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Score-based models, trained with denoising score matching, are remarkably effective in generating high dimensional data. However, the high variance of their training objective hinders optimisation. We attempt to reduce it with a control variate, derived via a $k$-th order Taylor expansion on the training objective and its gradient. We prove an equivalence between the two and demonstrate empirically the effectiveness of our approach on a low dimensional problem setting; and study its effect on larger problems., Comment: 14 pages, ICML Structured Probabilistic Inference & Generative Modeling 2024

This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of reconciling general relativity with quantum mechanics. We propose that matter particles can be described as radiation confined within dynamically curved spacetime regions, without the need for quantization of space and time, and using standard field equations and natural Planck units. Specifically, we investigate a cyclic or oscillating radiation-dominated micro cosmos undergoing repeated bouncing. Our methodology employs integration, with carefully defined initial conditions. The results include several observable properties characteristic of quantum particles. We calculate the total mass, revealing a compelling inverse proportionality between mass and radius identical with the de Broglie relationship. Applying this model to protons, we discover a profound and surprisingly simple relationship between the proton's radius and mass expressed in Planck units. This enables a definition of the proton radius that aligns remarkably well with the 2018 CODATA value. Furthermore, our analysis demonstrates that the radial density profile of the proton (or nucleon), averaged over a cycle time, increases toward the center. The problem of embedding the micro cosmos within a background spacetime is also described. These results underscore the relevance of general relativity in the domain of nuclear physics. Moreover, the model offers a fresh perspective that can stimulate new ideas in the ongoing quest to unify general relativity with quantum physics., Comment: 18 pages, 5 figures

In this work, we address the problem of assessing and constructing feedback for early-stage writing automatically using machine learning. Early-stage writing is typically vastly different from conventional writing due to phonetic spelling and lack of proper grammar, punctuation, spacing etc. Consequently, early-stage writing is highly non-trivial to analyze using common linguistic metrics. We propose to use sequence-to-sequence models for "translating" early-stage writing by students into "conventional" writing, which allows the translated text to be analyzed using linguistic metrics. Furthermore, we propose a novel robust likelihood to mitigate the effect of noise in the dataset. We investigate the proposed methods using a set of numerical experiments and demonstrate that the conventional text can be predicted with high accuracy., Comment: 9 pages, 1 figure, 1 table, to be published in the proceedings of the Northern Lights Deep Learning Conference 2024

The NASA's Double-Asteroid Redirection Test (DART) was a unique planetary defence and technology test mission, the first of its kind. The main spacecraft of the DART mission impacted the target asteroid Dimorphos, a small moon orbiting asteroid (65803) Didymos, on 2022 September 26. The impact brought up a mass of ejecta which, together with the direct momentum transfer from the collision, caused an orbital period change of 33 +/- 1 minutes, as measured by ground-based observations. We report here the outcome of the optical monitoring campaign of the Didymos system from the Danish 1.54 m telescope at La Silla around the time of impact. The observations contributed to the determination of the changes in the orbital parameters of the Didymos-Dimorphos system, as reported by arXiv:2303.02077, but in this paper we focus on the ejecta produced by the DART impact. We present photometric measurements from which we remove the contribution from the Didymos-Dimorphos system using a H-G photometric model. Using two photometric apertures we determine the fading rate of the ejecta to be 0.115 +/- 0.003 mag/d (in a 2" aperture) and 0.086 +/- 0.003 mag/d (5") over the first week post-impact. After about 8 days post-impact we note the fading slows down to 0.057 +/- 0.003 mag/d (2" aperture) and 0.068 +/- 0.002 mag/d (5"). We include deep-stacked images of the system to illustrate the ejecta evolution during the first 18 days, noting the emergence of dust tails formed from ejecta pushed in the anti-solar direction, and measuring the extent of the particles ejected sunward to be at least 4000 km., Comment: 20 pages, 6 figures. Accepted for publication in The Planetary Science Journal

In geospatial planning, it is often essential to represent objects in a vectorized format, as this format easily translates to downstream tasks such as web development, graphics, or design. While these problems are frequently addressed using semantic segmentation, which requires additional post-processing to vectorize objects in a non-trivial way, we present an Image-to-Sequence model that allows for direct shape inference and is ready for vector-based workflows out of the box. We demonstrate the model's performance in various ways, including perturbations to the image input that correspond to variations or artifacts commonly encountered in remote sensing applications. Our model outperforms prior works when using ground truth bounding boxes (one object per image), achieving the lowest maximum tangent angle error., Comment: ICLR 2023 Workshop on Machine Learning in Remote Sensing

