When I was a naive undergraduate and disenchanted with the prospect of becoming a math professor, I enrolled in graduate school at MIT to work on computer music. My career as an electroacoustic scholar ended quickly but opened my eyes to the world of interactive sound art. In this talk, …
Identification of the nature of interactions between different cortical regions is an important step towards better understanding of healthy and diseased brain function. Electroencephalography (EEG) and magnetoencephalography (MEG) offer a window on the electrical behavior of cortical neuronal populations through non-invasive measurement of the electric and magnetic fields, respectively, they …
The fact that sparse vectors can be recovered from a small number of linear measurements has important and exciting implications for engineering and statistics. However, despite the vast amount of recent work in the field of compressed sensing, a sharp characterization between what can and cannot be recovered in the …
A self-contained lecture on the Discrete Fourier Transform and its relation to the time and frequency representations of a signal. By describing time-shift and frequency-shift operators with a structure known as the Heisenberg group, explicit steps can be given for producing an FFT algorithm. Pseudocode and programmable examples will be …
Learning/estimating networks from multi-variate time series data is an important problem that arises in many applications including computational neuroscience, social network analysis, and any others. Prior approaches either do not scale to multiple time series or rely on very restrictive parametric assumptions. In this talk, I present two approaches that …
The Belgian chocolate problem asks for the range of a process parameter for which simultaneous stabilization of three processes by a rational controller is possible. In this talk I introduce a new algebraic method that produces solutions with larger process parameters than standard optimization techniques yield. These solutions turn out …
This talk presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of the subspace. The algorithm is derived …
The arithmetic-geometric mean inequality states that the arithmetic mean of a set of positive numbers is always greater than the geometric mean unless all of the numbers are equal to one another. Does a similar inequality hold for positive definite matrices? The answer is not straightforward as positive definite matrices …
One of the major driving forces in the area of applied and computational harmonic analysis during the last two decades is the development and the analysis of redundant systems that produce sparse approximations for classes of functions of interest. Such redundant systems include wavelet frames, ridgelets, curvelets and shearlets, to …
The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. In this talk, I introduce a simple algorithm, termed one-step thresholding (OST) algorithm, for model-order agnostic model selection in linear inference problems. I …