Bayesian Learning of Conditional Kernel Mean Embeddings for Automatic Likelihood-Free Inference

In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations. However, they demand large quantities of simulation calls. Critically, hyperparameters that determine measures of simulation discrepancy crucially balance inference accuracy and sample efficiency, yet are difficult to tune. In this paper, we present kernel embedding likelihood-free inference (KELFI), a holistic framework that automatically learns model hyperparameters to improve inference accuracy given limited simulation budget. By leveraging likelihood smoothness with conditional mean embeddings, we nonparametrically approximate likelihoods and posteriors as surrogate densities and sample from closed-form posterior mean embeddings, whose hyperparameters are learned under its approximate marginal likelihood. Our modular framework demonstrates improved accuracy and efficiency on challenging inference problems in ecology.Comment: To appear in the Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019, Naha, Okinawa, Japa

Transductive Learning for Multi-Task Copula Processes

We tackle the problem of multi-task learning with copula process. Multivariable prediction in spatial and spatial-temporal processes such as natural resource estimation and pollution monitoring have been typically addressed using techniques based on Gaussian processes and co-Kriging. While the Gaussian prior assumption is convenient from analytical and computational perspectives, nature is dominated by non-Gaussian likelihoods. Copula processes are an elegant and flexible solution to handle various non-Gaussian likelihoods by capturing the dependence structure of random variables with cumulative distribution functions rather than their marginals. We show how multi-task learning for copula processes can be used to improve multivariable prediction for problems where the simple Gaussianity prior assumption does not hold. Then, we present a transductive approximation for multi-task learning and derive analytical expressions for the copula process model. The approach is evaluated and compared to other techniques in one artificial dataset and two publicly available datasets for natural resource estimation and concrete slump prediction

Directional grid maps: modeling multimodal angular uncertainty in dynamic environments

Robots often have to deal with the challenges of operating in dynamic and sometimes unpredictable environments. Although an occupancy map of the environment is sufficient for navigation of a mobile robot or manipulation tasks with a robotic arm in static environments, robots operating in dynamic environments demand richer information to improve robustness, efficiency, and safety. For instance, in path planning, it is important to know the direction of motion of dynamic objects at various locations of the environment for safer navigation or human-robot interaction. In this paper, we introduce directional statistics into robotic mapping to model circular data. Primarily, in collateral to occupancy grid maps, we propose directional grid maps to represent the location-wide long-term angular motion of the environment. Being highly representative, this defines a probability measure-field over the longitude-latitude space rather than a scalar-field or a vector field. Withal, we further demonstrate how the same theory can be used to model angular variations in the spatial domain, temporal domain, and spatiotemporal domain. We carried out a series of experiments to validate the proposed models using a variety of robots having different sensors such as RGB cameras and LiDARs on simulated and real-world settings in both indoor and outdoor environments.Comment: To appear in the proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 201

Index Set Fourier Series Features for Approximating Multi-dimensional Periodic Kernels

Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large datasets often make modelling periodicity untenable for otherwise powerful non-parametric methods like Gaussian Processes (GPs) which typically incur an $\mathcal{O}(N^3)$ computational burden and, consequently, are unable to scale to larger datasets. To this end we introduce a method termed \emph{Index Set Fourier Series Features} to tractably exploit multivariate Fourier series and efficiently decompose periodic kernels on higher-dimensional data into a series of basis functions. We show that our approximation produces significantly less predictive error than alternative approaches such as those based on random Fourier features and achieves better generalisation on regression problems with periodic data

Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit

The Navier-Stokes-Voigt model of viscoelastic incompressible fluid has been recently proposed as a regularization of the three-dimensional Navier-Stokes equations for the purpose of direct numerical simulations. Besides the kinematic viscosity parameter, $\nu>0$, this model possesses a regularizing parameter, $\alpha> 0$, a given length scale parameter, so that $\frac{\alpha^2}{\nu}$ is the relaxation time of the viscoelastic fluid. In this work, we derive several statistical properties of the invariant measures associated with the solutions of the three-dimensional Navier-Stokes-Voigt equations. Moreover, we prove that, for fixed viscosity, $\nu>0$, as the regularizing parameter $\alpha$ tends to zero, there exists a subsequence of probability invariant measures converging, in a suitable sense, to a strong stationary statistical solution of the three-dimensional Navier-Stokes equations, which is a regularized version of the notion of stationary statistical solutions - a generalization of the concept of invariant measure introduced and investigated by Foias. This fact supports earlier numerical observations, and provides an additional evidence that, for small values of the regularization parameter $\alpha$, the Navier-Stokes-Voigt model can indeed be considered as a model to study the statistical properties of the three-dimensional Navier-Stokes equations and turbulent flows via direct numerical simulations