We present a novel pipeline for learning the conditional distribution of a building roof mesh given pixels from an aerial image, under the assumption that roof geometry follows a set of regular patterns. Unlike alternative methods that require multiple images of the same object, our approach enables estimating 3D roof meshes using only a single image for predictions. The approach employs the PolyGen, a deep generative transformer architecture for 3D meshes. We apply this model in a new domain and investigate the sensitivity of the image resolution. We propose a novel metric to evaluate the performance of the inferred meshes, and our results show that the model is robust even at lower resolutions, while qualitatively producing realistic representations for out-of-distribution samples., Comment: Copyright 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Bayesian optimization (BO) is a popular method for black-box optimization, which relies on uncertainty as part of its decision-making process when deciding which experiment to perform next. However, not much work has addressed the effect of uncertainty on the performance of the BO algorithm and to what extent calibrated uncertainties improve the ability to find the global optimum. In this work, we provide an extensive study of the relationship between the BO performance (regret) and uncertainty calibration for popular surrogate models and compare them across both synthetic and real-world experiments. Our results confirm that Gaussian Processes are strong surrogate models and that they tend to outperform other popular models. Our results further show a positive association between calibration error and regret, but interestingly, this association disappears when we control for the type of model in the analysis. We also studied the effect of re-calibration and demonstrate that it generally does not lead to improved regret. Finally, we provide theoretical justification for why uncertainty calibration might be difficult to combine with BO due to the small sample sizes commonly used., Comment: 14 pages, 4 figures, 2 tables

The body of research on classification of solar panel arrays from aerial imagery is increasing, yet there are still not many public benchmark datasets. This paper introduces two novel benchmark datasets for classifying and localizing solar panel arrays in Denmark: A human annotated dataset for classification and segmentation, as well as a classification dataset acquired using self-reported data from the Danish national building registry. We explore the performance of prior works on the new benchmark dataset, and present results after fine-tuning models using a similar approach as recent works. Furthermore, we train models of newer architectures and provide benchmark baselines to our datasets in several scenarios. We believe the release of these datasets may improve future research in both local and global geospatial domains for identifying and mapping of solar panel arrays from aerial imagery. The data is accessible at https://osf.io/aj539/., Comment: 7 pages, 2 figures, to access the dataset, see https://osf.io/aj539/

Black-box variational inference (BBVI) now sees widespread use in machine learning and statistics as a fast yet flexible alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, stochastic optimization methods for BBVI remain unreliable and require substantial expertise and hand-tuning to apply effectively. In this paper, we propose Robust and Automated Black-box VI (RABVI), a framework for improving the reliability of BBVI optimization. RABVI is based on rigorously justified automation techniques, includes just a small number of intuitive tuning parameters, and detects inaccurate estimates of the optimal variational approximation. RABVI adaptively decreases the learning rate by detecting convergence of the fixed--learning-rate iterates, then estimates the symmetrized Kullback--Leibler (KL) divergence between the current variational approximation and the optimal one. It also employs a novel optimization termination criterion that enables the user to balance desired accuracy against computational cost by comparing (i) the predicted relative decrease in the symmetrized KL divergence if a smaller learning were used and (ii) the predicted computation required to converge with the smaller learning rate. We validate the robustness and accuracy of RABVI through carefully designed simulation studies and on a diverse set of real-world model and data examples.

We report the first unambiguous detection and mass measurement of an isolated stellar-mass black hole (BH). We used the Hubble Space Telescope (HST) to carry out precise astrometry of the source star of the long-duration (t_E~270 days), high-magnification microlensing event MOA-2011-BLG-191/OGLE-2011-BLG-0462 (hereafter designated as MOA-11-191/OGLE-11-462), in the direction of the Galactic bulge. HST imaging, conducted at eight epochs over an interval of six years, reveals a clear relativistic astrometric deflection of the background star's apparent position. Ground-based photometry of MOA-11-191/OGLE-11-462 shows a parallactic signature of the effect of the Earth's motion on the microlensing light curve. Combining the HST astrometry with the ground-based light curve and the derived parallax, we obtain a lens mass of 7.1 +/- 1.3 Msun and a distance of 1.58 +/- 0.18 kpc. We show that the lens emits no detectable light, which, along with having a mass higher than is possible for a white dwarf or neutron star, confirms its BH nature. Our analysis also provides an absolute proper motion for the BH. The proper motion is offset from the mean motion of Galactic-disk stars at similar distances by an amount corresponding to a transverse space velocity of ~45 km/s, suggesting that the BH received a 'natal kick' from its supernova explosion. Previous mass determinations for stellar-mass BHs have come from radial-velocity measurements of Galactic X-ray binaries, and from gravitational radiation emitted by merging BHs in binary systems in external galaxies. Our mass measurement is the first for an isolated stellar-mass BH using any technique., Comment: 37 pages, Published in ApJ

