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--- Timezone: CET
Creation date: 2015-03-01
Creation time: 13-29-07
--- Number of references
13
article
Scholkopf2012
A Kernel Two-Sample Test
Journal of Machine Learning Research
2012
3
13
723−773
We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD). We present two distribution-free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
Research Group Borgwardt
Department Logothetis
http://jmlr.csail.mit.edu/papers/v13/gretton12a.html
arthurAGretton
karstenKBorgwardt
raschMRasch
bsBSchölkopf
smolaASmola
article
RaschLK2009
From Neurons to Circuits: Linear Estimation of Local Field Potentials
Journal of Neuroscience
2009
11
29
44
13785-13796
Extracellular physiological recordings are typically separated into two frequency bands: local field potentials (LFPs) (a circuit property) and spiking multiunit activity (MUA). Recently, there has been increased interest in LFPs because of their correlation with functional magnetic resonance imaging blood oxygenation level-dependent measurements and the possibility of studying local processing and neuronal synchrony. To further understand the biophysical origin of LFPs, we asked whether it is possible to estimate their time course based on the spiking activity from the same electrode or nearby electrodes. We used “signal estimation theory” to show that a linear filter operation on the activity of one or a few neurons can explain a significant fraction of the LFP time course in the macaque monkey primary visual cortex. The linear filter used to estimate the LFPs had a stereotypical shape characterized by a sharp downstroke at negative time lags and a slower positive upstroke for positive time lags. The filter was similar across different neocortical regions and behavioral conditions, including spontaneous activity and visual stimulation. The estimations had a spatial resolution of ∼1 mm and a temporal resolution of ∼200 ms. By considering a causal filter, we observed a temporal asymmetry such that the positive time lags in the filter contributed more to the LFP estimation than the negative time lags. Additionally, we showed that spikes occurring within ∼10 ms of spikes from nearby neurons yielded better estimation accuracies than nonsynchronous spikes. In summary, our results suggest that at least some circuit-level local properties of the field potentials can be predicted from the activity of one or a few neurons.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Logothetis
http://www.jneurosci.org/content/29/44/13785.full.pdf+html
10.1523/JNEUROSCI.2390-09.2009
raschMRasch
nikosNKLogothetis
GKreimann
article
4946
Inferring Spike Trains From Local Field Potentials
Journal of Neurophysiology
2008
3
99
3
1461-1476
We investigated whether it is possible to
infer spike trains solely on the basis of the underlying local field
potentials (LFPs). Using support vector machines and linear regression
models, we found that in the primary visual cortex (V1) of
monkeys, spikes can indeed be inferred from LFPs, at least with
moderate success. Although there is a considerable degree of variation
across electrodes, the low-frequency structure in spike trains (in the
100-ms range) can be inferred with reasonable accuracy, whereas
exact spike positions are not reliably predicted. Two kinds of features
of the LFP are exploited for prediction: the frequency power of bands
in the high gamma-range (40&amp;amp;amp;amp;amp;#8211;90 Hz) and information contained in lowfrequency
oscillations ( 10 Hz), where both phase and power modulations
are informative. Information analysis revealed that both
features code (mainly) independent aspects of the spike-to-LFP relationship,
with the low-frequency LFP phase coding for temporally
clustered spiking activity. Although both features and prediction
quality are similar during seminatural movie stimuli and spontaneous
activity, prediction performance during spontaneous activity degrades
much more slowly with increasing electrode distance. The general
trend of data obtained with anesthetized animals is qualitatively
mirrored in that of a more limited data set recorded in V1 of non-anesthetized
monkeys. In contrast to the cortical field potentials, thalamic LFPs
(e.g., LFPs derived from recordings in the dorsal lateral geniculate
nucleus) hold no useful information for predicting spiking activity.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
Department Logothetis
http://jn.physiology.org/cgi/reprint/99/3/1461
Biologische Kybernetik
Max-Planck-Gesellschaft
en
doi:10.1152/jn.00919.2007
raschMJRasch
arthurAGretton
yusukeYMurayama
WMaass
nikosNKLogothetis
article
5115
Phase-of-Firing Coding of Natural Visual Stimuli in Primary Visual Cortex
Current Biology
2008
3
18
5
375-380
We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts.
