17,787 research outputs found
Times series averaging from a probabilistic interpretation of time-elastic kernel
At the light of regularized dynamic time warping kernels, this paper
reconsider the concept of time elastic centroid (TEC) for a set of time series.
From this perspective, we show first how TEC can easily be addressed as a
preimage problem. Unfortunately this preimage problem is ill-posed, may suffer
from over-fitting especially for long time series and getting a sub-optimal
solution involves heavy computational costs. We then derive two new algorithms
based on a probabilistic interpretation of kernel alignment matrices that
expresses in terms of probabilistic distributions over sets of alignment paths.
The first algorithm is an iterative agglomerative heuristics inspired from the
state of the art DTW barycenter averaging (DBA) algorithm proposed specifically
for the Dynamic Time Warping measure. The second proposed algorithm achieves a
classical averaging of the aligned samples but also implements an averaging of
the time of occurrences of the aligned samples. It exploits a straightforward
progressive agglomerative heuristics. An experimentation that compares for 45
time series datasets classification error rates obtained by first near
neighbors classifiers exploiting a single medoid or centroid estimate to
represent each categories show that: i) centroids based approaches
significantly outperform medoids based approaches, ii) on the considered
experience, the two proposed algorithms outperform the state of the art DBA
algorithm, and iii) the second proposed algorithm that implements an averaging
jointly in the sample space and along the time axes emerges as the most
significantly robust time elastic averaging heuristic with an interesting noise
reduction capability. Index Terms-Time series averaging Time elastic kernel
Dynamic Time Warping Time series clustering and classification
Systematic coarse graining: "Four lessons and a caveat" from nonequilibrium statistical mechanics
With the guidance offered by nonequilibrium statistical thermodynamics,
simulation techniques are elevated from brute-force computer experiments to
systematic tools for extracting complete, redundancy-free and consistent coarse
grained information for dynamic systems. We sketch the role and potential of
Monte Carlo, molecular dynamics and Brownian dynamics simulations in the
thermodynamic approach to coarse graining. A melt of entangled linear
polyethylene molecules serves us as an illustrative example.Comment: 15 pages, 4 figure
The miracle of the Septuagint and the promise of data mining in economics
This paper argues that the sometimes-conflicting results of a modern revisionist literature on data mining in econometrics reflect different approaches to solving the central problem of model uncertainty in a science of non-experimental data. The literature has entered an exciting phase with theoretical development, methodological reflection, considerable technological strides on the computing front and interesting empirical applications providing momentum for this branch of econometrics. The organising principle for this discussion of data mining is a philosophical spectrum that sorts the various econometric traditions according to their epistemological assumptions (about the underlying data-generating-process DGP) starting with nihilism at one end and reaching claims of encompassing the DGP at the other end; call it the DGP-spectrum. In the course of exploring this spectrum the reader will encounter various Bayesian, specific-to-general (S-G) as well general-to-specific (G-S) methods. To set the stage for this exploration the paper starts with a description of data mining, its potential risks and a short section on potential institutional safeguards to these problems.Data mining, model selection, automated model selection, general to specific modelling, extreme bounds analysis, Bayesian model selection
Combining stochastic programming and optimal control to solve multistage stochastic optimization problems
In this contribution we propose an approach to solve a multistage stochastic programming problem which allows us to obtain a time and nodal decomposition of the original problem. This double decomposition is achieved applying a discrete time optimal control formulation to the original stochastic programming problem in arborescent form. Combining the arborescent formulation of the problem with the point of view of the optimal control theory naturally gives as a first result the time decomposability of the optimality conditions, which can be organized according to the terminology and structure of a discrete time optimal control problem into the systems of equation for the state and adjoint variables dynamics and the optimality conditions for the generalized Hamiltonian. Moreover these conditions, due to the arborescent formulation of the stochastic programming problem, further decompose with respect to the nodes in the event tree. The optimal solution is obtained by solving small decomposed subproblems and using a mean valued fixed-point iterative scheme to combine them. To enhance the convergence we suggest an optimization step where the weights are chosen in an optimal way at each iteration.Stochastic programming, discrete time control problem, decomposition methods, iterative scheme
Automated reduction of submillimetre single-dish heterodyne data from the James Clerk Maxwell Telescope using ORAC-DR
With the advent of modern multi-detector heterodyne instruments that can
result in observations generating thousands of spectra per minute it is no
longer feasible to reduce these data as individual spectra. We describe the
automated data reduction procedure used to generate baselined data cubes from
heterodyne data obtained at the James Clerk Maxwell Telescope. The system can
automatically detect baseline regions in spectra and automatically determine
regridding parameters, all without input from a user. Additionally it can
detect and remove spectra suffering from transient interference effects or
anomalous baselines. The pipeline is written as a set of recipes using the
ORAC-DR pipeline environment with the algorithmic code using Starlink software
packages and infrastructure. The algorithms presented here can be applied to
other heterodyne array instruments and have been applied to data from
historical JCMT heterodyne instrumentation.Comment: 18 pages, 13 figures, submitted to Monthly Notices of the Royal
Astronomical Societ
Exact Mean Computation in Dynamic Time Warping Spaces
Dynamic time warping constitutes a major tool for analyzing time series. In
particular, computing a mean series of a given sample of series in dynamic time
warping spaces (by minimizing the Fr\'echet function) is a challenging
computational problem, so far solved by several heuristic and inexact
strategies. We spot some inaccuracies in the literature on exact mean
computation in dynamic time warping spaces. Our contributions comprise an exact
dynamic program computing a mean (useful for benchmarking and evaluating known
heuristics). Based on this dynamic program, we empirically study properties
like uniqueness and length of a mean. Moreover, experimental evaluations reveal
substantial deficits of state-of-the-art heuristics in terms of their output
quality. We also give an exact polynomial-time algorithm for the special case
of binary time series
How single neuron properties shape chaotic dynamics and signal transmission in random neural networks
While most models of randomly connected networks assume nodes with simple
dynamics, nodes in realistic highly connected networks, such as neurons in the
brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the
dynamical properties of nodes (such as single neurons) and recurrent
connections interact to shape the effective dynamics in large randomly
connected networks. A novel dynamical mean-field theory for strongly connected
networks of multi-dimensional rate units shows that the power spectrum of the
network activity in the chaotic phase emerges from a nonlinear sharpening of
the frequency response function of single units. For the case of
two-dimensional rate units with strong adaptation, we find that the network
exhibits a state of "resonant chaos", characterized by robust, narrow-band
stochastic oscillations. The coherence of stochastic oscillations is maximal at
the onset of chaos and their correlation time scales with the adaptation
timescale of single units. Surprisingly, the resonance frequency can be
predicted from the properties of isolated units, even in the presence of
heterogeneity in the adaptation parameters. In the presence of these
internally-generated chaotic fluctuations, the transmission of weak,
low-frequency signals is strongly enhanced by adaptation, whereas signal
transmission is not influenced by adaptation in the non-chaotic regime. Our
theoretical framework can be applied to other mechanisms at the level of single
nodes, such as synaptic filtering, refractoriness or spike synchronization.
These results advance our understanding of the interaction between the dynamics
of single units and recurrent connectivity, which is a fundamental step toward
the description of biologically realistic network models in the brain, or, more
generally, networks of other physical or man-made complex dynamical units
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