Antigen test kits have been used extensively as a screening tool during the worldwide pandemic of coronavirus (SARS-CoV-2). While it is generally expected that taking samples for analysis with PCR testing gives more reliable results than using antigen test kits, the overall sensitivity and specificity of the two protocols in the field have not yet been estimated without assuming that the PCR test constitutes a gold standard. We use latent class models to estimate the in situ performance of both PCR and antigen testing, using data from the Danish national registries. The results are based on 240,000 paired tests results sub-selected from the 55 million test results that were obtained in Denmark during the period from February 2021 until June 2021. We found that the specificity of both tests is very high in our data sample (>99.7%), while the sensitivity of PCR sampling was estimated to be 95.7% (95% CI: 92.8-98.4%) and that of the antigen test kits used in Denmark over the study period was estimated at 53.8% (95% CI: 49.8-57.9%). Our findings can be used as supplementary information for consideration when implementing serial testing strategies that employ a confirmatory PCR sample following a positive result from an antigen test kit, such as the policy used in Denmark. We note that while this strategy reduces the number of false positives associated with antigen test screening, it also increases the false negatives. We demonstrate that the balance of trading false positives for false negatives only favours the use of serial testing when the expected true prevalence is low. Our results contain substantial uncertainty in the estimates for sensitivity due to the relatively small number of positive test results over this period: validation of our findings in a population with higher prevalence would therefore be highly relevant for future work.

As the rate of data collection continues to grow rapidly, developing visualization tools that scale to immense data sets is a serious and ever-increasing challenge. Existing approaches generally seek to decouple storage and visualization systems, performing just-in-time data reduction to transparently avoid overloading the visualizer. We present a new architecture in which the visualizer and data store are tightly coupled. Unlike systems that read raw data from storage, the performance of our system scales linearly with the size of the final visualization, essentially independent of the size of the data. Thus, it scales to massive data sets while supporting interactive performance (sub-100 ms query latency). This enables a new class of visualization clients that automatically manage data, quickly and transparently requesting data from the underlying database without requiring the user to explicitly initiate queries. It lays a groundwork for supporting truly interactive exploration of big data and opens new directions for research on scalable information visualization systems., Comment: 14 pages; Originally published in May 2018 as a technical report in the UC Berkeley EECS Technical Report Series (see https://www2.eecs.berkeley.edu/Pubs/TechRpts/2018/EECS-2018-85.html)

Current black-box variational inference (BBVI) methods require the user to make numerous design choices -- such as the selection of variational objective and approximating family -- yet there is little principled guidance on how to do so. We develop a conceptual framework and set of experimental tools to understand the effects of these choices, which we leverage to propose best practices for maximizing posterior approximation accuracy. Our approach is based on studying the pre-asymptotic tail behavior of the density ratios between the joint distribution and the variational approximation, then exploiting insights and tools from the importance sampling literature. Our framework and supporting experiments help to distinguish between the behavior of BBVI methods for approximating low-dimensional versus moderate-to-high-dimensional posteriors. In the latter case, we show that mass-covering variational objectives are difficult to optimize and do not improve accuracy, but flexible variational families can improve accuracy and the effectiveness of importance sampling -- at the cost of additional optimization challenges. Therefore, for moderate-to-high-dimensional posteriors we recommend using the (mode-seeking) exclusive KL divergence since it is the easiest to optimize, and improving the variational family or using model parameter transformations to make the posterior and optimal variational approximation more similar. On the other hand, in low-dimensional settings, we show that heavy-tailed variational families and mass-covering divergences are effective and can increase the chances that the approximation can be improved by importance sampling.

Recent work reported the discovery of a gamma-ray burst (GRB) associated with the galaxy GN-z11 at $z\sim 11$. The extreme improbability of the transient source being a GRB in the very early Universe requires robust elimination of all plausible alternative hypotheses. We identify numerous examples of similar transient signals in separate archival MOSFIRE observations and argue that Solar system objects -- natural or artificial -- are a far more probable explanation for these phenomena. An appendix has been added in response to additional points raised in Jiang et al. (2021), which do not change the conclusion.

