Results for "Marc Peter Deisenroth"
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A Probabilistic Perspective on Gaussian Filtering and SmoothingJun 10 2010Jun 08 2011We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances ... More Distributed Gaussian ProcessesFeb 10 2015May 22 2015To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-the-art sparse GP approximations, ... More Meta Reinforcement Learning with Latent Variable Gaussian ProcessesMar 20 2018Jul 07 2018Learning from small data sets is critical in many practical applications where data collection is time consuming or expensive, e.g., robotics, animal experiments or drug design. Meta learning is one way to increase the data efficiency of learning algorithms ... More Multi-modal filtering for non-linear estimationDec 31 2013Multi-modal densities appear frequently in time series and practical applications. However, they cannot be represented by common state estimators, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which additionally suffer ... More Multi-Task Policy SearchJul 02 2013Feb 12 2014Learning policies that generalize across multiple tasks is an important and challenging research topic in reinforcement learning and robotics. Training individual policies for every single potential task is often impractical, especially for continuous ... More Manifold Gaussian Processes for RegressionFeb 24 2014Apr 11 2016Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too restrictive. One way to ... More A Brief Survey of Deep Reinforcement LearningAug 19 2017Sep 28 2017Deep reinforcement learning is poised to revolutionise the field of AI and represents a step towards building autonomous systems with a higher level understanding of the visual world. Currently, deep learning is enabling reinforcement learning to scale ... More The reparameterization trick for acquisition functionsDec 01 2017Bayesian optimization is a sample-efficient approach to solving global optimization problems. Along with a surrogate model, this approach relies on theoretically motivated value heuristics (acquisition functions) to guide the search process. Maximizing ... More Maximizing acquisition functions for Bayesian optimizationMay 25 2018Dec 02 2018Bayesian optimization is a sample-efficient approach to global optimization that relies on theoretically motivated value heuristics (acquisition functions) to guide its search process. Fully maximizing acquisition functions produces the Bayes' decision ... More Neural Embeddings of Graphs in Hyperbolic SpaceMay 29 2017Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The success of neural ... More Detecting the Age of Twitter UsersJan 18 2016Twitter provides an extremely rich and open source of data for studying human behaviour at scale. It has been used to advance our understanding of social network structure, the viral flow of information and how new ideas develop. Enriching Twitter with ... More Learning deep dynamical models from image pixelsOct 28 2014Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In ... More Identification of Gaussian Process State Space ModelsMay 30 2017Nov 07 2017The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior ... More Real-Time Community Detection in Large Social Networks on a LaptopJan 15 2016Sep 04 2016For a broad range of research, governmental and commercial applications it is important to understand the allegiances, communities and structure of key players in society. One promising direction towards extracting this information is to exploit the rich ... More Customer Lifetime Value Prediction Using EmbeddingsMar 07 2017Jul 06 2017We describe the Customer LifeTime Value (CLTV) prediction system deployed at ASOS.com, a global online fashion retailer. CLTV prediction is an important problem in e-commerce where an accurate estimate of future value allows retailers to effectively allocate ... More Robust Filtering and Smoothing with Gaussian ProcessesMar 20 2012We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are ... More Orthogonally Decoupled Variational Gaussian ProcessesSep 24 2018Jan 15 2019Gaussian processes (GPs) provide a powerful non-parametric framework for reasoning over functions. Despite appealing theory, its superlinear computational and memory complexities have presented a long-standing challenge. State-of-the-art sparse variational ... More Gaussian Process Conditional Density EstimationOct 30 2018Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model complexity, ... More Degree Bounds on Homology and a Conjecture of DerksenOct 01 2014Harm Derksen made a conjecture concerning degree bounds for the syzygies of rings of polynomial invariants in the non-modular case. We provide counterexamples to this conjecture, but also prove a slightly weakened version. We also prove some general results ... More On tensor factorizations of Hopf algebrasOct 23 2014We prove a variety results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on direct product ... More Bouncing alternatives to inflationMar 23 2015Although the inflationary paradigm is the most widely accepted explanation for the current cosmological observations, it does not necessarily correspond to what actually happened in the early stages of our Universe. To decide on this issue, two paths ... More Kinematic Morphing Networks for Manipulation Skill TransferMar 05 2018The transfer of a robot skill between different geometric environments is non-trivial since a wide variety