Roy Fox: September 24th

Optimal Selective Attention and Action in Reactive Agents

Intelligent agents, interacting with their environment, operate under constraints on what they can observe and how they can act. Unbounded agents can use standard Reinforcement Learning to optimize their inference and control under purely external constraints. Bounded agents, on the other hand, are subject to internal constraints as well. This only allows them to partially notice their observations, and to partially intend their actions, requiring rational selection of attention and action.

In this talk we will see how to find the optimal information-constrained policy in reactive (memoryless) agents. We will discuss a number of reasons why internal constraints are often best modeled as bounds on information-theoretic quantities, and why we can focus on reactive agents with hardly any loss of generality. We will link the solution of the constrained problem to that of soft clustering, and present some of its nice properties, such as principled dimensionality reduction.

Søren Hauberg: September 10th

Grassmann Averages for Scalable Robust PCA 

As the collection of large datasets becomes increasingly
automated, the occurrence of outliers will increase --
or in terms of buzzwords: "big data implies big outliers".
While principal component analysis (PCA) is often used
to reduce the size of data, and scalable solutions exist,
it is well-known that outliers can arbitrarily corrupt
the results. Unfortunately, state-of-the-art approaches
for robust PCA do not scale beyond small-to-medium sized
datasets. To address this, we introduce the Grassmann
Average (GA), which expresses dimensionality reduction
as an average of the subspaces spanned by the data.
Because averages can be efficiently computed, we immediately
gain scalability. GA is inherently more robust than PCA,
but we show that they coincide for Gaussian data.
We exploit that averages can be made robust to formulate
the Robust Grassmann Average (RGA) as a form of robust PCA.
Robustness can be with respect to vectors (subspaces) or
elements of vectors; we focus on the latter and use a
trimmed average. The resulting Trimmed Grassmann Average
(TGA) is particularly appropriate for computer vision
because it is robust to pixel outliers.
The algorithm has low computational complexity and minimal
memory requirements, making it scalable to "big noisy data."
We demonstrate TGA for background modeling, video restoration,
and shadow removal. We show scalability by performing robust
PCA on the entire Star Wars IV movie; a task beyond any
currently existing method.

Work in collaboration with Aasa Feragen (DIKU) and Michael
J. Black (MPI-IS).

Brian London: September 2nd

Characterizing the oscillatory neural dynamics of voluntary motion

Daniel Soudry: July 9th

We will discuss the following book chapter:

F. Bach, R. Jenatton, J. Mairal and G. Obozinski. Convex optimization with sparsity-inducing norms. In S. Sra, S. Nowozin, S. J. Wright., editors, Optimization for Machine Learning, MIT Press, 2011.

http://www.di.ens.fr/~fbach/opt_book.pdf

Vamsi Krishna Potluru: July 2nd

Efficient Sparse NMF for fMRI data analysis

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L0 norm, however its optimization is NP-hard. Mixed norms, such as L1/L2 measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L1 norm. However, present algorithms designed for optimizing the mixed norm L1/L2 are slow and other formulations for sparse NMF have been proposed such as those based on L1 and L0 norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacri ficing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets [1]. Also, recently, its computational efficiency has been exploited for evaluating the sparse NMF model for fMRI analysis [2]. And the authors show that the sparse NMF model is competitive with other state-of-the-art matrix factorization methods such as ICA, sparse PCA and even restricted Boltzmann machines.

Links: 

1. http://arxiv.org/abs/1301.3527

2. http://www.sciencedirect.com/science/article/pii/S1053811914002080

Home: http://www.vamsi.guru

Winrich Freiwald: June 25th

Faces, Attention, and the Temporal Lobe

Josh Merel: June 4th

Josh will present about linear matrix inequalities and their relevance for control theory problems.

References:
"Linear Matrix Inequalities in System and Control Theory"
"Linear Controller Design: Limits of Performance" (both by Boyd).