Multiplicative Updates for Optimization Problems with Dynamics

Kazemipour, Abbas; Babadi, Behtash; Wu, Min; Podgorski, Kaspar; Druckmann, Shaul

doi:10.1101/234526

“…The term that must be estimated is the spikes, W = [w 1 ,w 2 ,…,w T ]. We estimate W by maximizing the likelihood of Y using a multiplicative update algorithm related to Richardson-Lucy deconvolution 33 . Importantly, regularization is unnecessary because S has low rank by design.…”

Section: Computational Recovery Of Neural Activitymentioning

confidence: 99%

Kilohertz frame-rate two-photon tomography

Kazemipour

¹

,

Novák

²

,

Flickinger

³

et al. 2019

Self Cite

View full text Add to dashboard Cite

Point-scanning two-photon microscopy enables high-resolution imaging within scattering specimens such as the mammalian brain, but sequential acquisition of voxels fundamentally limits its speed. We developed a two-photon imaging technique that scans lines of excitation across a focal plane at multiple angles and computationally recovers high-resolution images, attaining voxel rates of over 1 billion Hz in structured samples. Using a static image as a prior for recording neural activity, we imaged visually-evoked and spontaneous glutamate release across hundreds of dendritic spines in mice at depths over 250 μm and frame-rates over 1 kHz. Dendritic glutamate transients in anaesthetized mice are synchronized within spatially-contiguous domains spanning tens of microns at frequencies ranging from 1-100 Hz. We demonstrate millisecond-resolved recordings of acetylcholine and voltage indicators, 3D single-particle tracking, and imaging in Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use:

show abstract

“…. L, necessary optimality criteria can be derived for each W l from the Karusch-Kuhn-Tucker (KKT) conditions (see, e.g., Kazemipour et al (2017)) as…”

Section: Nonnegative Tensor Factorizationmentioning

confidence: 99%

Bayesian Allocation Model: Inference by Sequential Monte Carlo for Nonnegative Tensor Factorizations and Topic Models using Polya Urns

Cemgil,

Kurutmaz,

Yildirim

et al. 2019

Preprint

0

View full text Add to dashboard Cite

We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian extensions, and the topic models such as the latent Dirichlet allocation. BAM is based on a Poisson process, whose events are marked by using a Bayesian network, where the conditional probability tables of this network are then integrated out analytically. We show that the resulting marginal process turns out to be a Pólya urn, an integer valued self-reinforcing process. This urn processes, which we name a Pólya-Bayes process, obey certain conditional independence properties that provide further insight about the nature of NTF. These insights also let us develop space efficient simulation algorithms that respect the potential sparsity of data: we propose a class of sequential importance sampling algorithms for computing NTF and approximating their marginal likelihood, which would be useful for model selection. The resulting methods can also be viewed as a model scoring method for topic models and discrete Bayesian networks with hidden variables. The new algorithms have favourable properties in the sparse data regime when contrasted with variational algorithms that become more accurate when the total sum of the elements of the observed tensor goes to infinity. We illustrate the performance on several examples and numerically study the behaviour of the algorithms for various data regimes.

show abstract

Kilohertz frame-rate two-photon tomography

Kazemipour

¹

,

Novák

²

,

Flickinger

³

et al. 2018

Preprint

Self Cite

View full text Add to dashboard Cite

Point-scanning two-photon microscopy enables high-resolution imaging within scattering specimens such as the mammalian brain, but sequential acquisition of voxels fundamentally limits imaging speed. We developed a two-photon imaging technique that scans lines of excitation across a focal plane at multiple angles and uses prior information to recover high-resolution images at over 1.4 billion voxels per second. Using a structural image as a prior for recording neural activity, we imaged visually-evoked and spontaneous glutamate release across hundreds of dendritic spines in mice at depths over 250 µm and frame-rates over 1 kHz. Dendritic glutamate transients in anaesthetized mice are synchronized within spatially-contiguous domains spanning tens of microns at frequencies ranging from 1-100 Hz. We demonstrate high-speed recording of acetylcholine and calcium sensors, 3D single-particle tracking, and imaging in densely-labeled cortex. Our method surpasses limits on the speed of raster-scanned imaging imposed by fluorescence lifetime.The study of brain function relies on measurement tools that achieve high spatial resolution over large volumes at high rates 1 . Fluorescent sensors enable imaging of activity in large numbers of individual neurons or synapses on scales ranging from micrometers to millimeters 2-7 . However, the intact mammalian brain is opaque, and obtaining high-resolution images deeper than approximately 50 µm below its surface requires specialized techniques that are insensitive to light absorption and scattering. Two-photon imaging uses nonlinear absorption to confine fluorescence excitation to the highintensity focus of a laser, reducing excitation by scattered light. Since fluorescence is generated only at the focus, scattered emission light can be collected without forming an optical image. Instead, images are computationally assembled by scanning the focus in space. However, this serial approach creates a tradeoff between achievable frame-rates and pixels per frame. Common fluorophores have fluorescence lifetimes of approximately 3 ns, requiring approximately 10 ns between consecutive measurements to avoid crosstalk 8,9 . The maximum achievable frame-rate for a 1-megapixel rasterscanned fluorescence image is therefore approximately 100 Hz, and is further limited in practice by factors such as photodamage and scanner bandwidth 1 . Biophysical events underlying neuronal communication, such as action potentials and neurotransmitter release 3,10,11 , occur on millisecond timescales. Kilohertz megapixel in vivo imaging would enable monitoring of these signals at speeds commensurate with signaling in the brain.The pixel rate bottleneck can be avoided by efficient sampling 1,4 . When recording activity, raster images are usually reduced to a lower-dimensional space after acquisition, e.g. by selecting regions of interest 12,13 . Random-Access Microscopy 14-16 samples that space more directly by only scanning targeted sets of pixels, with an access time cost to move between targets. When targets are suf...

show abstract

Multiplicative Updates for Optimization Problems with Dynamics

Cited by 3 publications

References 26 publications

Kilohertz frame-rate two-photon tomography

Kilohertz frame-rate two-photon tomography

Bayesian Allocation Model: Inference by Sequential Monte Carlo for Nonnegative Tensor Factorizations and Topic Models using Polya Urns

Kilohertz frame-rate two-photon tomography

Contact Info

Product

Resources

About