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  • 1.
    Alfelt, Gustav
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Bodnar, Taras
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Goodness-of-fit tests for centralized Wishart processes2019Inngår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArtikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we present several goodness-of-fit tests for the centralized Wishart process, a popular matrix-variate time series model used to capture the stochastic properties of realized covariance matrices. The new test procedures are based on the extended Bartlett decomposition derived from the properties of the Wishart distribution and allows to obtain sets of independently and standard normally distributed random variables under the null hypothesis. Several tests for normality and independence are then applied to these variables in order to support or to reject the underlying assumption of a centralized Wishart process. In order to investigate the influence of estimated parameters on the suggested testing procedures in the finite-sample case, a simulation study is conducted. Finally, the new test methods are applied to real data consisting of realized covariance matrices computed for the returns on six assets traded on the New York Stock Exchange.

  • 2. Battistin, Claudia
    et al.
    Hertz, John
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Niels Bohr Institute, Denmark.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Roudi, Yasser
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Kavli Institute for Systems Neuroscience/Centre for Neural Computation, Norway.
    Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins2015Inngår i: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, artikkel-id P05021Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless-Anderson-Palmer (TAP) equations for reconstructing the connections.

  • 3.
    Bodnar, Taras
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Mazur, Stepan
    Podgórski, Krzysztof
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tangency portfolio weights for singular covariance matrix in small and large dimensions: Estimation and test theory2019Inngår i: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 201, s. 40-57Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper we derive the finite-sample distribution of the estimated weights of the tangency portfolio when both the population and the sample covariance matrices are singular. These results are used in the derivation of a statistical test on the weights of the tangency portfolio where the distribution of the test statistic is obtained under both the null and alternative hypotheses. Moreover, we establish the high-dimensional asymptotic distribution of the estimated weights of the tangency portfolio when both the portfolio dimension and the sample size increase to infinity. The theoretical findings are implemented in an empirical application dealing with the returns on the stocks included into the S&P 500 index.

  • 4.
    Gullberg, Joanna
    Högskolan i Halmstad, Sektionen för lärarutbildning (LUT), Forskning om utbildning och lärande inom lärarutbildningen (FULL).
    PEDAGOGERS SYN PÅ DERAS UNDERVISNING PÅEN TRADITIONELL SKOLA OCH EN MONTESSORISKOLA I MATEMATIKÄMNET.2011Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
  • 5.
    Hertz, John A.
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Roudi, Yasser
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Ising model for inferring network structure from spike data2013Inngår i: Principle of Neural Coding / [ed] Rodrigo Quian Quiroga, Stefano Panzeri, Boca/Raton: CRC Press, 2013, s. 527-546Kapittel i bok, del av antologi (Fagfellevurdert)
    Abstract [en]

    Now that spike trains from many neurons can be recorded simultaneously, there is a need for methods to decode these data to learn about the networks that these neurons are part of. One approach to this problem is to adjust the parameters of a simple model network to make its spike trains resemble the data as much as possible. The connections in the model network can then give us an idea of how the real neurons that generated the data are connected and how they influence each other. In this chapter we describe how to do this for the simplest kind of model: an Ising network. We derive algorithms for finding the best model connection strengths for fitting a given data set, as well as faster approximate algorithms based on mean field theory. We test the performance of these algorithms on data from model networks and experiments.

  • 6.
    Hertz, John
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Roudi, Yasser
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Thorning, Andreas
    Niels Bohr Institute, Copenhagen University, 2100 Copenhagen Ø, Denmark .
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Aurell, Erik
    Department of Computational Biology, Royal Institute of Technology, 106 91 Stockholm, Sweden .
    Zeng, Hong-Li
    Department of Applied Physics, Helsinki University of Technology, 02015 TKK Espoo, Finland .
    Inferring network connectivity using kinetic Ising models2010Inngår i: BMC neuroscience (Online), ISSN 1471-2202, E-ISSN 1471-2202, Vol. 11, nr Suppl 1, s. P51-Artikkel i tidsskrift (Fagfellevurdert)
  • 7.
    Hertz, John
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Roudi, Yasser
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Ising model for inferring network structure from spike data: In Principal of Neural CodingArtikkel i tidsskrift (Fagfellevurdert)
  • 8. Hertz, John
    et al.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Correales, Alvaro
    Stochastic activation in a genetic switch model2018Inngår i: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 98, nr 5, artikkel-id 052403Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study a biological autoregulation process, involving a protein that enhances its own transcription, in a parameter region where bistability would be present in the absence of fluctuations. We calculate the rate of fluctuation-induced rare transitions between locally stable states using a path integral formulation and Master and Chapman-Kolmogorov equations. As in simpler models for rare transitions, the rate has the form of the exponential of a quantity S-0 (a barrier) multiplied by a prefactor eta. We calculate S-0 and eta first in the bursting limit (where the ratio gamma of the protein and mRNA lifetimes is very large). In this limit, the calculation can be done almost entirely analytically, and the results are in good agreement with simulations. For finite gamma numerical calculations are generally required. However, S-0 can be calculated analytically to first order in 1/gamma, and the result agrees well with the full numerical calculation for all gamma > 1. Employing a method used previously on other problems, we find we can account qualitatively for the way the prefactor eta varies with gamma, but its value is 15-20% higher than that inferred from simulations.