The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Logothetis
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6VRT-4S0GXTD-7-B&_cdi=6243&_user=29041&_orig=search&_coverDate=03%2F11%2F2008&_sk=999819994&view=c&wchp=dGLzVlz-zSkzk&md5=cb1a6bb2099bc83600ddc8cc9656be3b&ie=/sdarticle.pdf
Biologische Kybernetik
Max-Planck-Gesellschaft
en
http://dx.doi.org/10.1016/j.cub.2008.02.023
MAMontemurro
raschMJRasch
yusukeYMurayama
nikosNKLogothetis
stefanoSPanzeri
article
3981
Integrating Structured Biological data by Kernel Maximum Mean Discrepancy
Bioinformatics
2006
8
22
4: ISMB 2006 Conference Proceedings
e49-e57
Motivation: Many problems in data integration in bioinformatics can be posed as one common question: Are two sets of observations generated by the same distribution? We propose a kernel-based statistical test for this problem, based on the fact that two distributions are different if and only if there exists at least one function having different expectation on the two distributions. Consequently we use the maximum discrepancy between function means as the basis of a test statistic.
The Maximum Mean Discrepancy (MMD) can take advantage of the kernel trick, which allows us to apply it not only to vectors, but strings, sequences, graphs, and other common structured data types arising in molecular biology.
Results: We study the practical feasibility of an MMD-based test on three central data integration tasks: Testing cross-platform comparability of microarray data, cancer diagnosis, and data-content based schema matching for two different protein function classification schemas. In all of these experiments, including high-dimensional ones, MMD is very accurate in finding samples that were generated from the same distribution, and outperforms its best competitors.
Conclusions: We have defined a novel statistical test of whether two samples are from the same distribution, compatible with both multivariate and structured data, that is fast, easy to implement, and works well, as confirmed by our experiments.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
http://bioinformatics.oxfordjournals.org/cgi/reprint/22/14/e49
Biologische Kybernetik
Max-Planck-Gesellschaft
en
10.1093/bioinformatics/btl242
karstenKMBorgwardt
arthurAGretton
raschMRasch
H-PKriegel
bsBSchölkopf
smolaASmola
article
4702
A functional hypothesis for adult hippocampal neurogenesis: Avoidance of catastrophic interference in the dentate gyrus
Hippocampus
2006
1
16
3
329-343
The dentate gyrus is part of the hippocampal memory system and special in that it generates new neurons throughout life. Here we discuss the question of what the functional role of these new neurons might be. Our hypothesis is that they help the dentate gyrus to avoid the problem of catastrophic interference when adapting to new environments. We assume that old neurons are rather stable and preserve an optimal encoding learned for known environments while new neurons are plastic to adapt to those features that are qualitatively new in a new environment. A simple network simulation demonstrates that adding new plastic neurons is indeed a successful strategy for adaptation without catastrophic interference.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www3.interscience.wiley.com/cgi-bin/fulltext/112305178/PDFSTART
Biologische Kybernetik
Max-Planck-Gesellschaft
en
10.1002/hipo.20167
LWiskott
raschMJRasch
GKempermann
article
4701
On the Kinetic Design of Transcription
Genome Informatics
2005
9
16
1
73
We analyse a stochastic model of transcription that describes transcription initiation by promoter activation and subsequent polymerase recruitment. Explicit expressions are derived for the control of an activator on the mean mRNA number and for the mRNA noise. Both properties are strongly influenced by the kinetics of promoter activation, mRNA synthesis and degradation. Low transcriptional noise is obtained either when the transcription initiation complex has a long life-time or when its components associate and dissociate rapidly. However, the ability of an activator to regulate the mRNA level is low in the first and high in the second case. Large noise is generated when the initial activation step of the promoter is slow. In this case, transcription can be burst-like; the mRNA distribution becomes bimodal while regulability of the mean copy number is maintained.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.jsbi.org/journal/IBSB05/IBSB05F020.html
Biologische Kybernetik
Max-Planck-Gesellschaft
en
THöfer
raschMJRasch
inproceedings
4193
A Kernel Method for the Two-Sample-Problem
Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference
2007
9
513-520
We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a reproducing kernel Hilbert space (RKHS). The first test is based on a large deviation bound for the test statistic, while the second is
based on the asymptotic distribution of this statistic.
The test statistic can be computed in $O(m^2)$ time. We apply our approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where our test performs strongly.
We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.
http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/NIPS2006_0583_4193[0].pdf
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
http://nips.cc/Conferences/2006/
Schölkopf, B. , J. Platt, T. Hofmann
MIT Press
Cambridge, MA, USA
Advances in Neural Information Processing Systems 19
Biologische Kybernetik
Max-Planck-Gesellschaft
Vancouver, BC, Canada
Twentieth Annual Conference on Neural Information Processing Systems (NIPS 2006)
en
0-262-19568-2
arthurAGretton
karstenKMBorgwardt
raschMRasch
bsBSchölkopf
smolaASmola
inproceedings
4426
A Kernel Approach to Comparing Distributions
Proceedings of the Twenty-Second AAAI Conference on Artificial Intelligence (AAAI-07)
2007
7
1637-1641
We describe a technique for comparing distributions without
the need for density estimation as an intermediate step.
