@article {65047, title = {Multiplicative updates for optimization problems with dynamics.}, journal = {IEEE Xplore}, year = {2018}, month = {2018 Apr 16}, abstract = {

We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative deconvolution, point-process smoothing, ML estimation for Poisson Observations, nonnegative least squares and nonnegative matrix factorization (NMF). Our algorithm can also account for temporal and spatial structure and regularization. We will analyze the performance of our algorithm on simultaneously recorded neuronal calcium imaging and electrophysiology data.

}, doi = {10.1109/ACSSC.2017.8335723}, author = {Abbas Kazemipour and Behtash Babadi and wu, min and Podgorski, Kaspar and Shaul Druckmann} } @article {47957, title = {Sampling Requirements for Stable Autoregressive Estimation}, journal = {CoRR}, volume = {abs/1605.01436}, year = {2016}, abstract = {

We consider the problem of estimating the parameters of a linear autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the\ l1-regularized least squares as well as a greedy estimator of the parameters and characterize the sampling trade-offs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear models where the covariates are i.i.d. and independent of the observation history to autoregressive processes with highly inter-dependent covariates. We also derive sufficient conditions on the sparsity level that guarantee the minimax optimality of the\ l1-regularized least squares estimate. Applying these techniques to simulated data as well as real-world datasets from crude oil prices and traffic speed data confirm our predicted theoretical performance gains in terms of estimation accuracy and model selection.

}, url = {http://arxiv.org/abs/1605.01436}, author = {Abbas Kazemipour and Sina Miran and Piya Pal and Behtash Babadi and Min Wu} } @article {47956, title = {Robust estimation of self-exciting point process models with application to neuronal modeling.}, journal = {CoRR}, volume = {abs/1507.03955}, year = {2015}, abstract = {

We consider the problem of estimating discrete selfexciting point process models from limited binary observations, where the history of the process serves as the covariate. We analyze the performance of two classes of estimators, namely the {\textquoteleft}1-regularized maximum likelihood and greedy estimators, for a canonical self-exciting point process and characterize the sampling tradeoffs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear and generalized linear models with i.i.d. covariates to point processes with highly inter-dependent covariates. We further provide simulation studies as well as application to real spiking data from mouse{\textquoteright}s lateral geniculate nucleus and ferret{\textquoteright}s retinal ganglion cells which agree with our theoretical predictions.

}, url = {http://arxiv.org/abs/1507.03955}, author = {Abbas Kazemipour and Min Wu and Behtash Babadi} }