  • 9.
    Jafari-Mamaghani, Mehrdad
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Transfer entropy expressions for a class of non-Gaussian distributionsManuskript (preprint) (Annet vitenskapelig)
    Abstract [en]

    Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I − IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

  • 10.
    Jafari-Mamaghani, Mehrdad
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Karolinska Institutet, Sweden.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Transfer Entropy Expressions for a Class of Non-Gaussian Distributions2014Inngår i: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 16, nr 3, s. 1743-1755Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I - IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.

  • 11. Lock, John G.
    et al.
    Jafari-Mamaghani, Mehrdad
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Karolinska Institute, Sweden.
    Shafqat-Abbasi, Hamdah
    Gong, Xiaowei
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Strömblad, Staffan
    Plasticity in the Macromolecular-Scale Causal Networks of Cell Migration2014Inngår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, nr 2, s. e90593-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Heterogeneous and dynamic single cell migration behaviours arise from a complex multi-scale signalling network comprising both molecular components and macromolecular modules, among which cell-matrix adhesions and F-actin directly mediate migration. To date, the global wiring architecture characterizing this network remains poorly defined. It is also unclear whether such a wiring pattern may be stable and generalizable to different conditions, or plastic and context dependent. Here, synchronous imaging-based quantification of migration systemorganization, represented by 87 morphological and dynamic macromolecular module features, and migration system behaviour, i.e., migration speed, facilitated Granger causality analysis. We thereby leveraged natural cellular heterogeneity to begin mapping the directionally specific causal wiring between organizational and behavioural features of the cell migration system. This represents an important advance on commonly used correlative analyses that do not resolve causal directionality. We identified organizational features such as adhesion stability and adhesion F-actin content that, as anticipated, causally influenced cell migration speed. Strikingly, we also found that cell speed can exert causal influence over organizationalfeatures, including cell shape and adhesion complex location, thus revealing causality in directions contradictory to previous expectations. Importantly, by comparing unperturbed and signalling-modulated cells, we provide proof-of-principle that causal interaction patterns are in fact plastic and context dependent, rather than stable and generalizable.

  • 12. Mielniczuk, Jan
    et al.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Consistency of multilayer perceptron regression estimators1993Inngår i: Neural Networks, Vol. 6, s. 1019-1022Artikkel i tidsskrift (Fagfellevurdert)
  • 13. Nellaker, Christoffer
    et al.
    Li, Fang
    Uhrzander, Fredrik
    Stockholms universitet.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Karlsson, Hakan
    Expression profiling of repetitive elements by melting temperature analysis: variation in HERV-W gag expression across human individuals and tissues2009Inngår i: BMC Genomics, ISSN 1471-2164, E-ISSN 1471-2164, Vol. 10, s. 532-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Background: Human endogenous retroviruses (HERV) constitute approximately 8% of the human genome and have long been considered ""junk"". The sheer number and repetitive nature of these elements make studies of their expression methodologically challenging. Hence, little is known of transcription of genomic regions harboring such elements. Results: Applying a recently developed technique for obtaining high resolution melting temperature data, we examined the frequency distributions of HERV-W gag element into 13 Tm categories in human tissues. Transcripts containing HERV-W gag sequences were expressed in non-random patterns with extensive variations in the expression between both tissues, including different brain regions, and individuals. Furthermore, the patterns of such transcripts varied more between individuals in brain regions than other tissues. Conclusion: Thus, regulated expression of non-coding regions of the human genome appears to include the HERV-W family of repetitive elements. Although it remains to be established whether such expression patterns represent leakage from transcription of functional regions or specific transcription, the current approach proves itself useful for studying detailed expression patterns of repetitive regions.