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior distribution,(2) the choice of divergence, and (3) the optimization of the variational objective. We show that even in the best-case scenario when the exact posterior belongs to the assumed variational family, common stochastic optimization methods lead to poor variational approximations if the problem dimension is moderately large. We also demonstrate that these methods are not robust across diverse model types. Motivated by these findings, we develop a more robust and accurate stochastic optimization framework by viewing the underlying optimization algorithm as producing a Markov chain. Our approach is theoretically motivated and includes a diagnostic for convergence and a novel stopping rule, both of which are robust to noisy evaluations of the objective function. We show empirically that the proposed framework works well on a diverse set of models: it can automatically detect stochastic optimization failure or inaccurate variational approximation

We formulate approximate Bayesian inference in non-conjugate temporal and spatio-temporal Gaussian process models as a simple parameter update rule applied during Kalman smoothing. This viewpoint encompasses most inference schemes, including expectation propagation (EP), the classical (Extended, Unscented, etc.) Kalman smoothers, and variational inference. We provide a unifying perspective on these algorithms, showing how replacing the power EP moment matching step with linearisation recovers the classical smoothers. EP provides some benefits over the traditional methods via introduction of the so-called cavity distribution, and we combine these benefits with the computational efficiency of linearisation, providing extensive empirical analysis demonstrating the efficacy of various algorithms under this unifying framework. We provide a fast implementation of all methods in JAX., Comment: Accepted to International Conference on Machine Learning (ICML) 2020

Gaussian processes are powerful non-parametric probabilistic models for stochastic functions. However, the direct implementation entails a complexity that is computationally intractable when the number of observations is large, especially when estimated with fully Bayesian methods such as Markov chain Monte Carlo. In this paper, we focus on a low-rank approximate Bayesian Gaussian processes, based on a basis function approximation via Laplace eigenfunctions for stationary covariance functions. The main contribution of this paper is a detailed analysis of the performance, and practical recommendations for how to select the number of basis functions and the boundary factor. Intuitive visualizations and recommendations, make it easier for users to improve approximation accuracy and computational performance. We also propose diagnostics for checking that the number of basis functions and the boundary factor are adequate given the data. The approach is simple and exhibits an attractive computational complexity due to its linear structure, and it is easy to implement in probabilistic programming frameworks. Several illustrative examples of the performance and applicability of the method in the probabilistic programming language Stan are presented together with the underlying Stan model code., Comment: 27 pages, 18 figures

Most research in Bayesian optimization (BO) has focused on \emph{direct feedback} scenarios, where one has access to exact values of some expensive-to-evaluate objective. This direction has been mainly driven by the use of BO in machine learning hyper-parameter configuration problems. However, in domains such as modelling human preferences, A/B tests, or recommender systems, there is a need for methods that can replace direct feedback with \emph{preferential feedback}, obtained via rankings or pairwise comparisons. In this work, we present preferential batch Bayesian optimization (PBBO), a new framework that allows finding the optimum of a latent function of interest, given any type of parallel preferential feedback for a group of two or more points. We do so by using a Gaussian process model with a likelihood specially designed to enable parallel and efficient data collection mechanisms, which are key in modern machine learning. We show how the acquisitions developed under this framework generalize and augment previous approaches in Bayesian optimization, expanding the use of these techniques to a wider range of domains. An extensive simulation study shows the benefits of this approach, both with simulated functions and four real data sets., Comment: 6 pages + 7 pages in supplementary material

Recently, new methods for model assessment, based on subsampling and posterior approximations, have been proposed for scaling leave-one-out cross-validation (LOO) to large datasets. Although these methods work well for estimating predictive performance for individual models, they are less powerful in model comparison. We propose an efficient method for estimating differences in predictive performance by combining fast approximate LOO surrogates with exact LOO subsampling using the difference estimator and supply proofs with regards to scaling characteristics. The resulting approach can be orders of magnitude more efficient than previous approaches, as well as being better suited to model comparison.