Quantum bit commitment protocol without quantum memory

Quantum protocols for bit commitment have been proposed and it is largely accepted that unconditionally secure quantum bit commitment is not possible; however, it can be more secure than classical bit commitment. In despite of its usefulness, quantum bit commitment protocols have not been experimentally implemented. The main reason is the fact that all proposed quantum bit commitment protocols require quantum memory. In this work, we show a quantum bit commitment protocol that does not require quantum memory and can be implemented with present technology.Comment: 12 pages, 2 figure

Stochastic Functional Gradient Path Planning in Occupancy Maps

Planning safe paths is a major building block in robot autonomy. It has been an active field of research for several decades, with a plethora of planning methods. Planners can be generally categorised as either trajectory optimisers or sampling-based planners. The latter is the predominant planning paradigm for occupancy maps. Trajectory optimisation entails major algorithmic changes to tackle contextual information gaps caused by incomplete sensor coverage of the map. However, the benefits are substantial, as trajectory optimisers can reason on the trade-off between path safety and efficiency. In this work, we improve our previous work on stochastic functional gradient planners. We introduce a novel expressive path representation based on kernel approximation, that allows cost effective model updates based on stochastic samples. The main drawback of the previous stochastic functional gradient planner was the cubic cost, stemming from its non-parametric path representation. Our novel approximate kernel based model, on the other hand, has a fixed linear cost that depends solely on the number of features used to represent the path. We show that the stochasticity of the samples is crucial for the planner and present comparisons to other state-of-the-art planning methods in both simulation and with real occupancy data. The experiments demonstrate the advantages of the stochastic approximate kernel method for path planning in occupancy maps

Hybrid Parallel Quantum Key Distribution Protocol

The practical realizations of BB84 quantum key distribution protocol using single-photon or weak coherent states have normally presented low efficiency, in the meaning that most bits sent by Alice are not useful for the final key. In this work, we show an optical setup to improve the transmission rate of useful bits putting together two ideas, parallel quantum key distribution and physical encryption using mesoscopic coherent states. The final result is a four time faster quantum key distribution setup.Comment: 16 pages, 4 figure

Learning to Navigate by Growing Deep Networks

Adaptability is central to autonomy. Intuitively, for high-dimensional learning problems such as navigating based on vision, internal models with higher complexity allow to accurately encode the information available. However, most learning methods rely on models with a fixed structure and complexity. In this paper, we present a self-supervised framework for robots to learn to navigate, without any prior knowledge of the environment, by incrementally building the structure of a deep network as new data becomes available. Our framework captures images from a monocular camera and self labels the images to continuously train and predict actions from a computationally efficient adaptive deep architecture based on Autoencoders (AE), in a self-supervised fashion. The deep architecture, named Reinforced Adaptive Denoising Autoencoders (RA-DAE), uses reinforcement learning to dynamically change the network structure by adding or removing neurons. Experiments were conducted in simulation and real-world indoor and outdoor environments to assess the potential of self-supervised navigation. RA-DAE demonstrates better performance than equivalent non-adaptive deep learning alternatives and can continue to expand its knowledge, trading-off past and present information.Comment: 10 pages, Australasian Conference on Robotics and Automation, 201

Learning Non-Stationary Space-Time Models for Environmental Monitoring

One of the primary aspects of sustainable development involves accurate understanding and modeling of environmental phenomena. Many of these phenomena exhibit variations in both space and time and it is imperative to develop a deeper understanding of techniques that can model space-time dynamics accurately. In this paper we propose NOSTILL-GP - NOn-stationary Space TIme variable Latent Length scale GP, a generic non-stationary, spatio-temporal Gaussian Process (GP) model. We present several strategies, for efficient training of our model, necessary for real-world applicability. Extensive empirical validation is performed using three real-world environmental monitoring datasets, with diverse dynamics across space and time. Results from the experiments clearly demonstrate general applicability and effectiveness of our approach for applications in environmental monitoring.Comment: AAAI-1