  • 14. Nellåker, Christoffer
    et al.
    Uhrzander, Fredrik
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematisk statistik.
    Karlsson, Håkan
    Mixture models for analysis of melting temperature data2008Inngår i: BMC Bioinformatics, Vol. 9:370Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Background

    In addition to their use in detecting undesired real-time PCR products, melting temperatures are useful for detecting variations in the desired target sequences. Methodological improvements in recent years allow the generation of high-resolution melting-temperature (Tm) data. However, there is currently no convention on how to statistically analyze such high-resolution Tm data.

    Results

    Mixture model analysis was applied to Tm data. Models were selected based on Akaike's information criterion. Mixture model analysis correctly identified categories in Tm data obtained for known plasmid targets. Using simulated data, we investigated the number of observations required for model construction. The precision of the reported mixing proportions from data fitted to a preconstructed model was also evaluated.

    Conclusion

    Mixture model analysis of Tm data allows the minimum number of different sequences in a set of amplicons and their relative frequencies to be determined. This approach allows Tm data to be analyzed, classified, and compared in an unbiased manner.

  • 15.
    Roudi, Yasser
    et al.
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hertz, John
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita).
    Fast and realiable methods for extracting functional connectivity in large populations2009Inngår i: BMC neuroscience (Online), ISSN 1471-2202, E-ISSN 1471-2202, BMC Neuroscience, ISSN 1471-2202, Vol. 10, nr Suppl 1, s. 09-Artikkel i tidsskrift (Fagfellevurdert)
  • 16. Roudi, Yasser
    et al.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hertz, John
    Ising model for neural data: Model quality and approximate methods for extracting functional connectivity2009Inngår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 79, nr 5, s. 51915-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study pairwise Ising models for describing the statistics of multineuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods-inversion of the Thouless-Anderson-Palmer equations and an approximation proposed by Sessak and Monasson-are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate their magnitude. This effect is described qualitatively by infinite-range spin-glass theory for the normal phase. We also show that a globally correlated input to the neurons in the network leads to a small increase in the average coupling. However, the pair-to-pair variation in the couplings is much larger than this and reflects intrinsic properties of the network. Finally, we study the quality of these models by comparing their entropies with that of the data. We find that they perform well for small subsets of the neurons in the network, but the fit quality starts to deteriorate as the subset size grows, signaling the need to include higher-order correlations to describe the statistics of large networks.

  • 17.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Age-dependent cell cycle models2001Inngår i: Journal of Theoretical Biology, nr 213, s. 89-101Artikkel i tidsskrift (Fagfellevurdert)
  • 18.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Asymptotic Stability of the Mass Distribution in the Case of the Linear and Exponential Growth in Probabilistic Models of the Cell Cycle2000Rapport (Annet vitenskapelig)
  • 19.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Cell cycle progression2004Inngår i: Comptes Rendues: Biologies, nr 327, s. 193-200Artikkel i tidsskrift (Fagfellevurdert)
  • 20.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Dynamics of integrate and fire models2007Inngår i: Mathematical Modeling of Biological Systems, Vol. II, s. 235-246Artikkel i tidsskrift (Fagfellevurdert)
  • 21.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Spike statistics for a high-conductance cortical network model2007Inngår i: 5th Nordic Neuroinformatics Workshop: Life Science Center, Espoo, Finland, 2007Konferansepaper (Annet vitenskapelig)
  • 22.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hertz, John
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Niels Bohr Institute, Copenhagen, Denmark.
    NETWORK INFERENCE WITH HIDDEN UNITS2014Inngår i: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 11, nr 1, s. 149-165Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We derive learning rules for finding the connections between units in stochastic dynamical networks from the recorded history of a visible subset of the units. We consider two models. In both of them, the visible units are binary and stochastic. In one model the hidden units are continuous-valued, with sigmoidal activation functions, and in the other they are binary and stochastic like the visible ones. We derive exact learning rules for both cases. For the stochastic case, performing the exact calculation requires, in general, repeated summations over an number of configurations that grows exponentially with the size of the system and the data length, which is not feasible for large systems. We derive a mean field theory, based on a factorized ansatz for the distribution of hidden-unit states, which offers an attractive alternative for large systems. We present the results of some numerical calculations that illustrate key features of the two models and, for the stochastic case, the exact and approximate calculations.

