Gold Order	B-TSort Order	B-AON Order
NIPS Dataset
we study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. we show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch. In particular, we use this approach to obtain sparse principal components and show that for m data points in n dimensions, o(-2k maxm, n) elements gives an - additive approximation to the sparse PCA problem (k is the stable rank of the data matrix). we demonstrate our algorithms extensively on image, text, biological and financial data. the results show that not only are we able to recover the sparse pcas from the incomplete data, but by using our sparse sketch, the running time drops by a factor of five or more.	we study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. we show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch. In particular, we use this approach to obtain sparse principal components and show that for m data points in n dimensions, o(-2k max, n) elements gives an - additive approximation to the sparse PCA problem (k is the stable rank of the data matrix). we show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch. The results show that not only are we able to recover the sparse pcas from the incomplete data, but by using our sparse sketch, the running time drops by a factor of five or more. we demonstrate our algorithms extensively on image, text, biological and financial data.	we study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. in particular, we use this approach to obtain sparse principal components and show that for m data points in n dimensions, o(-2k maxm, n) elements gives an - additive approximation to the sparse PCA problem (k is the stable rank of the data matrix). we show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch. The results show that not only are we able to recover the sparse pcas from the incomplete data, but by using our sparse sketch, the runningtime drops by a factor of five or more. we demonstrate our algorithms extensively on image, text, biological and financial data.
we develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types . a natural model for chromatin data in one cell type is a hidden markov model (hmm) ; we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure . the main challenge with learning parameters of such models is that iterative methods such as em are very slow , while naive spectral methods result in time and space complexity exponential in the number of cell types . we exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets . we provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types . finally , we show that beyond our specific model , some of our algorithmic ideas can be applied to other graphical models .	a natural model for chromatin data in one cell type is a hidden markov model (hmm) ; we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure . the main challenge with learning parameters of such models is that iterative methods such as em are very slow , while naive spectral methods result in time and space complexity exponential in the number of cell types . we develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types . we exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets . we provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types . finally , we show that beyond our specific model , some of our algorithmic ideas can be applied to other graphical models .	the main challenge with learning parameters of such models is that iterative methods such as em are very slow , while naive spectral methods result in time and space complexity exponential in the number of cell types . a natural model for chromatin data in one cell type is a hidden markov model (hmm) ; we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure . 'we develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types . we exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets . we provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types . finally , we show that beyond our specific model , some of our algorithmic ideas can be applied to other geographical models .