TY - JOUR AB - A short, 14-amino-acid segment called SP1, located in the Gag structural protein1, has a critical role during the formation of the HIV-1 virus particle. During virus assembly, the SP1 peptide and seven preceding residues fold into a six-helix bundle, which holds together the Gag hexamer and facilitates the formation of a curved immature hexagonal lattice underneath the viral membrane2,3. Upon completion of assembly and budding, proteolytic cleavage of Gag leads to virus maturation, in which the immature lattice is broken down; the liberated CA domain of Gag then re-assembles into the mature conical capsid that encloses the viral genome and associated enzymes. Folding and proteolysis of the six-helix bundle are crucial rate-limiting steps of both Gag assembly and disassembly, and the six-helix bundle is an established target of HIV-1 inhibitors4,5. Here, using a combination of structural and functional analyses, we show that inositol hexakisphosphate (InsP6, also known as IP6) facilitates the formation of the six-helix bundle and assembly of the immature HIV-1 Gag lattice. IP6 makes ionic contacts with two rings of lysine residues at the centre of the Gag hexamer. Proteolytic cleavage then unmasks an alternative binding site, where IP6 interaction promotes the assembly of the mature capsid lattice. These studies identify IP6 as a naturally occurring small molecule that promotes both assembly and maturation of HIV-1. AU - Dick, Robert AU - Zadrozny, Kaneil K AU - Xu, Chaoyi AU - Schur, Florian AU - Lyddon, Terri D AU - Ricana, Clifton L AU - Wagner, Jonathan M AU - Perilla, Juan R AU - Ganser, Pornillos Barbie K AU - Johnson, Marc C AU - Pornillos, Owen AU - Vogt, Volker ID - 150 IS - 7719 JF - Nature TI - Inositol phosphates are assembly co-factors for HIV-1 VL - 560 ER - TY - JOUR AB - The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results we need for other articles and also introduces several objects interesting by themselves. AU - Kalinin, Nikita AU - Shkolnikov, Mikhail ID - 303 IS - 6 JF - Discrete and Continuous Dynamical Systems- Series A TI - Introduction to tropical series and wave dynamic on them VL - 38 ER - TY - CONF AB - Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with a greedily constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions. AU - Locatello, Francesco AU - Dresdner, Gideon AU - Khanna, Rajiv AU - Valera, Isabel AU - Rätsch, Gunnar ID - 14202 SN - 9781510884472 T2 - Advances in Neural Information Processing Systems TI - Boosting black box variational inference VL - 31 ER - TY - CONF AB - Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a mixture of densities by greedily adding components to the mixture. However, as is the case with many other variational inference algorithms, its theoretical properties have not been studied. In the present work, we study the convergence properties of this approach from a modern optimization viewpoint by establishing connections to the classic Frank-Wolfe algorithm. Our analyses yields novel theoretical insights regarding the sufficient conditions for convergence, explicit rates, and algorithmic simplifications. Since a lot of focus in previous works for variational inference has been on tractability, our work is especially important as a much needed attempt to bridge the gap between probabilistic models and their corresponding theoretical properties. AU - Locatello, Francesco AU - Khanna, Rajiv AU - Ghosh, Joydeep AU - Rätsch, Gunnar ID - 14201 T2 - Proceedings of the 21st International Conference on Artificial Intelligence and Statistics TI - Boosting variational inference: An optimization perspective VL - 84 ER - 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 - TY - CONF AB - We present layered concurrent programs, a compact and expressive notation for specifying refinement proofs of concurrent programs. A layered concurrent program specifies a sequence of connected concurrent programs, from most concrete to most abstract, such that common parts of different programs are written exactly once. These programs are expressed in the ordinary syntax of imperative concurrent programs using gated atomic actions, sequencing, choice, and (recursive) procedure calls. Each concurrent program is automatically extracted from the layered program. We reduce refinement to the safety of a sequence of concurrent checker programs, one each to justify the connection between every two consecutive concurrent programs. These checker programs are also automatically extracted from the layered program. Layered concurrent programs have been implemented in the CIVL verifier which has been successfully used for the verification of several complex concurrent programs. AU - Kragl, Bernhard AU - Qadeer, Shaz ID - 160 TI - Layered Concurrent Programs VL - 10981 ER -