The Annals of Applied Statistics

Exact spike train inference via $\ell_{0}$ optimization

Sean Jewell and Daniela Witten

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In recent years new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons simultaneously in behaving animals. For each neuron a fluorescence trace is measured; this can be seen as a first-order approximation of the neuron’s activity over time. Determining the exact time at which a neuron spikes on the basis of its fluorescence trace is an important open problem in the field of computational neuroscience.

Recently, a convex optimization problem involving an $\ell_{1}$ penalty was proposed for this task. In this paper we slightly modify that recent proposal by replacing the $\ell_{1}$ penalty with an $\ell_{0}$ penalty. In stark contrast to the conventional wisdom that $\ell_{0}$ optimization problems are computationally intractable, we show that the resulting optimization problem can be efficiently solved for the global optimum using an extremely simple and efficient dynamic programming algorithm. Our R-language implementation of the proposed algorithm runs in a few minutes on fluorescence traces of 100,000 timesteps. Furthermore, our proposal leads to substantial improvements over the previous $\ell_{1}$ proposal, in simulations as well as on two calcium imaging datasets.

R-language software for our proposal is available on CRAN in the package LZeroSpikeInference. Instructions for running this software in python can be found at https://github.com/jewellsean/LZeroSpikeInference.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 4 (2018), 2457-2482.

Dates
Received: November 2017
First available in Project Euclid: 13 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1542078052

Digital Object Identifier
doi:10.1214/18-AOAS1162

Mathematical Reviews number (MathSciNet)
MR3875708

Keywords
Neuroscience calcium imaging changepoint detection dynamic programming

Citation

Jewell, Sean; Witten, Daniela. Exact spike train inference via $\ell_{0}$ optimization. Ann. Appl. Stat. 12 (2018), no. 4, 2457--2482. doi:10.1214/18-AOAS1162. https://projecteuclid.org/euclid.aoas/1542078052