of environments exists, sensor observations as well as robot motions are high-dimensional, and the environment might only be partially observed. ... More MIS: a MIRIAD Interferometry Singledish toolkitFeb 06 2012Building on the "drPACS" contribution at ADASS XX of a simple Unix pipeline infrastructure, we implemented a pipeline toolkit using the package MIRIAD to combine Interferometric and Single Dish data (MIS). This was prompted by our observations made with ... More Knots with only two strict essential surfacesApr 09 2004Dec 23 2004We consider irreducible 3-manifolds M that arise as knot complements in closed 3-manifolds and that contain at most two connected strict essential surfaces. The results in the paper relate the boundary slopes of the two surfaces to their genera and numbers ... More Betti numbers and injectivity radiiJan 30 2009We give lower bounds on the maximal injectivity radius for a closed orientable hyperbolic 3-manifold M with first Betti number 2, under some additional topological hypotheses. A corollary of the main result is that if M has first Betti number 2 and contains ... More Margulis numbers for Haken manifoldsJun 17 2010Jun 27 2011For every closed hyperbolic Haken 3-manifold and, more generally, for any hyperbolic 3-manifold M which is homeomorphic to the interior of a Haken manifold, the number 0.286 is a Margulis number. If M has non-zero first Betti number, or if M is closed ... More Singular surfaces, mod 2 homology, and hyperbolic volume, IIJan 24 2007Oct 19 2010If M is a closed simple 3-manifold whose fundamental group contains a genus-g surface group for some g>1, and if the dimension of H_1(M;Z_2) is at least max(3g-1,6), we show that M contains a closed, incompressible surface of genus at most g. This improves ... More Four-free groups and hyperbolic geometryJun 06 2008Sep 15 2011We give new information about the geometry of closed, orientable hyperbolic 3-manifolds with 4-free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a closed orientable ... More Volume and homology of one-cusped hyperbolic 3-manifoldsJul 29 2007Oct 28 2008Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that pi_1(M) has no subgroup isomorphic to a genus-2 surface group, and that either (a) H_1(M;Z_p) has dimension at least 5 for some prime p, or (b) ... More The Relaxed Square PropertyJul 11 2014Graph products are characterized by the existence of non-trivial equivalence relations on the edge set of a graph that satisfy a so-called square property. We investigate here a generalization, termed RSP-relations. The class of graphs with non-trivial ... More Square Property, Equitable Partitions, and Product-like GraphsJan 29 2013Sep 02 2013Equivalence relations on the edge set of a graph $G$ that satisfy restrictive conditions on chordless squares play a crucial role in the theory of Cartesian graph products and graph bundles. We show here that such relations in a natural way induce equitable ... More Ramanujan duals and automorphic spectrumApr 01 1992We introduce the notion of the automorphic dual of a matrix algebraic group defined over $Q$. This is the part of the unitary dual that corresponds to arithmetic spectrum. Basic functorial properties of this set are derived and used both to deduce arithmetic ... More Non-Gaussianity excess problem in classical bouncing cosmologiesJun 16 2014Jan 13 2015The simplest possible classical model leading to a cosmological bounce is examined in the light of the non-Gaussianities it can generate. Concentrating solely on the transition between contraction and expansion, and assuming initially purely Gaussian ... More Soft Walls in Dynamic AdS/QCD and the Techni-dilatonAug 26 2015Dynamic AdS/QCD is a modification of AdS/QCD that includes the running of the anomalous dimension of the q-bar q quark bilinear and in which the generation of the constituent quark mass plays the role of an IR wall. The model allows one to move away smoothly ... More Emulating dynamic non-linear simulators using Gaussian processesFeb 21 2018Feb 18 2019The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate ... More Singular surfaces, mod 2 homology, and hyperbolic volume, IJun 20 2005Feb 03 2008This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that \pi_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at least 4g-1 ... More A classical bounce: constraints and consequencesFeb 08 2008Jun 18 2008We perform a detailed investigation of the simplest possible cosmological model in which a bounce can occur, namely that where the dynamics is led by a simple massive scalar field in a general self-interacting potential and a background spacetime with ... More Emulating dynamic non-linear simulators using Gaussian processesFeb 21 2018Jun 09 2018In this paper, we examine the emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate. Such computer models simulate the evolution of some real-world phenomena over time, for example models of the ... More A Comparison of Models for Uncertain Network DesignJan 11 2019To solve a real-world problem, the modeler usually needs to make a trade-off between model complexity and usefulness. This is also true for robust optimization, where a wide range of models for uncertainty, so-called uncertainty sets, have been proposed. ... More Conductance fluctuations and boundary conditionsJun 13 2001The conductance fluctuations for various types for two-- and three--dimensional disordered systems with hard wall and periodic boundary