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

Volker Pernice: March 27th 

Title: Correlations and connectivity in populations of neurons

Abstract: Due to their ubiquity in experiments and their importance for neural network dynamics and function, covariances between neural spike trains have been studied extensively. Their origin and their relation to the structure of the network of synaptic connections can be understood in the framework of linearly interacting point processes. This model also approximately describes the covariances in networks of leaky integrate-and-fire neurons. Because direct as well as indirect connections generate covariances, the solution to the inverse problem of inferring network structure from covariances is not unique. However, the ambiguity can partly be resolved under the assumption of a sparse network.

Josh Merel: March 20

Josh will talk about single index models and multiple index models. Some references:

  

  -  example single index model estimation - http://snowbird.djvuzone.org/2008/abstracts/183.pdf

  -  newer (better?) single index model estimation - http://arxiv.org/abs/1104.2018

  -  a video-lecture on this stuff and applications - http://videolectures.net/nipsworkshops2012_ravikumar_single/

   - previous well-known work employing Bregman divergence (for reference) - http://jmlr.csail.mit.edu/papers/volume6/banerjee05b/banerjee05b.pdf

If there is time he will also review spike train kernels and propose a (new?) kernel - looking for feedback on this.  Some references:

    - easier version - http://arxiv.org/abs/1302.5964

    - full version - http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00309?journalCode=neco

    - antecedent work - http://www.magicbroom.info/Papers/ShpigelmanSiPaVa05.pdf

Arian Maleki: March 13


Title: Minimax image denoising via anisotropic nonlocal means


Abstract: Image denoising is a fundamental primitive in image processing and computer vision. Denoising algorithms have evolved from the classical linear and median filters to more modern schemes like total variation denoising, wavelet thresholding, and bilateral filters. A particularly successful denoising scheme is the nonlocal means (NLM) algorithm, which estimates each pixel value as a weighted average of other, similar noisy pixels. I start my talk by proving that the popular nonlocal means (NLM) denoising algorithm does not "optimally" denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses in order to set its smoothing weights. In response, I introduce the anisotropic nonlocal means (ANLM) algorithm and prove that it is near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin, up to 2dB in mean square error.

Cosyne Wrap-up: March 5

Will do a post-Cosyne wrap-up. We will talk about interesting posters, talks and gossip.