697 research outputs found
Extended Object Tracking: Introduction, Overview and Applications
This article provides an elaborate overview of current research in extended
object tracking. We provide a clear definition of the extended object tracking
problem and discuss its delimitation to other types of object tracking. Next,
different aspects of extended object modelling are extensively discussed.
Subsequently, we give a tutorial introduction to two basic and well used
extended object tracking approaches - the random matrix approach and the Kalman
filter-based approach for star-convex shapes. The next part treats the tracking
of multiple extended objects and elaborates how the large number of feasible
association hypotheses can be tackled using both Random Finite Set (RFS) and
Non-RFS multi-object trackers. The article concludes with a summary of current
applications, where four example applications involving camera, X-band radar,
light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are
highlighted.Comment: 30 pages, 19 figure
Deep Gaussian Processes
In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a
deep belief network based on Gaussian process mappings. The data is modeled as
the output of a multivariate GP. The inputs to that Gaussian process are then
governed by another GP. A single layer model is equivalent to a standard GP or
the GP latent variable model (GP-LVM). We perform inference in the model by
approximate variational marginalization. This results in a strict lower bound
on the marginal likelihood of the model which we use for model selection
(number of layers and nodes per layer). Deep belief networks are typically
applied to relatively large data sets using stochastic gradient descent for
optimization. Our fully Bayesian treatment allows for the application of deep
models even when data is scarce. Model selection by our variational bound shows
that a five layer hierarchy is justified even when modelling a digit data set
containing only 150 examples.Comment: 9 pages, 8 figures. Appearing in Proceedings of the 16th
International Conference on Artificial Intelligence and Statistics (AISTATS)
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Collaborative sparse regression using spatially correlated supports - Application to hyperspectral unmixing
This paper presents a new Bayesian collaborative sparse regression method for
linear unmixing of hyperspectral images. Our contribution is twofold; first, we
propose a new Bayesian model for structured sparse regression in which the
supports of the sparse abundance vectors are a priori spatially correlated
across pixels (i.e., materials are spatially organised rather than randomly
distributed at a pixel level). This prior information is encoded in the model
through a truncated multivariate Ising Markov random field, which also takes
into consideration the facts that pixels cannot be empty (i.e, there is at
least one material present in each pixel), and that different materials may
exhibit different degrees of spatial regularity. Secondly, we propose an
advanced Markov chain Monte Carlo algorithm to estimate the posterior
probabilities that materials are present or absent in each pixel, and,
conditionally to the maximum marginal a posteriori configuration of the
support, compute the MMSE estimates of the abundance vectors. A remarkable
property of this algorithm is that it self-adjusts the values of the parameters
of the Markov random field, thus relieving practitioners from setting
regularisation parameters by cross-validation. The performance of the proposed
methodology is finally demonstrated through a series of experiments with
synthetic and real data and comparisons with other algorithms from the
literature
Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk
The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed
Scalable approximate inference methods for Bayesian deep learning
This thesis proposes multiple methods for approximate inference in deep Bayesian neural networks split across three parts.
The first part develops a scalable Laplace approximation based on a block- diagonal Kronecker factored approximation of the Hessian. This approximation accounts for parameter correlations – overcoming the overly restrictive independence assumption of diagonal methods – while avoiding the quadratic scaling in the num- ber of parameters of the full Laplace approximation. The chapter further extends the method to online learning where datasets are observed one at a time. As the experiments demonstrate, modelling correlations between the parameters leads to improved performance over the diagonal approximation in uncertainty estimation and continual learning, in particular in the latter setting the improvements can be substantial.
The second part explores two parameter-efficient approaches for variational inference in neural networks, one based on factorised binary distributions over the weights, one extending ideas from sparse Gaussian processes to neural network weight matrices. The former encounters similar underfitting issues as mean-field Gaussian approaches, which can be alleviated by a MAP-style method in a hierarchi- cal model. The latter, based on an extension of Matheron’s rule to matrix normal distributions, achieves comparable uncertainty estimation performance to ensembles with the accuracy of a deterministic network while using only 25% of the number of parameters of a single ResNet-50.
The third part introduces TyXe, a probabilistic programming library built on top of Pyro to facilitate turning PyTorch neural networks into Bayesian ones. In contrast to existing frameworks, TyXe avoids introducing a layer abstraction, allowing it to support arbitrary architectures. This is demonstrated in a range of applications, from image classification with torchvision ResNets over node labelling with DGL graph neural networks to incorporating uncertainty into neural radiance fields with PyTorch3d
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