David Pfau: May 15th


Title: Robust Learning of Low-Dimensional Dynamics from Large Neural Ensembles

Abstract:  Progress in neural recording technology has made it possible to record spikes from ever larger populations of neurons. To cope with this deluge, a common strategy is to reduce the dimensionality of the data, most commonly by principal component analysis (PCA). In recent years a number of extensions to PCA have been introduced in the neuroscience literature, including jPCA and demixed principal component analysis (dPCA). A downside of these methods is that they do not treat either the discrete nature of spike data or the positivity of firing rates in a statistically principled way. In fact it is common practice to smooth the data substantially or average over many trials, losing information about fine temporal structure and inter-trial variability.

A more principled approach is to fit a state space model directly from spike data, where the latent state is low dimensional. Such models can account for the discreteness of spikes by using point-process models for the observations, and can incorporate temporal dependencies into the latent state model. State space models can include complex interactions such as switching linear dynamics and direct coupling between neurons. These methods have drawbacks too: they are typically fit by approximate EM or other methods that are prone to local minima, the number of latent dimensions must be chosen ahead of time (though nonparametric Bayesian models could avoid this issue) and a certain class of possible dynamics must be chosen before doing dimensionality reduction.

We attempt to combine the computational tractability of PCA and related methods with the statistical richness of state space models. Our approach is convex and based on recent advances in system identification using nuclear norm minimization, a relaxation of matrix rank minimization. Our contribution is threefold. 1) Low-dimensional subspaces can be accurately recovered, even when the dynamics are unknown and nonstationary. 2) Spectral methods can faithfully recover the parameters of state space models when applied to data projected into the recovered subspace. 3) Low-dimensional common inputs can be separated from sparse local interactions, suggesting that these techniques could be useful for inferring synaptic connectivity.

Suraj Keshri: May 8th


Title: Inferring neural connectivity

Abstract: Advances in large-scale multineuronal recordings have made it possible to study the simultaneous activity of complete ensembles of neurons. These techniques in principle provide the opportunity to discern the architecture of neuronal networks. However, current technologies can sample only small fraction of the underlying circuitry, therefore unmeasured neurons probably have a large collective impact on network dynamics and coding properties For example, it is well understood that common input plays an essential role in the interpretation of pairwise cross-correlograms. To infer the correct connectivity and computations in the circuit requires modelling tools that account for unrecorded neurons. We develop a model for fast inference of neural connectivity under the constraint that we only observe a subset of neurons in the population at a time.

Ben Shababo: May 1st


Title: Optimal Sequential Stimulation of Neural Populations For Inferring Functional Connectivity

Abstract: In this talk, we will review ongoing work in which we use methods from Bayesian experimental design, a subset of Active Learning, to guide an circuit mapping experiment. Specifically, the experimental paradigm we assume includes the recording of some output from a single cell - such as membrane voltage or current - and the ability to stimulate some subset of nearby neurons. The goal of the experiment is to learn the vector of weights that describe the influence of the cells we can stimulate on the cell we are recording from. In Bayesian experimental design the objective is to maximize the mutual information between the data and the parameters one wishes to learn which in turn entails a probabilistic model. For our model, we use a spike-and-slab prior on the weights with a linear gaussian likelihood. Furthermore, since this algorithm must perform in an online setting, we speed up the algorithm by approximating the optimization with a greedy version of the algorithm and by using online Bayesian updating of the posterior during stimulus selection. We will present results that show that within a specific regime our procedure outperforms random stimulation. We will also present some ideas we are currently incorporating into our model to make it more robust and applicable for the current state of experimental technology.

David Greenberg: April 24th 

Title: Accurate Optical AP Detection During ‘Natural’ Behavior: Two Inference Problems

Abstract: Two-photon calcium imaging can detect single action potentials in populations of spatially resolved neurons in vivo, but using it to quantitatively compare spiking and behavior requires solving several problems of analysis and experimental technique. This talk will focus on two such problems: accurately inferring spike counts from fluorescence signals, and measuring visual input in freely moving animals. For optical action potentials detection several algorithms exist along with a growing corpus of ground truth datasets. I will describe these as well as some current work to develop algorithms that are effective on a wide range of in vivo data, to develop metrics for testing spike inference, and to create a public database of ground truth measurements. In the second half of my talk, I will describe a system for eye tracking in freely moving rats compatible with two-photon imaging through optical fibers. I will also briefly describe some insights into the activity of cortical populations and rodent visual behavior provided by these methods.

Kamiar Rahnama Rad: April 17th

Title: A simple proof for the Marchenko-Pastur law

Abstract: I review the proof of the Wigner semicircle law for Wigner matrices using the Stieltjes transform method described here. Using this method, I will present a new simple proof to the old Marchenko-Pastur law, which describes the asymptotic behavior of singular values of large sample covariance matrices.

Attila Losonczy: April 10th 

Title: Functional imaging hippocampal microcircuits in behaving mice.

Abstract: I my talk I will introduce recently developed methods for functional two-photon imaging genetically and anatomically-defined cellular and subcellular components of the hippocampal CA1 microcircuit in awake behaving  mice. I will review some advantages of this approach as well as current experimental and analytical challenges to dissect the role of identified presynaptic and postsynaptic circuit motifs in hippocampal memory behaviors.

Eftychios Pnevmatikakis: April 3rd

Title: A brief introduction to determinantal point processes

Abstract: a brief introduction to determinantal point processes, a class of probabilistic models that model global negative interactions, yet allow for tractable inference. Material will be drawn from http://arxiv.org/abs/1207.6083  from (chapters 1-4). Time permitting, we will also discuss the approach of this paper: http://books.nips.cc/papers/files/nips25/NIPS2012_1357.pdf