Export citation

References

  • Ahrens, M. B., Orger, M. B., Robson, D. N., Li, J. M. and Keller, P. J. (2013). Whole-brain functional imaging at cellular resolution using light-sheet microscopy. Nat. Methods 10 413–420.
  • Allen Institute for Brain Science (2016). Stimulus set and response analysis. Technical report, Allen Institute, Seattle, WA.
  • Aue, A. and Horváth, L. (2013). Structural breaks in time series. J. Time Series Anal. 34 1–16.
  • Auger, I. E. and Lawrence, C. E. (1989). Algorithms for the optimal identification of segment neighborhoods. Bull. Math. Biol. 51 39–54.
  • Bien, J. and Witten, D. (2016). Penalized estimation in complex models. In Handbook of Big Data. 285–303. CRC Press, Boca Raton, FL.
  • Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge Univ. Press, Cambridge.
  • Boysen, L., Kempe, A., Liebscher, V., Munk, A. and Wittich, O. (2009). Consistencies and rates of convergence of jump-penalized least squares estimators. Ann. Statist. 37 157–183.
  • Braun, J. V. and Müller, H.-G. (1998). Statistical methods for DNA sequence segmentation. Statist. Sci. 13 142–162.
  • Brunel, N. and Wang, X.-J. (2003). What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. J. Neurophysiol. 90 415–430.
  • Cavallari, S., Panzeri, S. and Mazzoni, A. (2016). Comparison of the dynamics of neural interactions between current-based and conductance-based integrate-and-fire recurrent networks. Frontiers in Neural Circuits 8.
  • Chen, T.-W., Wardill, T. J., Sun, Y., Pulver, S. R., Renninger, S. L., Baohan, A., Schreiter, E. R., Kerr, R. A., Orger, M. B., Jayaraman, V. et al. (2013). Ultrasensitive fluorescent proteins for imaging neuronal activity. Nature 499 295–300.
  • Dalalyan, A. S., Hebiri, M. and Lederer, J. (2017). On the prediction performance of the Lasso. Bernoulli 23 552–581.
  • Davies, P. L. and Kovac, A. (2001). Local extremes, runs, strings and multiresolution. Ann. Statist. 29 1–65.
  • Davis, R. A., Lee, T. C. M. and Rodriguez-Yam, G. A. (2006). Structural break estimation for nonstationary time series models. J. Amer. Statist. Assoc. 101 223–239.
  • de Rooi, J. and Eilers, P. (2011). Deconvolution of pulse trains with the $L_{0}$ penalty. Anal. Chim. Acta 705 218–226.
  • de Rooi, J. J., Ruckebusch, C. and Eilers, P. H. C. (2014). Sparse deconvolution in one and two dimensions: Applications in endocrinology and single-molecule fluorescence imaging. Anal. Chem. 86 6291–6298.
  • Deneux, T., Kaszas, A., Szalay, G., Katona, G., Lakner, T., Grinvald, A., Rózsa, B. and Vanzetta, I. (2016). Accurate spike estimation from noisy calcium signals for ultrafast three-dimensional imaging of large neuronal populations in vivo. Nat. Commun. 7 12190.
  • Dombeck, D. A., Khabbaz, A. N., Collman, F., Adelman, T. L. and Tank, D. W. (2007). Imaging large-scale neural activity with cellular resolution in awake, mobile mice. Neuron 56 43–57.
  • Friedrich, J. and Paninski, L. (2016). Fast active set methods for online spike inference from calcium imaging. In Advances in Neural Information Processing Systems 1984–1992.
  • Friedrich, J., Zhou, P. and Paninski, L. (2017). Fast online deconvolution of calcium imaging data. PLoS Comput. Biol. 13 e1005423.
  • Fryzlewicz, P. (2014). Wild binary segmentation for multiple change-point detection. Ann. Statist. 42 2243–2281.
  • GENIE Project (2015). Simultaneous imaging and loose-seal cell-attached electrical recordings from neurons expressing a variety of genetically encoded calcium indicators. CRCNS.org.
  • Grewe, B. F., Langer, D., Kasper, H., Kampa, B. M. and Helmchen, F. (2010). High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision. Nat. Methods 7 399–405.
  • Harchaoui, Z. and Lévy-Leduc, C. (2010). Multiple change-point estimation with a total variation penalty. J. Amer. Statist. Assoc. 105 1480–1493.
  • Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed. Springer, New York.
  • Hastie, T., Tibshirani, R. and Wainwright, M. (2015). Statistical Learning with Sparsity: The Lasso and Generalizations. Monographs on Statistics and Applied Probability 143. CRC Press, Boca Raton, FL.
  • Hawrylycz, M., Anastassiou, C., Arkhipov, A., Berg, J., Buice, M., Cain, N., Gouwens, N. W., Gratiy, S., Iyer, R., Lee, J. H. et al. (2016). Inferring cortical function in the mouse visual system through large-scale systems neuroscience. Proc. Natl. Acad. Sci. USA 113 7337–7344.
  • Hocking, T. D., Rigaill, G., Fearnhead, P. and Bourque, G. (2017). A log-linear time algorithm for constrained changepoint detection. Preprint. Available at ArXiv:1703.03352.
  • Holekamp, T. F., Turaga, D. and Holy, T. E. (2008). Fast three-dimensional fluorescence imaging of activity in neural populations by objective-coupled planar illumination microscopy. Neuron 57 661–672.
  • Hugelier, S., de Rooi, J. J., Bernex, R., Duwé, S., Devos, O., Sliwa, M., Dedecker, P., Eilers, P. H. and Ruckebusch, C. (2016). Sparse deconvolution of high-density super-resolution images. Sci. Rep. 6.