conditions are studied, all the way from the ballistic (metallic) regime to the localized regime. It is shown that ... More Production of non-gaussianities in a bouncing phaseMar 31 2014Jul 08 2014We compute the level of non-gaussianities produced by a cosmological bouncing phase in the minimal non-singular setup that lies within the context of General Relativity when the matter content consists of a simple scalar field with a standard kinetic ... More How to make Dupire's local volatility work with jumpsFeb 22 2013There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note we attempt to explain why. In particular, we propose ... More Coupled currents in cosmic stringsMar 25 2009We first examine the microstructure of a cosmic string endowed with two simple Abelian currents. This microstructure depends on two state parameters. We then provide the macroscopic description of such a string and show that it depends on an additional ... More Reciprocal Best Match GraphsMar 19 2019Reciprocal best matches play an important role in numerous applications in computational biology, in particular as the basis of many widely used tools for orthology assessment. Nevertheless, very little is known about their mathematical structure. Here, ... More Reciprocal Best Match GraphsMar 19 2019Apr 11 2019Reciprocal best matches play an important role in numerous applications in computational biology, in particular as the basis of many widely used tools for orthology assessment. Nevertheless, very little is known about their mathematical structure. Here, ... More Reciprocal Best Match GraphsMar 19 2019Apr 30 2019Reciprocal best matches play an important role in numerous applications in computational biology, in particular as the basis of many widely used tools for orthology assessment. Nevertheless, very little is known about their mathematical structure. Here, ... More Dehn surgery, homology and hyperbolic volumeAug 11 2005Jul 06 2009If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2) and H_1(M;Z_7) have dimension at most 3. The proof combines several deep results about hyperbolic ... More Dark-Matter Decays and Self-Gravitating HalosMar 01 2010May 26 2010We consider models in which a dark-matter particle decays to a slightly less massive daughter particle and a noninteracting massless particle. The decay gives the daughter particle a small velocity kick. Self-gravitating dark-matter halos that have a ... More X-ray flashes and X-ray rich Gamma Ray BurstsNov 13 2001X-ray flashes are detected in the Wide Field Cameras on BeppoSAX in the energy range 2-25 keV as bright X-ray sources lasting of the order of minutes, but remaining undetected in the Gamma Ray Bursts Monitor on BeppoSAX. They have properties very similar ... More Coupled Yu-Shiba-Rusinov states in molecular dimers on NbSe$_2$Jan 12 2017Nov 30 2017Magnetic impurities have a dramatic effect on superconductivity by breaking the time-reversal symmetry and inducing so-called Yu-Shiba-Rusinov (YSR) low energy bound states within the superconducting gap. The spatial extent of YSR states is greatly enhanced ... More BB interactions with static bottom quarks from Lattice QCDOct 12 2015The isospin, spin and parity dependent potential of a pair of $B$ mesons is computed using Wilson twisted mass lattice QCD with two flavours of degenerate dynamical quarks. The $B$ meson is addressed in the static-light approximation, i.e.\ the $b$ quarks ... More Characteristic subsurfaces and Dehn fillingNov 25 2002Let M be a compact, orientable, irreducible, atoroidal 3-manifold with boundary an incompressible torus. Techniques based on the characteristic submanifold theory are used to bound the intersection number of two slopes \alpha and \beta on the boundary ... More Lazy Model Expansion: Interleaving Grounding with SearchFeb 27 2014Feb 03 2015Finding satisfying assignments for the variables involved in a set of constraints can be cast as a (bounded) model generation problem: search for (bounded) models of a theory in some logic. The state-of-the-art approach for bounded model generation for ... More Investigation of $B\bar B$ four-quark systems using lattice QCDFeb 24 2016Feb 29 2016We investigate $B \bar B$ systems by computing potentials of two static quarks in the presence of two quarks of finite mass using lattice QCD. By solving the Schr\"odinger equation we check whether these potentials are sufficiently attractive to host ... More A Short Note on Undirected Fitch GraphsDec 05 2017The symmetric version of Fitch's xenology relation coincides with class of complete multipartite graph and thus cannot convey any non-trivial phylogenetic information. Shaking a Box of SandMar 03 2001Oct 16 2001We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (`glassy') dynamical regimes are extensively probed by ... More Propagation front of correlations in an interacting Bose gasFeb 24 2012May 21 2012We analyze the quench dynamics of a one-dimensional bosonic Mott insulator and focus on the time evolution of density correlations. For these we identify a pronounced propagation front, the velocity of which, once correctly extrapolated at large distances, ... More Braneworlds, graviton production, dynamical Casimir effectFeb 05 2009If our Universe is a 3+1 brane in a warped 4+1 dimensional bulk so that its expansion can be understood as the motion of the brane in the bulk, the time dependence of the boundary conditions for arbitrary bulk fields can lead to particle creation via ... More