61 research outputs found
Nonparametric estimation of mark's distribution of an exponential Shot-noise process
In this paper, we consider a nonlinear inverse problem occurring in nuclear
science. Gamma rays randomly hit a semiconductor detector which produces an
impulse response of electric current. Because the sampling period of the
measured current is larger than the mean inter arrival time of photons, the
impulse responses associated to different gamma rays can overlap: this
phenomenon is known as pileup. In this work, it is assumed that the impulse
response is an exponentially decaying function. We propose a novel method to
infer the distribution of gamma photon energies from the indirect measurements
obtained from the detector. This technique is based on a formula linking the
characteristic function of the photon density to a function involving the
characteristic function and its derivative of the observations. We establish
that our estimator converges to the mark density in uniform norm at a
logarithmic rate. A limited Monte-Carlo experiment is provided to support our
findings.Comment: Electronic Journal of Statistics, Institute of Mathematical
Statistics and Bernoulli Society, 201
Streaming Binary Sketching based on Subspace Tracking and Diagonal Uniformization
In this paper, we address the problem of learning compact
similarity-preserving embeddings for massive high-dimensional streams of data
in order to perform efficient similarity search. We present a new online method
for computing binary compressed representations -sketches- of high-dimensional
real feature vectors. Given an expected code length and high-dimensional
input data points, our algorithm provides a -bits binary code for preserving
the distance between the points from the original high-dimensional space. Our
algorithm does not require neither the storage of the whole dataset nor a
chunk, thus it is fully adaptable to the streaming setting. It also provides
low time complexity and convergence guarantees. We demonstrate the quality of
our binary sketches through experiments on real data for the nearest neighbors
search task in the online setting
Non-negative Independent Component Analysis Algorithm Based on 2D Givens Rotations and a Newton Optimization
ISBN 978-3-642-15994-7, SoftcoverInternational audienceIn this paper, we consider the Independent Component Analysis problem when the hidden sources are non-negative (Non-negative ICA). This problem is formulated as a non-linear cost function optimization over the special orthogonal matrix group SO(n). Using Givens rotations and Newton optimization, we developed an effective axis pair rotation method for Non-negative ICA. The performance of the proposed method is compared to those designed by Plumbley and simulations on synthetic data show the efficiency of the proposed algorithm
Geometrical Method Using Simplicial Cones for Overdetermined Nonnegative Blind Source Separation: Application to Real PET Images
International audienceThis paper presents a geometrical method for solving the overdetermined Nonnegative Blind Source Separation (N-BSS) problem. Considering each column of the mixed data as a point in the data space, we develop a Simplicial Cone Shrinking Algorithm for Unmixing Nonnegative Sources (SCSA-UNS). The proposed method estimates the mixing matrix and the sources by fitting a simplicial cone to the scatter plot of the mixed data. It requires weak assumption on the sources distribution, in particular the independence of the different sources is not necessary. Simulations on synthetic data show that SCSA-UNS outperforms other existing geometrical methods in noiseless case. Experiment on real Dynamic Positon Emission Tomography (PET) images illustrates the efficiency of the proposed method
Nonparametric inference of photon energy distribution from indirect measurements
International audienceWe consider a density estimation problem arising in nuclear physics. Gamma photons are impinging on a semiconductor detector, producing pulses of current. The integral of this pulse is equal to the total amount of charge created by the photon in the detector, which is linearly related to the photon energy. Because the inter-arrival of photons can be shorter than the charge collection time, pulses corresponding to different photons may overlap leading to a phenomenon known as pileup. The distortions on the photon energy spectrum estimate due to pileup become worse when the photon rate increases, making pileup correction techniques a must for high counting rate experiments. In this paper, we present a novel technique to correct pileup, which extends a method introduced in \cite{hall:park:2004} for the estimation of the service time from the busy period in M/G/ models. It is based on a novel formula linking the joint distribution of the energy and duration of the cluster of pulses and the distribution of the energy of the photons. We then assess the performance of this estimator by providing an expression of its integrated square error. A Monte-Carlo experiment is presented to illustrate on practical examples the benefits of the pileup correction
xDAWN algorithm to enhance evoked potentials: application to brain-computer interface.
International audienceA brain-computer interface (BCI) is a communication system that allows to control a computer or any other device thanks to the brain activity. The BCI described in this paper is based on the P300 speller BCI paradigm introduced by Farwell and Donchin . An unsupervised algorithm is proposed to enhance P300 evoked potentials by estimating spatial filters; the raw EEG signals are then projected into the estimated signal subspace. Data recorded on three subjects were used to evaluate the proposed method. The results, which are presented using a Bayesian linear discriminant analysis classifier , show that the proposed method is efficient and accurate
Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Space
This paper seeks to solve Multi-Source Domain Adaptation (MSDA), which aims
to mitigate data distribution shifts when transferring knowledge from multiple
labeled source domains to an unlabeled target domain. We propose a novel MSDA
framework based on dictionary learning and optimal transport. We interpret each
domain in MSDA as an empirical distribution. As such, we express each domain as
a Wasserstein barycenter of dictionary atoms, which are empirical
distributions. We propose a novel algorithm, DaDiL, for learning via
mini-batches: (i) atom distributions; (ii) a matrix of barycentric coordinates.
Based on our dictionary, we propose two novel methods for MSDA: DaDil-R, based
on the reconstruction of labeled samples in the target domain, and DaDiL-E,
based on the ensembling of classifiers learned on atom distributions. We
evaluate our methods in 3 benchmarks: Caltech-Office, Office 31, and CRWU,
where we improved previous state-of-the-art by 3.15%, 2.29%, and 7.71% in
classification performance. Finally, we show that interpolations in the
Wasserstein hull of learned atoms provide data that can generalize to the
target domain.Comment: 13 pages,8 figures,Accepted as a conference paper at the 26th
European Conference on Artificial Intelligenc
Regularized Gradient Algorithm for Non-Negative Independent Component Analysis
International audienceIndependent Component Analysis (ICA) is a well-known technique for solving blind source separation (BSS) problem. However "classical" ICA algorithms seem not suited for non-negative sources. This paper proposes a gradient descent approach for solving the Non- Negative Independent Component Analysis problem (NNICA). NNICA original separation criterion contains the discontinuous sign function whose minimization may lead to ill convergence (local minima) especially for sparse sources. Replacing the discontinuous function by a continuous one tanh, we propose a more accurate regularized Gradient algorithm called "Exact" Regularized Gradient (ERG) for NNICA. Experiments on synthetic data with different sparsity degrees illustrate the efficiency of the proposed method and a comparison shows that the proposed ERG outperforms existing methods
Multi-Source Domain Adaptation meets Dataset Distillation through Dataset Dictionary Learning
In this paper, we consider the intersection of two problems in machine
learning: Multi-Source Domain Adaptation (MSDA) and Dataset Distillation (DD).
On the one hand, the first considers adapting multiple heterogeneous labeled
source domains to an unlabeled target domain. On the other hand, the second
attacks the problem of synthesizing a small summary containing all the
information about the datasets. We thus consider a new problem called MSDA-DD.
To solve it, we adapt previous works in the MSDA literature, such as
Wasserstein Barycenter Transport and Dataset Dictionary Learning, as well as DD
method Distribution Matching. We thoroughly experiment with this novel problem
on four benchmarks (Caltech-Office 10, Tennessee-Eastman Process, Continuous
Stirred Tank Reactor, and Case Western Reserve University), where we show that,
even with as little as 1 sample per class, one achieves state-of-the-art
adaptation performance.Comment: 7 pages,4 figure
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