Microfading Spectrometry (MFS) is a method for assessing light sensitivity color (spectral) variations of cultural heritage objects. The MFS technique provides measurements of the surface under study, where each point of the surface gives rise to a time-series that represents potential spectral (color) changes due to sunlight exposition over time. Color fading is expected to be non-decreasing as a function of time and stabilize eventually. These properties can be expressed in terms of the partial derivatives of the functions. We propose a spatio-temporal model that takes this information into account by jointly modeling the spatio-temporal process and its derivative process using Gaussian processes (GPs). We fitted the proposed model to MFS data collected from the surface of prehistoric rock art paintings. A multivariate covariance function in a GP allows modeling trichromatic image color variables jointly with spatial distances and time points variables as inputs to evaluate the covariance structure of the data. We demonstrated that the colorimetric variables are useful for predicting the color fading time-series for new unobserved spatial locations. Furthermore, constraining the model using derivative sign observations for monotonicity was shown to be beneficial in terms of both predictive performance and application-specific interpretability., Comment: arXiv admin note: substantial text overlap with arXiv:1910.12575

For nonlinear supervised learning models, assessing the importance of predictor variables or their interactions is not straightforward because it can vary in the domain of the variables. Importance can be assessed locally with sensitivity analysis using general methods that rely on the model's predictions or their derivatives. In this work, we extend derivative based sensitivity analysis to a Bayesian setting by differentiating the R\'enyi divergence of a model's predictive distribution. By utilising the predictive distribution instead of a point prediction, the model uncertainty is taken into account in a principled way. Our empirical results on simulated and real data sets demonstrate accurate and reliable identification of important variables and interaction effects compared to alternative methods.

As the Internet of Things (IoT) emerges over the next decade, developing secure communication for IoT devices is of paramount importance. Achieving end-to-end encryption for large-scale IoT systems, like smart buildings or smart cities, is challenging because multiple principals typically interact indirectly via intermediaries, meaning that the recipient of a message is not known in advance. This paper proposes JEDI (Joining Encryption and Delegation for IoT), a many-to-many end-to-end encryption protocol for IoT. JEDI encrypts and signs messages end-to-end, while conforming to the decoupled communication model typical of IoT systems. JEDI's keys support expiry and fine-grained access to data, common in IoT. Furthermore, JEDI allows principals to delegate their keys, restricted in expiry or scope, to other principals, thereby granting access to data and managing access control in a scalable, distributed way. Through careful protocol design and implementation, JEDI can run across the spectrum of IoT devices, including ultra low-power deeply embedded sensors severely constrained in CPU, memory, and energy consumption. We apply JEDI to an existing IoT messaging system and demonstrate that its overhead is modest., Comment: Extended version of a paper accepted at USENIX Security 2019

Model inference, such as model comparison, model checking, and model selection, is an important part of model development. Leave-one-out cross-validation (LOO) is a general approach for assessing the generalizability of a model, but unfortunately, LOO does not scale well to large datasets. We propose a combination of using approximate inference techniques and probability-proportional-to-size-sampling (PPS) for fast LOO model evaluation for large datasets. We provide both theoretical and empirical results showing good properties for large data., Comment: Accepted to ICML 2019. This version is the submitted paper

A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and nonnegative matrix factorisation can be jointly formulated as a spectral mixture Gaussian process model with nonstationary priors over the amplitude variance parameters. Further, we formulate this nonlinear model's state space representation, making it amenable to infinite-horizon Gaussian process regression with approximate inference via expectation propagation, which scales linearly in the number of time steps and quadratically in the state dimensionality. By doing so, we are able to process audio signals with hundreds of thousands of data points. We demonstrate, on various tasks with empirical data, how this inference scheme outperforms more standard techniques that rely on extended Kalman filtering., Comment: Accepted to the Thirty-sixth International Conference on Machine Learning (ICML) 2019

In audio signal processing, probabilistic time-frequency models have many benefits over their non-probabilistic counterparts. They adapt to the incoming signal, quantify uncertainty, and measure correlation between the signal's amplitude and phase information, making time domain resynthesis straightforward. However, these models are still not widely used since they come at a high computational cost, and because they are formulated in such a way that it can be difficult to interpret all the modelling assumptions. By showing their equivalence to Spectral Mixture Gaussian processes, we illuminate the underlying model assumptions and provide a general framework for constructing more complex models that better approximate real-world signals. Our interpretation makes it intuitive to inspect, compare, and alter the models since all prior knowledge is encoded in the Gaussian process kernel functions. We utilise a state space representation to perform efficient inference via Kalman smoothing, and we demonstrate how our interpretation allows for efficient parameter learning in the frequency domain., Comment: Accepted to International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2019