  • Jackson, B., Scargle, J. D., Barnes, D., Arabhi, S., Alt, A., Gioumousis, P., Gwin, E., Sangtrakulcharoen, P., Tan, L. and Tsai, T. T. (2005). An algorithm for optimal partitioning of data on an interval. IEEE Signal Process. Lett. 12 105–108.
  • Johnson, N. A. (2013). A dynamic programming algorithm for the fused lasso and $L_{0}$-segmentation. J. Comput. Graph. Statist. 22 246–260.
  • Killick, R., Fearnhead, P. and Eckley, I. A. (2012). Optimal detection of changepoints with a linear computational cost. J. Amer. Statist. Assoc. 107 1590–1598.
  • Lee, C.-B. (1995). Estimating the number of change points in a sequence of independent normal random variables. Statist. Probab. Lett. 25 241–248.
  • Lin, K., Sharpnack, J., Rinaldo, A. and Tibshirani, R. J. (2016). Approximate recovery in changepoint problems, from $\ell_{2}$ estimation error rates. Preprint. Available at ArXiv:1606.06746.
  • Maidstone, R., Hocking, T., Rigaill, G. and Fearnhead, P. (2017). On optimal multiple changepoint algorithms for large data. Stat. Comput. 27 519–533.
  • Mammen, E. and van de Geer, S. (1997). Locally adaptive regression splines. Ann. Statist. 25 387–413.
  • Mazzoni, A., Panzeri, S., Logothetis, N. K. and Brunel, N. (2008). Encoding of naturalistic stimuli by local field potential spectra in networks of excitatory and inhibitory neurons. PLoS Comput. Biol. 4 e1000239, 20.
  • Olshen, A. B., Venkatraman, E., Lucito, R. and Wigler, M. (2004). Circular binary segmentation for the analysis of array-based DNA copy number data. Biostatistics 5 557–572.
  • Pnevmatikakis, E. A., Merel, J., Pakman, A. and Paninski, L. (2013). Bayesian spike inference from calcium imaging data. In Signals, Systems and Computers, 2013 Asilomar Conference on 349–353. IEEE.
  • Pnevmatikakis, E. A., Soudry, D., Gao, Y., Machado, T. A., Merel, J., Pfau, D., Reardon, T., Mu, Y., Lacefield, C., Yang, W. et al. (2016). Simultaneous denoising, deconvolution, and demixing of calcium imaging data. Neuron 89 285–299.
  • Prevedel, R., Yoon, Y.-G., Hoffmann, M., Pak, N., Wetzstein, G., Kato, S., Schrödel, T., Raskar, R., Zimmer, M., Boyden, E. S. et al. (2014). Simultaneous whole-animal 3D imaging of neuronal activity using light-field microscopy. Nat. Methods 11 727–730.
  • Qian, J. and Jia, J. (2012). On pattern recovery of the fused lasso. Preprint. Available at ArXiv:1211.5194.
  • Rinaldo, A. (2009). Properties and refinements of the fused lasso. Ann. Statist. 37 2922–2952.
  • Rojas, C. R. and Wahlberg, B. (2014). On change point detection using the fused lasso method. Preprint. Available at ArXiv:1401.5408.
  • Sasaki, T., Takahashi, N., Matsuki, N. and Ikegaya, Y. (2008). Fast and accurate detection of action potentials from somatic calcium fluctuations. J. Neurophysiol. 100 1668–1676.
  • Scott, A. J. and Knott, M. (1974). A cluster analysis method for grouping means in the analysis of variance. Biometrics 30 507–512.
  • Theis, L., Berens, P., Froudarakis, E., Reimer, J., Rosón, M. R., Baden, T., Euler, T., Tolias, A. S. and Bethge, M. (2016). Benchmarking spike rate inference in population calcium imaging. Neuron 90 471–482.
  • Tibshirani, R., Saunders, M., Rosset, S., Zhu, J. and Knight, K. (2005). Sparsity and smoothness via the fused lasso. J. R. Stat. Soc. Ser. B. Stat. Methodol. 67 91–108.
  • van Rossum, M. C. (2001). A novel spike distance. Neural Comput. 13 751–763.
  • Victor, J. D. and Purpura, K. P. (1996). Nature and precision of temporal coding in visual cortex: A metric-space analysis. J. Neurophysiol. 76 1310–1326.
  • Victor, J. D. and Purpura, K. P. (1997). Metric-space analysis of spike trains: Theory, algorithms and application. Network 8 127–164.
  • Vogelstein, J. T., Watson, B. O., Packer, A. M., Yuste, R., Jedynak, B. and Paninski, L. (2009). Spike inference from calcium imaging using sequential Monte Carlo methods. Biophys. J. 97 636–655.
  • Vogelstein, J. T., Packer, A. M., Machado, T. A., Sippy, T., Babadi, B., Yuste, R. and Paninski, L. (2010). Fast nonnegative deconvolution for spike train inference from population calcium imaging. J. Neurophysiol. 104 3691–3704.
  • Volgushev, M., Ilin, V. and Stevenson, I. H. (2015). Identifying and tracking simulated synaptic inputs from neuronal firing: Insights from in vitro experiments. PLoS Comput. Biol. 11 e1004167.
  • Yaksi, E. and Friedrich, R. W. (2006). Reconstruction of firing rate changes across neuronal populations by temporally deconvolved Ca2+ imaging. Nat. Methods 3 377–383.
  • Yao, Y.-C. (1988). Estimating the number of change-points via Schwarz’ criterion. Statist. Probab. Lett. 6 181–189.
  • Yao, Y.-C. and Au, S. T. (1989). Least-squares estimation of a step function. Sankhyā Ser. A 51 370–381.
  • Zou, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101 1418–1429.