20,759 research outputs found
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Lightweight Probabilistic Deep Networks
Even though probabilistic treatments of neural networks have a long history,
they have not found widespread use in practice. Sampling approaches are often
too slow already for simple networks. The size of the inputs and the depth of
typical CNN architectures in computer vision only compound this problem.
Uncertainty in neural networks has thus been largely ignored in practice,
despite the fact that it may provide important information about the
reliability of predictions and the inner workings of the network. In this
paper, we introduce two lightweight approaches to making supervised learning
with probabilistic deep networks practical: First, we suggest probabilistic
output layers for classification and regression that require only minimal
changes to existing networks. Second, we employ assumed density filtering and
show that activation uncertainties can be propagated in a practical fashion
through the entire network, again with minor changes. Both probabilistic
networks retain the predictive power of the deterministic counterpart, but
yield uncertainties that correlate well with the empirical error induced by
their predictions. Moreover, the robustness to adversarial examples is
significantly increased.Comment: To appear at CVPR 201
Hybrid modeling, HMM/NN architectures, and protein applications
We describe a hybrid modeling approach where the parameters of a model are calculated and modulated by another model, typically a neural network (NN), to avoid both overfitting and underfitting. We develop the approach for the case of Hidden Markov Models (HMMs), by deriving a class of hybrid HMM/NN architectures. These architectures can be trained with unified algorithms that blend HMM dynamic programming with NN backpropagation. In the case of complex data, mixtures of HMMs or modulated HMMs must be used. NNs can then be applied both to the parameters of each single HMM, and to the switching or modulation of the models, as a function of input or context. Hybrid HMM/NN architectures provide a flexible NN parameterization for the control of model structure and complexity. At the same time, they can capture distributions that, in practice, are inaccessible to single HMMs. The HMM/NN hybrid approach is tested, in its simplest form, by constructing a model of the immunoglobulin protein family. A hybrid model is trained, and a multiple alignment derived, with less than a fourth of the number of parameters used with previous single HMMs
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