Our approach relies on mapping the distributions into a Reproducing Kernel Hilbert Space. We apply this technique to
construct a two-sample test, which is used for determining
whether two sets of observations arise from the same distribution. We use this test in attribute matching for databases using the Hungarian marriage method, where it performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.
http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/Gretton_4426[0].pdf
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
http://www.aaai.org/Library/AAAI/aaai07contents.php
AAAI Press
Menlo Park, CA, USA
Biologische Kybernetik
Max-Planck-Gesellschaft
Association for the Advancement of Artificial Intelligence
Vancouver, BC, Canada
Twenty-Second AAAI Conference on Artificial Intelligence (IAAI-07)
en
978-1-577-35323-2
arthurAGretton
karstenKMBorgwardt
raschMRasch
bsBSchölkopf
smolaAJSmola
techreport
5111
A Kernel Method for the Two-sample Problem
2008
4
157
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time
approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg.~a Banach space). We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.
http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/MPIK-TR-157_5111[0].pdf
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Schölkopf
Biologische Kybernetik
Max-Planck-Gesellschaft
Max-Planck-Institute for Biological Cybernetics Tübingen
en
arthurAGretton
karstenKBorgwardt
raschMRasch
bsBSchölkopf
smolaASmola
poster
CalabreseRLK2008
Predicting local field potentials from spike trains
2008
11
38
459.9
Spiking activity provides information about the outputs of neurons. Recently, there has been increased interest in the study of local field potentials (LFPs), partly due to their correlation with fMRI BOLD measurements [1], to the possibility of studying local inputs [2] and as a tool to assess neuronal synchrony [3]. The LFP is operationally defined by low-pass filtering (100 Hz) the extracellular recordings, and its precise biophysical origin of remains only poorly understood. Recently, Rasch and colleagues used a SVM algorithm to infer the spiking activity at a given site from the LFPs [4]. To further understand the relationship between spikes and LFPs, we asked whether we could predict the detailed timecourse of the LFP based solely on the spiking activity of units recorded from the same electrode or nearby electrodes. We used a Wiener-Kolmogorov approach to derive the optimum linear filter that estimates the LFPs [5, 6]. We considered electrophysiological recordings in the macaque lateral geniculate nucleus and primary visual cortex during spontaneous activity (86 electrodes, 7 monkeys) [4]. We found that it is possible to predict LFPs from V1 solely using spike trains from single electrodes in that area. The mean correlation coefficient (r) between the predictions and the actual LFP varied between 0.23 and 0.65. We found that the estimations were highly significant (p < 10, based on generating a Poisson spike train with the same rate and re-estimating the filters). In contrast, trying to predict LGN LFPs resulted in a performance hardly above chance level. The reconstruction filter was closely related to the spike-triggered average of the LFPs. A causal filter that used only the spikes occurring before the actual time of the LFP yielded a higher error (p < 0.01) than a filter that used only the spikes occurring after. It was possible to predict LFPs in V1 from spike trains recorded in LGN (r = 0.3 to 0.7). The algorithm performed at chance level when trying to predict LFPs in LGN from spikes in V1. In sum, these results support the notion that LFPs represent the input and local processing while spikes represent the output and suggest that a linear convolution can account for a large fraction of the timecourse of the LFP. We have observed similar results in recordings from macaque monkey inferior temporal cortex and the human temporal lobe, suggesting that there may be a universal relationship between spikes and LFPs.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Logothetis
http://www.sfn.org/annual-meeting/past-and-future-annual-meetings
Washington, DC, USA
38th Annual Meeting of the Society for Neuroscience (Neuroscience 2008)
AMCalabrese
raschMJRasch
nikosNKLogothetis
GKreiman
poster
4703
What is the functional role of adult neurogenesis in the hippocampus?
