arXiv subjects

Thomas B. Schön

Publications and source records attributed to Thomas B. Schön.

At least 91 records · Page 5Linked to original sources

arXiv2019

Deep Convolutional Networks in System Identification

Recent developments within deep learning are relevant for nonlinear system identification problems. In this paper, we establish connections between the deep learning and the system identification communities. It has recently been shown that convolutional architectures are at least as capable as recurrent architectures when it comes to sequence modeling tasks. Inspired by these results we explore the explicit relationships between the recently proposed temporal convolutional network (TCN) and two classic system identification model structures; Volterra series and block-oriented models. We end the paper with an experimental study where we provide results on two real-world problems, the well-known Silverbox dataset and a newer dataset originating from ground vibration experiments on an F-16 fighter aircraft.

eess.SY↗

arXiv2019

Reliable Semi-Supervised Learning when Labels are Missing at Random

Semi-supervised learning methods are motivated by the availability of large datasets with unlabeled features in addition to labeled data. Unlabeled data is, however, not guaranteed to improve classification performance and has in fact been reported to impair the performance in certain cases. A fundamental source of error arises from restrictive assumptions about the unlabeled features, which result in unreliable classifiers that underestimate their prediction error probabilities. In this paper, we develop a semi-supervised learning approach that relaxes such assumptions and is capable of providing classifiers that reliably quantify the label uncertainty. The approach is applicable using any generative model with a supervised learning algorithm. We illustrate the approach using both handwritten digit and cloth classification data where the labels are missing at random.

stat.ML↗

arXiv2019

A Fast and Robust Algorithm for Orientation Estimation using Inertial Sensors

We present a novel algorithm for online, real-time orientation estimation. Our algorithm integrates gyroscope data and corrects the resulting orientation estimate for integration drift using accelerometer and magnetometer data. This correction is computed, at each time instance, using a single gradient descent step with fixed step length. This fixed step length results in robustness against model errors, e.g. caused by large accelerations or by short-term magnetic field disturbances, which we numerically illustrate using Monte Carlo simulations. Our algorithm estimates a three-dimensional update to the orientation rather than the entire orientation itself. This reduces the computational complexity by approximately 1/3 with respect to the state of the art. It also improves the quality of the resulting estimates, specifically when the orientation corrections are large. We illustrate the efficacy of the algorithm using experimental data.

eess.SP↗

arXiv2019

Deep kernel learning for integral measurements

Deep kernel learning refers to a Gaussian process that incorporates neural networks to improve the modelling of complex functions. We present a method that makes this approach feasible for problems where the data consists of line integral measurements of the target function. The performance is illustrated on computed tomography reconstruction examples.

stat.ML↗

arXiv2019

Probabilistic approach to limited-data computed tomography reconstruction

In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from measured data. In contrast to other established methods, this comes with the advantage of not requiring any manual parameter tuning, which usually arises in classical regularization strategies. Our method uses a basis function expansion technique for the Gaussian process which significantly reduces the computational complexity and avoids the need for numerical integration. The approach also allows for reformulation of come classical regularization methods as Laplacian and Tikhonov regularization as Gaussian process regression, and hence provides an efficient algorithm and principled means for their parameter tuning. Results from simulated and real data indicate that this approach is less sensitive to streak artifacts as compared to the commonly used method of filtered backprojection.

cs.CV↗

arXiv2019

Robust exploration in linear quadratic reinforcement learning

This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we minimize the worst-case cost, accounting for system uncertainty given the observed data. The method balances exploitation and exploration, exciting the system in such a way so as to reduce uncertainty in the model parameters to which the worst-case cost is most sensitive. Numerical simulations and application to a hardware-in-the-loop servo-mechanism demonstrate the approach, with appreciable performance and robustness gains over alternative methods observed in both.

math.OC↗

arXiv2019

Inferring Heterogeneous Causal Effects in Presence of Spatial Confounding

We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for by estimating a nuisance function. Here we develop a method that eliminates the nuisance function, while mitigating the resulting errors-in-variables. The result is a robust and accurate inference method for spatially varying heterogeneous causal effects. The properties of the method are demonstrated on synthetic as well as real data from Germany and the US.

stat.ME↗

arXiv2019

Data Consistency Approach to Model Validation

In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The contribution in this paper is a general criterion to evaluate the consistency of a set of statistical models with respect to observed data. This is achieved by automatically gauging the models' ability to generate data that is similar to the observed data. Importantly, the criterion follows from the model class itself and is therefore directly applicable to a broad range of inference problems with varying data types, ranging from independent univariate data to high-dimensional time-series. The proposed data consistency criterion is illustrated, evaluated and compared to several well-established methods using three synthetic and two real data sets.

stat.ME↗

arXiv2019

Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.

stat.CO↗

arXiv2019

Nonlinear input design as optimal control of a Hamiltonian system

We propose an input design method for a general class of parametric probabilistic models, including nonlinear dynamical systems with process noise. The goal of the procedure is to select inputs such that the parameter posterior distribution concentrates about the true value of the parameters; however, exact computation of the posterior is intractable. By representing (samples from) the posterior as trajectories from a certain Hamiltonian system, we transform the input design task into an optimal control problem. The method is illustrated via numerical examples, including MRI pulse sequence design.

