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Using formal methods to support testing
Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent
years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing
Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
The widespread use of multi-sensor technology and the emergence of big
datasets has highlighted the limitations of standard flat-view matrix models
and the necessity to move towards more versatile data analysis tools. We show
that higher-order tensors (i.e., multiway arrays) enable such a fundamental
paradigm shift towards models that are essentially polynomial and whose
uniqueness, unlike the matrix methods, is guaranteed under verymild and natural
conditions. Benefiting fromthe power ofmultilinear algebra as theirmathematical
backbone, data analysis techniques using tensor decompositions are shown to
have great flexibility in the choice of constraints that match data properties,
and to find more general latent components in the data than matrix-based
methods. A comprehensive introduction to tensor decompositions is provided from
a signal processing perspective, starting from the algebraic foundations, via
basic Canonical Polyadic and Tucker models, through to advanced cause-effect
and multi-view data analysis schemes. We show that tensor decompositions enable
natural generalizations of some commonly used signal processing paradigms, such
as canonical correlation and subspace techniques, signal separation, linear
regression, feature extraction and classification. We also cover computational
aspects, and point out how ideas from compressed sensing and scientific
computing may be used for addressing the otherwise unmanageable storage and
manipulation problems associated with big datasets. The concepts are supported
by illustrative real world case studies illuminating the benefits of the tensor
framework, as efficient and promising tools for modern signal processing, data
analysis and machine learning applications; these benefits also extend to
vector/matrix data through tensorization. Keywords: ICA, NMF, CPD, Tucker
decomposition, HOSVD, tensor networks, Tensor Train
DeepCare: A Deep Dynamic Memory Model for Predictive Medicine
Personalized predictive medicine necessitates the modeling of patient illness
and care processes, which inherently have long-term temporal dependencies.
Healthcare observations, recorded in electronic medical records, are episodic
and irregular in time. We introduce DeepCare, an end-to-end deep dynamic neural
network that reads medical records, stores previous illness history, infers
current illness states and predicts future medical outcomes. At the data level,
DeepCare represents care episodes as vectors in space, models patient health
state trajectories through explicit memory of historical records. Built on Long
Short-Term Memory (LSTM), DeepCare introduces time parameterizations to handle
irregular timed events by moderating the forgetting and consolidation of memory
cells. DeepCare also incorporates medical interventions that change the course
of illness and shape future medical risk. Moving up to the health state level,
historical and present health states are then aggregated through multiscale
temporal pooling, before passing through a neural network that estimates future
outcomes. We demonstrate the efficacy of DeepCare for disease progression
modeling, intervention recommendation, and future risk prediction. On two
important cohorts with heavy social and economic burden -- diabetes and mental
health -- the results show improved modeling and risk prediction accuracy.Comment: Accepted at JBI under the new name: "Predicting healthcare
trajectories from medical records: A deep learning approach
A detectability criterion and data assimilation for non-linear differential equations
In this paper we propose a new sequential data assimilation method for
non-linear ordinary differential equations with compact state space. The method
is designed so that the Lyapunov exponents of the corresponding estimation
error dynamics are negative, i.e. the estimation error decays exponentially
fast. The latter is shown to be the case for generic regular flow maps if and
only if the observation matrix H satisfies detectability conditions: the rank
of H must be at least as great as the number of nonnegative Lyapunov exponents
of the underlying attractor. Numerical experiments illustrate the exponential
convergence of the method and the sharpness of the theory for the case of
Lorenz96 and Burgers equations with incomplete and noisy observations
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