Ronen Talmon Thesis

In this work we consider the problem of estimating a covariance matrix subject to both types of models simultaneously.We demonstrate the attractiveness of the combined model and propose a novel estimator to address it.When one examines longer substrings of DNA, they appear less repetitive, or more unique; permutations-based algorithms benefit from this property.

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imaging of mixtures of different types of molecules.

I work on “” which represent heterogeneous molecules as higher-dimension objects.

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The first of these is a latent linear factor model, also strongly related to PCA, which is manifested as a low rank component in the covariance matrix.

The second is undirected graphical model structure (Markov random field), which is related to presence of zeros in the inverse covariance (precision) matrix.

In 2015-2018 I was a postdoc in the Program in Applied and Computational Mathematics at Princeton University, working with Amit Singer.

In 2014-2015 I was a Gibbs Assistant Professor in the Applied Mathematics Program at Yale University, where I also got my Ph D, working with Vladimir Rokhlin and Raphy Coifman.

We show that our estimator outperforms other alternatives on both synthetic and real-world data, explore a few of its theoretical properties such as consistency, and develop a fast algorithm for solving the associated optimization problem.

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