Will Fithian: October 22nd

Optimal Inference After Model Selection

To perform inference after model selection, we propose controlling the selective type I error; i.e., the error rate of a test given that it was performed. By doing so, we recover long-run frequency properties among selected hypotheses analogous to those that apply in the classical (non-adaptive) context. Our proposal is closely related to data splitting and has a similar intuitive justification, but is more powerful. Exploiting the classical theory of Lehmann and Scheffe (1955), we derive most powerful unbiased selective tests and confidence intervals for inference in exponential family models after arbitrary selection procedures. For linear regression, we derive new selective z-tests that generalize recent proposals for inference after model selection and improve on their power, and new selective t-tests that do not require knowledge of the error variance.

This is joint work with Dennis Sun and Jonathan Taylor, available online at http://arxiv.org/abs/1410.2597

Dean Freestone: October 15th

Data-Driven Mean Field Neural Modeling

Abstract: This research provides an overview of new methods for functional brain mapping via a process of model inversion. By estimating parameters of a computational model, we demonstrate a method for tracking functional connectivity and other parameters that influence neural dynamics. The estimation results provide an imaging modality of neural processes that cannot be directly measured using electrophysiological measurements alone.
The method is based on approximating brain networks using an interconnected neural mass model. Neural mass models describe the functional activity of the brain from a top-down perspective, capturing particular important experimental phenomena. The models can be related to biology by lumped quantities, where for example, the resting-membrane potentials, reversal potentials and firing thresholds are all lumped into one parameter. The lumping of parameters is a result of a trade-off between biological realism, where insights into brain mechanisms can still be gained, and parsimony, where models can be inverted and fit to patient-specific data.
The ability to track the hidden aspects of neurophysiology will have a profound impact on the way we understand and treat epilepsy. For example, the framework will provide insights into seizure initiation and termination on a patient-specific basis. It will enable investigation into the effect a particular drug has on specific neural populations and connectivity structures using minimally invasive measurements.

Bio: Dr Freestone is currently a Senior Research Fellow in the Department of Medicine for St. Vincent’s Hospital at the University of Melbourne, Australia, and Fulbright Post-Doctoral Scholar at Columbia University, USA. He has previously completed a Post-Doc position at the University of Melbourne in the NeuroEngineering Research Group. He completed his PhD at the University of Melbourne, Australia and the University of Edinburgh, UK. His work has focused on developing methods for epileptic seizure prediction and control.

Ran Rubin: October 8th

Supervised Learning and Support Vectors for Deterministic Spiking Neurons

To signal the onset of salient sensory features or execute well-timed motor sequences, neuronal circuits must transform streams of incoming spike trains into precisely timed firing. In this talk I will investigate the efficiency and fidelity with which neurons can perform such computations. I'll present a theory that characterizes the capacity of feedforward networks to generate desired spike sequences and discuss its results and implications. Additionally, I'll present the Finite Precision algorithm: a biologically plausible learning rule that allows feedforward and recurrent networks to learn multiple mappings between inputs and desired spike sequences with preassigned required precision. This framework can be applied to reconstruct synaptic weights from spiking activity. Time permitting, I'll present further theoretical developments that extend the concept of 'large-margin' to dynamical systems with event based outputs, such as spiking neural networks. These extensions allow us to define optimal solutions that implement the required input-output transformation in a robust manner and open the way for incorporating dynamic, non-linear, spatio-temporal integration through the use of the kernel method.

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