  • 23.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematisk statistik.
    Hertz, John
    Spike pattern distributions in model cortical networks2008Inngår i: COSYNE-Computational and Systems Neuroscience 2008, Salt Lake City, 2008Konferansepaper (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    We can learn something about coding in large populations of neurons from models of the spike pattern distributions constructed from data. In our work, we do this for data generated from computational models of local cortical networks. This permits us to explore how features of the neuronal and synaptic properties of the network are related to those of the spike pattern distribution model. We employ the approach of Schneidman et al [1] and model this distribution by a Sherrington-Kirkpatrick (SK) model: P[S] = Z-1exp(½ΣijJijSiSj+ΣihiSi). In the work reported here, we analyze spike records from a simple model of a cortical column in a high-conductance state for two different cases: one with stationary tonic firing and the other with a rapidly time-varying input that produces rapid variations in firing rates. The average cross-correlation coefficient in the former is an order of magnitude smaller than that in the latter.

    To estimate the parameters Jij and hi we use a technique [2] based on inversion of the Thouless-Anderson-Palmer equations from spin glass theory. We have performed these fits for groups of neurons of sizes from 12 to 200 for tonic firing and from 6 to 800 for the case of the rapidly time-varying “stimulus”. The first two figures show that the distributions of Jij’s in the two cases are quite similar, both growing slightly narrower with increasing N. They are also qualitatively similar to those found by Schneidman et al and by Tkačik et al [3] for data from retinal networks. As in their work, it does not appear to be necessary to include higher order couplings. The means, which are much smaller than the standard deviations, also decrease with N, and the one for tonic firing is less than half that for the stimulus-driven network.

    However, the models obtained never appear to be in a spin glass phase for any of the sizes studied, in contrast to the finding of Tkačik et al, who reported spin glass behaviour at N=120. This is shown in the third figure panel. The x axis is 1/J, where J = N1/2std(Jij) and the y axis is H/J, where H is the total “field” N-1Σi(hi+ΣjJij‹Sj›). The green curve marks the Almeida-Thouless line separating the normal and spin glass phases in this parameter plane. All our data, for N ≤800 (the number of excitatory neurons in the originally-simulated network), lie in the normal region, and extrapolation from our results predicts spin glass behaviour only for N>5000.

    [1] E. Schneidman et al., Nature 440 1007-1012 (2006)

    [2] T. Tanaka, Phys Rev E 58 2302-2310 (1998); H. J. Kappen and F. B Rodriguez, Neural Comp 10 1137-1156 (1998)

    [3] G. Tkačik et al., arXiv:q-bio.NC/0611072 v1 (2006)

  • 24.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Matematisk statistik.
    Hertz, John
    Testing Algorithms for Extracting Functional Connectivity from Spike Data2008Inngår i: 1st INCF Congress of Neuroinformatics: Databasing and Modeling the Brain, 2008Konferansepaper (Annet (populærvitenskap, debatt, mm))
    Abstract [en]

    We can learn something about how large neuronal networks function from models of their spike pattern distributions constructed from data. We do this using the approach introduced by Schneidman et al [1], modeling this distribution by an Ising model: P[S] = Z-1exp(ΣJijSiSj + ΣihiSi). In the work reported here, we explore the accuracy of two algorithms for extracting the model parameters Jij and hi by testing them on data generated by networks in which these parameters are known.

    Both algorithms use, as input, the firing rates and mutual correlations of the neurons in the network. The first algorithm is straightforward Boltzmann learning. It will yield the parameters correctly if the input statistics are known exactly,but it may be very slow to converge. The second, very fast, algorithm [2] is based on inversion of the Thouless-Anderson-Palmer equations from spin glass theory. It is derived from a small-Jij expansion, but it is in principle correct for all Jij when the network is infinitely large and densely connected.

    In practice, however, the rates and correlations used as inputs to the algorithms are estimates based on a finite number of measurements. Therefore, there will be errors in the extracted model parameters. Errors will also occur if the data are incomplete, i.e., if the rates and correlations are not measured for all neurons or all pairs. This case is highly relevant to the experimental situation, since in practice it is only possible to record from a small fraction of the neurons in a network.