Low-power and lossy networks (LLNs) enable diverse applications integrating many resource-constrained embedded devices, often requiring interconnectivity with existing TCP/IP networks as part of the Internet of Things. But TCP has received little attention in LLNs due to concerns about its overhead and performance, leading to LLN-specific protocols that require specialized gateways for interoperability. We present a systematic study of a well-designed TCP stack in IEEE 802.15.4-based LLNs, based on the TCP protocol logic in FreeBSD. Through careful implementation and extensive experiments, we show that modern low-power sensor platforms are capable of running full-scale TCP and that TCP, counter to common belief, performs well despite the lossy nature of LLNs. By carefully studying the interaction between the transport and link layers, we identify subtle but important modifications to both, achieving TCP goodput within 25% of an upper bound (5-40x higher than prior results) and low-power operation commensurate to CoAP in a practical LLN application scenario. This suggests that a TCP-based transport layer, seamlessly interoperable with existing TCP/IP networks, is viable and performant in LLNs., Comment: 22 pages; Accepted at NSDI 2020; Updated Table 6

Inverse dynamic analysis using musculoskeletal modeling is a powerful tool, which is utilized in a range of applications to estimate forces in ligaments, muscles, and joints, non-invasively. To date, the conventional input used in this analysis is derived from optical motion capture (OMC) and force plate (FP) systems, which restrict the application of musculoskeletal models to gait laboratories. To address this problem, we propose a musculoskeletal model, capable of estimating the internal forces based solely on inertial motion capture (IMC) input and a ground reaction force and moment (GRF&M) prediction method. We validated the joint angle and kinetic estimates of the lower limbs against an equally constructed musculoskeletal model driven by OMC and FP system. The sagittal plane joint angles of ankle, knee, and hip presented excellent Pearson correlations (\rho = 0.95, 0.99, and 0.99, respectively) and root-mean-squared differences (RMSD) of 4.1 $\pm$ 1.3$\circ$, 4.4 $\pm$ 2.0$\circ$, and 5.7 $\pm$ 2.1$\circ$, respectively. The GRF&M predicted using IMC input were found to have excellent correlations for three components (vertical:\rho = 0.97, RMSD=9.3 $\pm$ 3.0 %BW, anteroposterior: \rho = 0.91, RMSD=5.5 $\pm$ 1.2 %BW, sagittal: \rho = 0.91, RMSD=1.6 $\pm$ 0.6 %BW*BH), and strong correlations for mediolateral (\rho = 0.80, RMSD=2.1 $\pm$ 0.6%BW ) and transverse (\rho = 0.82, RMSD=0.2 $\pm$ 0.1 %BW*BH). The proposed IMC-based method removes the complexity and space-restrictions of OMC and FP systems and could enable applications of musculoskeletal models in either monitoring patients during their daily lives or in wider clinical practice., Comment: 19 pages, 4 figures, 3 tables

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined relevance has several drawbacks that prevent the selection of optimal input variables in terms of predictive performance. To improve on this, we propose two novel variable selection methods for Gaussian process models that utilize the predictions of a full model in the vicinity of the training points and thereby rank the variables based on their predictive relevance. Our empirical results on synthetic and real world data sets demonstrate improved variable selection compared to automatic relevance determination in terms of variability and predictive performance., Comment: Minor changes to text, additions to supplementary material

EEG based brain state decoding has numerous applications. State of the art decoding is based on processing of the multivariate sensor space signal, however evidence is mounting that EEG source reconstruction can assist decoding. EEG source imaging leads to high-dimensional representations and rather strong a priori information must be invoked. Recent work by Edelman et al. (2016) has demonstrated that introduction of a spatially focal source space representation can improve decoding of motor imagery. In this work we explore the generality of Edelman et al. hypothesis by considering decoding of face recognition. This task concerns the differentiation of brain responses to images of faces and scrambled faces and poses a rather difficult decoding problem at the single trial level. We implement the pipeline using spatially focused features and show that this approach is challenged and source imaging does not lead to an improved decoding. We design a distributed pipeline in which the classifier has access to brain wide features which in turn does lead to a 15% reduction in the error rate using source space features. Hence, our work presents supporting evidence for the hypothesis that source imaging improves decoding.

