Daryl Hochman: May 29th

Title: Optical Imaging Data Acquired From the Human Brain

Abstract: The amount of light absorbed and scattered by brain tissue is altered by neuronal activity. Imaging of “intrinsic optical signals” (ImIOS) is the technique of mapping these dynamic optical changes with high spatial and temporal resolution.  ImIOS of the exposed brains of awake patients, performed during their neurosurgical treatment for intractable epilepsy, has unique advantages for studying certain aspects of the human brain.  Better methods for the analysis and visualization of ImIOS data are motivated by at least two reasons.  First, ImIOS can be used for investigating basic biological questions concerning the regulation of blood flow in the human brain during normal and epileptic activity.  Second, optical imaging has the potential to be a practical clinical tool for localizing functional and epileptic brain regions in the operating room.  My talk will focus on explaining the types of questions that can be investigated with optical imaging of the human brain, and illustrating the spatial and temporal features of these types of data that could benefit from better methods for their visualization and analysis.

A couple of relevant references:
1) https://www.ncbi.nlm.nih.gov/pubmed/21640137
2) https://www.ncbi.nlm.nih.gov/pubmed/1495561

Lars Buesing: May 22nd

Title: Dynamical System Models for Characterizing Multi-Electrode Recordings of Cortical Population Activity

Abstract: Multi-electrode techniques now make it possible to record from up to hundreds of cortical neurons simultaneously, and thus open the door to unprecedented insights into cortical neural population activity and the associated computations. However, in order to exploit this potential we need computationally tractable statistical methods that are able to see beyond signal and variability in individual neurons to structured activity that underlies reliable population computation. Such methods will very likely depend on analyzing the activity of the ensemble as a whole, rather than on simple single-neuron or pairwise analysis. In this talk I will argue that Dynamical System models, and more specifically Linear Dynamical Systems with Poisson observations (PLDS), meet these desiderata, while at the same time providing a parsimonious, statistically accurate description of the data. I will present a fast, robust algorithm for fitting PLDS models, which is based on spectral subspace methods. This algorithm substantially improves over standard approximate Expectation-Maximization for PLDS models in terms of both computational efficiency as well as quality of estimated parameters, hence greatly facilitating the application of these models to real multi-electrode recordings. Finally, I will show how Dynamical System models can be used to characterize fundamental dynamical properties of multi-electrode recordings from motor areas of awake, behaving macaque monkeys.This analysis reveals that different epochs of task-relevant behavior manifest themselves in different dynamics of the recorded neural population.

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.