    Two particular kinds of error statistics are of special interest: variances of the differences between true and extracted parameters, and variances of the differences between parameters extracted for two independent sets of training data. We study the relation between the two, since the first is what we are interested in but only the second can be computed in the realistic situation, where we do not know the parameters a priori. We also examine the variance of the difference between the true and extracted correlations.

    Finally, we apply the algorithms to the data of Schneidman et al from salamander retinal ganglion neurons.

    References

    --------------------------------------------------------------------------------

    1. E Schneidman et al, Nature 440 1007-1012 (2006); G Tkacik et al, arXiv:q-bio.NC/0611072 (2006)

    2. T Tanaka, Phys Rev E 58 2302-2310 (1998); H J Kappen and F B Rodriguez, Neural Comp 10 1137-1156 (1998)

  • 25.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten. Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Hertz, John
    Nordita.
    Roudi, Yasser
    Kavli Institute for Systems Neuroscience.
    Inferring network connectivity using kinectic Ising models2010Inngår i: BMC neuroscience (Online), ISSN 1471-2202, E-ISSN 1471-2202, Vol. 11, nr 51Artikkel i tidsskrift (Fagfellevurdert)
  • 26.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Levy, William
    Another contribution by synaptic failures to energy efficient processing by neurons2004Inngår i: Neurocomputing, Vol. 58-60, s. 59-66Artikkel i tidsskrift (Fagfellevurdert)
  • 27.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Levy, William
    Synaptic failures and a Gaussian excitation distribution2005Inngår i: Neurocomputing, Vol. 65-66, s. 891-899Artikkel i tidsskrift (Fagfellevurdert)
  • 28.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Roudi, Yasser
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Kavli Institute for Systems Neuroscience, NTNU, Norway.
    Marsili, Matteo
    Hertz, John
    Stockholms universitet, Nordiska institutet för teoretisk fysik (Nordita). Niels Bohr Institute, Denmark.
    The effect of nonstationarity on models inferred from neural data2013Inngår i: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, artikkel-id P03005Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Neurons subject to a common nonstationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations can be distinguished with machine learning techniques, provided that the data are rich enough. In order to do this, we study the problem of inferring a kinetic Ising model, stationary or nonstationary, from the available data. We apply the inference procedure to two data sets: one from salamander retinal ganglion cells and the other from a realistic computational cortical network model. We show that many aspects of the concerted activity of the salamander retinal neurons can be traced simply to the external input. A model of non-interacting neurons subject to a nonstationary external field outperforms a model with stationary input with couplings between neurons, even accounting for the differences in the number of model parameters. When couplings are added to the nonstationary model, for the retinal data, little is gained: the inferred couplings are generally not significant. Likewise, the distribution of the sizes of sets of neurons that spike simultaneously and the frequency of spike patterns as a function of their rank (Zipf plots) are well explained by an independent-neuron model with time-dependent external input, and adding connections to such a model does not offer significant improvement. For the cortical model data, robust couplings, well correlated with the real connections, can be inferred using the nonstationary model. Adding connections to this model slightly improves the agreement with the data for the probability of synchronous spikes but hardly affects the Zipf plot.

  • 29.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Sundberg, Rolf
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Statistical modelling and saddle point approximation of tail probabilities for accumulated splice loss in fibre optic networks2000Inngår i: J. Applied Statistics, ISSN 0266-4763, Vol. 27, nr 2, s. 245-256Artikkel i tidsskrift (Fagfellevurdert)
  • 30.
    Tyrcha, Joanna
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Sundberg, Rolf
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Lindskog, Peter
    Sundström, Bernt
    Statistical modelling and saddle point approximation of tail probabilities for accumulated splice loss in fibre optic networks1998Rapport (Annet vitenskapelig)
  • 31. Wu, Xiangbao
    et al.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Levy, William
    A neural network solution to the transverse patterning problem depends on repetition of the input code1998Inngår i: Biol. Cybern., nr 79, s. 203-213Artikkel i tidsskrift (Fagfellevurdert)
  • 32. Wu, Xiangbao
    et al.
    Tyrcha, Joanna
    Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.
    Levy, William
    A special role for input codes in solving the transverse patterning problem1997Inngår i: Computational Neuroscience: Trends in Research, s. 885-889Artikkel i tidsskrift (Fagfellevurdert)
1 - 32 of 32
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