eess.SY↗

arXiv2019

Conditionally Independent Multiresolution Gaussian Processes

The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full independence across resolutions. This assumption simplifies the inference, but it underestimates the uncertainties in transitioning from one resolution to another. This in turn results in models which are prone to overfitting in the sense of excessive sensitivity to the chosen resolution, and predictions which are non-smooth at the boundaries. Our contribution is a new construction which instead assumes conditional independence among GPs across resolutions. We show that relaxing the full independence assumption enables robustness against overfitting, and that it delivers predictions that are smooth at the boundaries. Our new model is compared against current state of the art on 2 synthetic and 9 real-world datasets. In most cases, our new conditionally independent construction performed favorably when compared against models based on the full independence assumption. In particular, it exhibits little to no signs of overfitting.

stat.ML↗

arXiv2019

Evaluating model calibration in classification

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their ability to represent uncertainty about predictions. In safety-critical applications, it is pivotal for a model to possess an adequate sense of uncertainty, which for probabilistic classifiers translates into outputting probability distributions that are consistent with the empirical frequencies observed from realized outcomes. A classifier with such a property is called calibrated. In this work, we develop a general theoretical calibration evaluation framework grounded in probability theory, and point out subtleties present in model calibration evaluation that lead to refined interpretations of existing evaluation techniques. Lastly, we propose new ways to quantify and visualize miscalibration in probabilistic classification, including novel multidimensional reliability diagrams.

cs.LG↗

arXiv2019

Automatic Diagnosis of Short-Duration 12-Lead ECG using a Deep Convolutional Network

We present a model for predicting electrocardiogram (ECG) abnormalities in short-duration 12-lead ECG signals which outperformed medical doctors on the 4th year of their cardiology residency. Such exams can provide a full evaluation of heart activity and have not been studied in previous end-to-end machine learning papers. Using the database of a large telehealth network, we built a novel dataset with more than 2 million ECG tracings, orders of magnitude larger than those used in previous studies. Moreover, our dataset is more realistic, as it consist of 12-lead ECGs recorded during standard in-clinics exams. Using this data, we trained a residual neural network with 9 convolutional layers to map 7 to 10 second ECG signals to 6 classes of ECG abnormalities. Future work should extend these results to cover a large range of ECG abnormalities, which could improve the accessibility of this diagnostic tool and avoid wrong diagnosis from medical doctors.

eess.SP↗

arXiv2019

Constructing the Matrix Multilayer Perceptron and its Application to the VAE

Like most learning algorithms, the multilayer perceptrons (MLP) is designed to learn a vector of parameters from data. However, in certain scenarios we are interested in learning structured parameters (predictions) in the form of symmetric positive definite matrices. Here, we introduce a variant of the MLP, referred to as the matrix MLP, that is specialized at learning symmetric positive definite matrices. We also present an application of the model within the context of the variational autoencoder (VAE). Our formulation of the VAE extends the vanilla formulation to the cases where the recognition and the generative networks can be from the parametric family of distributions with dense covariance matrices. Two specific examples are discussed in more detail: the dense covariance Gaussian and its generalization, the power exponential distribution. Our new developments are illustrated using both synthetic and real data.

stat.ML↗

arXiv2018

Optimal controller/observer gains of discounted-cost LQG systems

The linear-quadratic-Gaussian (LQG) control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is known and where it is estimated through an observer. The situation is different when the cost function has an exponential discount factor, also known as a prescribed degree of stability. In this case, the optimal control strategy is only available when the state is known. This paper builds on from that result, deriving an optimal control strategy when working with an estimated state. Expressions for the resulting optimal expected cost are also given.

eess.SY↗

arXiv2018

Probabilistic modelling and reconstruction of strain

This paper deals with modelling and reconstruction of strain fields, relying upon data generated from neutron Bragg-edge measurements. We propose a probabilistic approach in which the strain field is modelled as a Gaussian process, assigned a covariance structure customised by incorporation of the so-called equilibrium constraints. The computational complexity is significantly reduced by utilising an approximation scheme well suited for the problem. We illustrate the method on simulations and real data. The results indicate a high potential and can hopefully inspire the concept of probabilistic modelling to be used within other tomographic applications as well.

physics.data-an↗

arXiv2018

Data-Driven Impulse Response Regularization via Deep Learning

We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical finite-dimensional model structures. Inspired by this development and the success of deep learning we propose a new flexible data-driven model. Our experiments indicate that the new model is capable of exploiting even more of the hidden patterns that are present in the input-output data as compared to the non-parametric models.

eess.SY↗

arXiv2018

Smoothing with Couplings of Conditional Particle Filters

In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and confidence intervals can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly-informative observations, and a realistic Lotka-Volterra model with an intractable transition density.

stat.ME↗