Bayesian optimization (BO) is a global optimization strategy designed to find the minimum of an expensive black-box function, typically defined on a compact subset of $\mathcal{R}^d$, by using a Gaussian process (GP) as a surrogate model for the objective. Although currently available acquisition functions address this goal with different degree of success, an over-exploration effect of the contour of the search space is typically observed. However, in problems like the configuration of machine learning algorithms, the function domain is conservatively large and with a high probability the global minimum does not sit on the boundary of the domain. We propose a method to incorporate this knowledge into the search process by adding virtual derivative observations in the \gp at the boundary of the search space. We use the properties of GPs to impose conditions on the partial derivatives of the objective. The method is applicable with any acquisition function, it is easy to use and consistently reduces the number of evaluations required to optimize the objective irrespective of the acquisition used. We illustrate the benefits of our approach in an extensive experimental comparison., Comment: 6 pages, 7 figures

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets., Comment: 58 pages, 17 figures

We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (EEG) source localization problem. We propose a probabilistic model that takes this structure into account by generalizing the structured spike and slab prior and the associated Expectation Propagation inference scheme. Based on numerical experiments, we demonstrate the viability of the model and the approximate inference scheme., Comment: 6 pages, 6 figures, accepted for presentation at SPARS 2015

The EMCCD is a type of CCD that delivers fast readout times and negligible readout noise, making it an ideal detector for high frame rate applications which improve resolution, like lucky imaging or shift-and-add. This improvement in resolution can potentially improve the photometry of faint stars in extremely crowded fields significantly by alleviating crowding. Alleviating crowding is a prerequisite for observing gravitational microlensing in main sequence stars towards the galactic bulge. However, the photometric stability of this device has not been assessed. The EMCCD has sources of noise not found in conventional CCDs, and new methods for handling these must be developed. We aim to investigate how the normal photometric reduction steps from conventional CCDs should be adjusted to be applicable to EMCCD data. One complication is that a bias frame cannot be obtained conventionally, as the output from an EMCCD is not normally distributed. Also, the readout process generates spurious charges in any CCD, but in EMCCD data, these charges are visible as opposed to the conventional CCD. Furthermore we aim to eliminate the photon waste associated with lucky imaging by combining this method with shift-and-add. A simple probabilistic model for the dark output of an EMCCD is developed. Fitting this model with the expectation-maximization algorithm allows us to estimate the bias, readout noise, amplification, and spurious charge rate per pixel and thus correct for these phenomena. To investigate the stability of the photometry, corrected frames of a crowded field are reduced with a PSF fitting photometry package, where a lucky image is used as a reference. We find that it is possible to develop an algorithm that elegantly reduces EMCCD data and produces stable photometry at the 1% level in an extremely crowded field., Comment: Submitted to Astronomy and Astrophysics

The EMCCD is a CCD type that delivers fast readout and negligible detector noise, making it an ideal detector for high frame rate applications. Because of the very low detector noise, this detector can potentially count single photons. Considering that an EMCCD has a limited dynamical range and negligible detector noise, one would typically apply an EMCCD in such a way that multiple images of the same object are available, for instance, in so called lucky imaging. The problem of counting photons can then conveniently be viewed as statistical inference of flux or photon rates, based on a stack of images. A simple probabilistic model for the output of an EMCCD is developed. Based on this model and the prior knowledge that photons are Poisson distributed, we derive two methods for estimating the most probable flux per pixel, one based on thresholding, and another based on full Bayesian inference. We find that it is indeed possible to derive such expressions, and tests of these methods show that estimating fluxes with only shot noise is possible, up to fluxes of about one photon per pixel per readout., Comment: Fixed a few typos compared to the published version

OCTOCAM is a multi-channel imager and spectrograph that has been proposed for the 10.4m GTC telescope. It will use dichroics to split the incoming light to produce simultaneous observations in 8 different bands, ranging from the ultraviolet to the near-infrared. The imaging mode will have a field of view of 2' x 2' in u, g, r, i, z, J, H and Ks bands, whereas the long-slit spectroscopic mode will cover the complete range from 4,000 to 23,000 {\AA} with a resolution of 700 - 1,700 (depending on the arm and slit width). An additional mode, using an image slicer, will deliver a spectral resolution of over 3,000. As a further feature, it will use state of the art detectors to reach high readout speeds of the order of tens of milliseconds. In this way, OCTOCAM will be occupying a region of the time resolution - spectral resolution - spectral coverage diagram that is not covered by a single instrument in any other observatory, with an exceptional sensitivity., Comment: 11 pages, 10 figures, SPIE 2010 Astronomical Instrumentation