2005
3
299
The hippocampus is a brain structure that is instrumental for episodic memory, i.e. for memorizing facts and events. It is often thought to be an intermediate memory that can store new input patterns quickly, which subsequently get transferred into more permanent cortical memory. The entorhinal cortex serves as an interface between hippocampus and other cortical areas. Within the hippocampal formation the different substructures form a loop: entorhinal cortex (layers II/III) - dentate gyrus - CA3 - CA1 - subiculum - entorhinal cortex (layers V/VI). Because of its recurrent connectivity, CA3 is thought to be the actual memory. Dentate gyrus would then be an encoding network, preparing the input patterns for storage in CA3; CA1 and subiculum would perform the decoding to reconstruct the stored patterns in entorhinal cortex. The dentate gyrus is special in that it generates new neurons throughout life, a phenomenon referred to as adult neurogenesis. Why does adult neurogenesis occur in the dentate gyrus and not in any of the other structures? Assume the dentate gyrus adapts to the environment the animal lives in in order to optimize its encoding for the input-pattern distribution encountered in this environment. If the animal moves to another environment, new adaptation takes place and the dentate gyrus is faces with the problem of catastrophic interference. As a new encoding is learned the old encoding degrades quickly and as a consequence old patterns could not be addressed and retrieved from the CA3-memory. In artificial neural networks catastrophic interference is usually avoided by interleaved training, i.e. the training patterns are presented repeatedly in an alternating fashion. However, this is not possible in real life, because many patterns occur only once. How can the dentate gyrus solve this problem? We hypothesize that new neurons are the solution to this problem. If the dentate gyrus keeps old neurons and their connections fixed but adds new neurons that are plastic, it can adapt to qualitatively new input patterns but at the same time maintain the encoding capabilities for old patterns. Note that new neurons are required only for qualitatively new patterns and not for new patterns that belong to the old input distribution, because we assume the encoding to be characteristic for a distribution and not for individual patterns. As a proof of principle we have simulated a linear auto-encoder network modelling the loop within the hippocampal formation. We assume that the animal first lives in environment A with a certain input-pattern statistics, then moves to a new environment B with a different input-pattern statistics, and finally returns to environment A. We assume that the animal has time to adapt to environment A and then B, but when it returns to A we only test the performance without giving the time for new adaptation. We also assume that the decoding (CA1/subiculum) stays plastic and can adapt to environment A and B in any case (but not when the animal returns to A). We have considered three different scenarios: (a) No DG-adaptation: The dentate gyrus adapts to environment A and keeps the synaptic weights fixed after that. No adaptation to environment B occurs. (b) Neurogenesis: The dentate gyrus starts with fewer units and first adapts to environment A. In environment B the old units and connections are fixed but a few new units are added and used to adapt to the new input-pattern distribution. (c) Full adaptation: The dentate gyrus always fully adapts to the current environment, first A then B. In the simulations we find that the networks always perform reasonably well on the pattern distributions they are adapted to. However, in scenario (a) the performance is poor in environment B, because although the decoding can adapt to environment B the encoding is still optimal for A and misses important dimensions of B. Performance is also poor when the animal returns to A, because the decoding has adapted to B. In scenario (c) performance is particularly poor when the animal returns to environment A, because the network is then fully adapted to B. Only in scenario (b) is the effect of catastrophic interference largely avoided and the performance good in environments A and B and also as the animal returns to A. Our model is consistent with a number of anatomical and physiological facts: New neurons are found to be more plastic than old ones as required by our model. Since new units are only required for qualitatively new input patterns, there is decreasing need for neurogenesis with age, because the animal has more and more experience and encounters fewer and fewer qualitatively new stimuli. This is consistent with the decrease in neurogenesis observed experimentally. A relatively small number of newly added units can have a large effect, since only missing dimensions have to be newly encoded. This is consistent with the relatively low level of neurogenesis of 30% new neurons in mice over the whole lifetime. Since the generation of new neurons takes weeks but the demand for new neurons can be on a much shorter time scale when the animal changes its environment, it is reasonable that new neurons are generated all the time to have some in stock when needed. New neurons not needed die after some time. This is what is found experimentally. The level of neurogenesis is regulated by rather unspecific factors such as physical activity or hunger. It is clear that if new neurons are only needed if qualitatively new input-pattern distributions are encountered, there are no specific factors that would be available earlyenough. Thus the unspecific factors might actually be fairly descent predictors for the need of new neurons, since hunger andrunning fosters exploration of new environments. In summary we hypothesize that adult neurogenesis in the dentate gyrus helps to solve the problem of catastrophic interference when an animal adapts to new environments. Our network simulations confirm that adding new neurons can reduce the effect of catastrophic interference significantly. The model is also qualitatively consistent with a number of anatomical and physiological facts about adult neurogenesis. See http://cogprints.org/4012/ for more information.
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
http://www.cosyne.org/c/index.php?title=Cosyne_05
Biologische Kybernetik
Max-Planck-Gesellschaft
Salt Lake City, UT, USA
Computational and Systems Neuroscience Meeting (COSYNE 2005)
LWiskott
raschMJRasch
GKempermann
thesis
5260
Analysis of neural signals: Interdependence, information coding, and relation to network models
2008
6
3
http://www.kyb.tuebingen.mpg.de/fileadmin/user_upload/files/publications/RASCH_thesis_5260[0].pdf
http://www.kyb.tuebingen.mpg.de
http://www.kyb.tuebingen.mpg.de
Department Logothetis
Biologische Kybernetik
Max-Planck-Gesellschaft
Graz University of Technology, Graz, Austria
PhD
en
raschMJRasch