framework building on ideas from interpretable discrete dimensionality reduction and deep generative modeling. This framework allows us to learn discrete representations of time series, which give rise to smooth and interpretable embeddings with superior clustering performance. We introduce a new way to overcome the non-differentiability in discrete representation learning and present a gradient-based version of the traditional self-organizing map algorithm that is more performant than the original. Furthermore, to allow for a probabilistic interpretation of our method, we integrate a Markov model in the representation space. This model uncovers the temporal transition structure, improves clustering performance even further and provides additional explanatory insights as well as a natural representation of uncertainty. We evaluate our model in terms of clustering performance and interpretability on static (Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST images, a chaotic Lorenz attractor system with two macro states, as well as on a challenging real world medical time series application on the eICU data set. Our learned representations compare favorably with competitor methods and facilitate downstream tasks on the real world data. AU - Fortuin, Vincent AU - Hüser, Matthias AU - Locatello, Francesco AU - Strathmann, Heiko AU - Rätsch, Gunnar ID - 14198 T2 - International Conference on Learning Representations TI - SOM-VAE: Interpretable discrete representation learning on time series ER - TY - CONF AB - We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal O(1/k−−√) convergence rate. We demonstrate that the same rate holds if the linear subproblems are solved approximately with additive or multiplicative error. In contrast with the relevant work, we are able to characterize the convergence when the non-smooth term is an indicator function. Specific applications of our framework include the non-smooth minimization, semidefinite programming, and minimization with linear inclusion constraints over a compact domain. Numerical evidence demonstrates the benefits of our framework. AU - Yurtsever, Alp AU - Fercoq, Olivier AU - Locatello, Francesco AU - Cevher, Volkan ID - 14203 T2 - Proceedings of the 35th International Conference on Machine Learning TI - A conditional gradient framework for composite convex minimization with applications to semidefinite programming VL - 80 ER - TY - JOUR AB - Adaptive introgression is common in nature and can be driven by selection acting on multiple, linked genes. We explore the effects of polygenic selection on introgression under the infinitesimal model with linkage. This model assumes that the introgressing block has an effectively infinite number of genes, each with an infinitesimal effect on the trait under selection. The block is assumed to introgress under directional selection within a native population that is genetically homogeneous. We use individual-based simulations and a branching process approximation to compute various statistics of the introgressing block, and explore how these depend on parameters such as the map length and initial trait value associated with the introgressing block, the genetic variability along the block, and the strength of selection. Our results show that the introgression dynamics of a block under infinitesimal selection is qualitatively different from the dynamics of neutral introgression. We also find that in the long run, surviving descendant blocks are likely to have intermediate lengths, and clarify how the length is shaped by the interplay between linkage and infinitesimal selection. Our results suggest that it may be difficult to distinguish introgression of single loci from that of genomic blocks with multiple, tightly linked and weakly selected loci. AU - Sachdeva, Himani AU - Barton, Nicholas H ID - 282 IS - 4 JF - Genetics TI - Introgression of a block of genome under infinitesimal selection VL - 209 ER - TY - CONF AB - Universal hashing found a lot of applications in computer science. In cryptography the most important fact about universal families is the so called Leftover Hash Lemma, proved by Impagliazzo, Levin and Luby. In the language of modern cryptography it states that almost universal families are good extractors. In this work we provide a somewhat surprising characterization in the opposite direction. Namely, every extractor with sufficiently good parameters yields a universal family on a noticeable fraction of its inputs. Our proof technique is based on tools from extremal graph theory applied to the \'collision graph\' induced by the extractor, and may be of independent interest. We discuss possible applications to the theory of randomness extractors and non-malleable codes. AU - Obremski, Marciej AU - Skorski, Maciej ID - 108 TI - Inverted leftover hash lemma VL - 2018 ER - TY - CONF AB - Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear O(1/t) rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate O(1/t2) for matching pursuit and steepest coordinate descent on convex objectives. AU - Locatello, Francesco AU - Raj, Anant AU - Karimireddy, Sai Praneeth AU - Rätsch, Gunnar AU - Schölkopf, Bernhard AU - Stich, Sebastian U. AU - Jaggi, Martin ID - 14204 T2 - Proceedings of the 35th International Conference on Machine Learning TI - On matching pursuit and coordinate descent VL - 80 ER -