Over the past five years evidence has mounted that long-duration (> 2 s) gamma-ray bursts (GRBs)--the most brilliant of all astronomical explosions--signal the collapse of massive stars in our Universe. This evidence was originally based on the probable association of one unusual GRB with a supernova, but now includes the association of GRBs with regions of massive star formation in distant galaxies, the appearance of supernova-like 'bumps' in the optical afterglow light curves of several bursts and lines of freshly synthesized elements in the spectra of a few X-ray afterglows. These observations support, but do not yet conclusively demonstrate, the idea that long-duration GRBs are associated with the deaths of massive stars, presumably arising from core collapse. Here we report evidence that a very energetic supernova (a hypernova) was temporally and spatially coincident with a GRB at redshift z = 0.1685. The timing of the supernova indicates that it exploded within a few days of the GRB, strongly suggesting that core-collapse events can give rise to GRBs, thereby favouring the 'collapsar' model., Comment: 19 pages, 3 figures

We report the identification of the optical afterglow of GRB 980613 in R- and I-band images obtained between 16 and 48 hours after the gamma-ray burst. Early near-infrared (NIR) H and K' observations are also reported. The afterglow was optically faint (R ~ 23) at discovery but did not exhibit an unusually rapid decay (power-law decay slope alpha < 1.8 at 2 sigma). The optical/NIR spectral index (beta_RH < 1.1) was consistent with the optical-to-X-ray spectral index (beta_RX ~ 0.6), indicating a maximal reddening of the afterglow of ~0.45 mag in R. Hence the dimness of the optical afterglow was mainly due to the fairly flat spectral shape rather than internal reddening in the host galaxy. We also present late-time HST/STIS images of the field in which GRB 980613 occurred, obtained 799 days after the burst. These images show that GRB 980613 was located close to a very compact, blue V = 26.1 object inside a complex region consisting of star-forming knots and/or interacting galaxy fragments. Therefore, GRB 980613 constitutes a strong case for the association of cosmological gamma-ray bursts with star-forming regions., Comment: 22 pages, 5 figures, ApJ, in press

We present optical lightcurves of the gravitationally lensed components A (=A1+A2+A3) and B of the quadruple quasar RX J0911.4+0551 (z = 2.80). The observations were primarily obtained at the Nordic Optical Telescope between 1997 March and 2001 April and consist of 74 I-band data points for each component. The data allow the measurement of a time delay of 146 +- 8 days (2 sigma) between A and B, with B as the leading component. This value is significantly shorter than that predicted from simple models and indicates a very large external shear. Mass models including the main lens galaxy and the surrounding massive cluster of galaxies at z = 0.77, responsible for the external shear, yield H_0 = 71 +- 4 (random, 2 sigma) +- 8 (systematic) km/s/Mpc. The systematic model uncertainty is governed by the surface-mass density (convergence) at the location of the multiple images., Comment: 12 pages, 3 figures, ApJL, in press (June 20, 2002)

We report on optical observations on GRB 000210 obtained with the 2.56-m Nordic Optical Telescope and the 1.54-m Danish Telescope starting 12.4 hours after the gamma-ray event. The content of the X-ray error box determined by the Chandra satellite is discussed., Comment: 3 pages, 1 postscript figure. To appear in the proceedings of the October 2000 Rome Workshop on ``Gamma-Ray Bursts in the Afterglow Era''

We present deep CCD photometry of the globular cluster M13 (NGC 6205) in the Stromgren uvby-Beta system, and determine a foreground reddening of E(b-y)= 0.015mag. From a fit to the main-sequence of metal-poor subdwarfs with Hipparcos parallaxes, we derive (m-M)_0=14.38 +- 0.10 which implies an age near 12 Gyr assuming [Fe/H]=-1.61 and [Alpha/Fe]=0.3. The distance independent ((b-y)_0, c_0) diagram indicates that M13 and metal-poor field subdwarfs of similar metallicity must be coeval to within +-1 Gyr. In addition, we find that, at any given (b-y)_0 color, there is a large spread in the c_0 index for M13 red-giant branch (RGB) stars. We suspect that this scatter, which extends at least as faint as the base of the RGB, is most likely due to star-to-star variations in the atmospheric abundances of the CNO elements. We also note the existence of what appears to be two separate stellar populations on the HB of M13. Among other possibilities, it could arise as the result of differences in the extent to which deep mixing occurs in the precursor red giants., Comment: 14 pages, including two encapsulated postscript figures. Accepted for publication in ApJL, Uses aasms4.sty