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.

David Blei: Feb 27th

Stochastic Variational Inference

Abstract:  We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Using stochastic variational inference, we analyze several large collections of documents: 300K articles from Nature, 1.8M articles from The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can handle the full data, and outperforms traditional variational inference on a subset. (Further, we show that the Bayesian nonparametric topic model outperforms its parametric counterpart.) Stochastic variational inference lets us apply complex Bayesian models to very large data sets.

You can read the paper here.

Carl Smith and Ari Pakman: Feb. 20

We review and present new results on spike-and-slab priors to impose sparsity in regression problems.

Outline:

- Why spike-and-slab?

- Variational Bayes approximation to the posterior

- Computing hyperparameters using Empirical Bayes.

- Singular and non-singular Markov Chains for MCMC.

- Gibbs sampler for the posterior sparsity variables.

- Extension to regression with positive coefficients.

- Example application: finding synaptic weights in a dendritic tree

Garud Iyengar: Feb 13

Title: Fast first-order augmented Lagrangian algorithms for sparse optimization problems

Abstract:

In this talk we will survey recent work on fast first-order algorithms for solving optimization problems with non-trivial conic constraints. These algorithms are augmented Lagrangian algorithms; however, unlike traditional augmented Lagrangian algorithms we update the penalty multiplier during the course of the algorithm. The algorithm iterates are epsilon-feasible and epsilon-optimal in O(log(1/epsilon))-multiplier update steps with an overal complexity of O(1/epsilon). We will discuss the key steps in the algorithm development and show numerical results for basis pursuit, principal component pursuit and stable principal component pursuit.

Joint work with N. Serhat Aybat (Penn State)

Michael Sobel: Dec. 19

The statistical literature on causal inference is based on notation that expresses the idea that a causal relationship sustains a counterfactual conditional (e.g, to say that taking the pill caused John to get better means John took the pill and got better and that had he not taken the pill, he would not have gotten better). Using this notation, causal estimands are defined and methods used to estimate these are evaluated for bias.

This talk is to introduce you to this notation and literature and to point to some issues such as mediation and interference that have been addressed (at least somewhat) in the literature that may be of interest and relevance to neuroscience.

Eftychios Pnevmatikakis: Dec 5

Tomorrow at 1PM I'm going to present some overview of the recent work on approximate message passing algorithms (AMP) with applications to compressed sensing (CS). 

I'm going to start with a brief overview of message passing algorithms [1] and then show how it was used in [2] to derive an AMP algorithm for the standard CS setup (basis pursuit, lasso). 

The time permitting I'm going to briefly present some extensions of this methodology to the case of more general graphical models [3]. 

Material will be drawn from the following sources:

[1] Kschischang, Frank R., Brendan J. Frey, and H-A. Loeliger. "Factor graphs and the sum-product algorithm." Information Theory, IEEE Transactions on 47.2 (2001): 498-519.

[2] Donoho, David L., Arian Maleki, and Andrea Montanari. "Message-passing algorithms for compressed sensing." Proceedings of the National Academy of Sciences 106.45 (2009): 18914-18919.

[3] Rangan, Sundeep, et al. "Hybrid approximate message passing with applications to structured sparsity." arXiv preprint arXiv:1111.2581 (2011).