Ph.D. Candidate in Electrical Engineering |

I study information theory, statistics, and geometry in Professor Ayfer Özgür's group. Before that I received a B.S. in Mathematics, B.S. in Electrical Engineering, and M.Eng. in Electrical Engineering and Computer Science all from the Massachusetts Institute of Technology. I'm currently working on isoperimetric inequalities and other geometric problems; and their application to multiterminal communication and statistical estimation. My Google scholar page can be found here.

**Projects:**

Statistical Estimation from Rate-Limited Samples: In this project we are investigating the problem of estimating a potentially high-dimensional parameter from quantized statistical samples. Quantization of data is of interest in many different settings, such as in machine learning systems where data is distributed across different machines or generated in a distributed fashion, and it needs to be communicated efficiently while preserving maximal information about an underlying parameter of interest. We have developed a geometric interpretation of the Fisher information from quantized statistical samples, and are using it develop tight bounds on the minimax risk for a variety of estimation problems.

Isoperimetric Inequalities and the Geometry of the Relay Channel: Since its inception in 1948, one of the main goals in information theory has been to extend its original scope of point-to-point communication to include networks of nodes exchanging information. In this project, we are developing a geometric framework for analyzing the capacity of networks, along with new tools related to high-dimensional geometry that can applied in this framework. In particular, we have developed a new isoperimetric result on high-dimensional spheres that led to a solution to a decades old conjecture about the capacity of the relay channel.

**Journal Articles:**

L. Barnes, Y. Han, A. Ozgur, Learning Distributions from their Samples under Communication Constraints, arxiv, 2019.[pdf]

L. Barnes, A. Ozgur, X. Wu, An Isoperimetric Result on High-dimensional Spheres, submitted, 2018.[pdf]

X. Wu, L. Barnes and A. Ozgur, "The capacity of the relay channel:" Solution to Cover's problem in the Gaussian Case, IEEE Transactions on Information Theory, Jan 2018.[pdf]

L. Barnes, G. Verghese, Uniform FIR Approximation of Causal Wiener Filters with Applications to Causal Coherence, Signal Processing, 2016.

**Conference Papers:**

L. Barnes, Y. Han, A. Ozgur, A Geometric Characterization of Fisher Information from Quantized Samples with Applications to Distributed Statistical Estimation, Proc. IEEE Allerton Conference on Communication, Control, and Computing (Allerton), 2018.[pdf]

X. Wu, L. Barnes, and A. Ozgur, The Geometry of the Relay Channel, Proc. IEEE International Symposium on Information Theory (ISIT), 2017.

L. Barnes, X. Wu, A. Ozgur, A solution to Cover's problem for the binary symmetric relay channel: Geometry of sets on the Hamming sphere, Proc. IEEE Allerton Conference on Communication, Control, and Computing (Allerton), 2017.

X. Wu, L. Barnes, and A. Ozgur, Cover’s Open Problem: “The Capacity of the Relay Channel”, Proc. IEEE Allerton Conference on Communication, Control, and Computing (Allerton), 2016.

**Teaching:**

STATS311/EE377 Information Theory and Statistics (Winter 2019)

EE261 The Fourier Transform (Summer 2018)

CME100 Vector Calculus for Engineers (Winter 2018)

EE261 The Fourier Transform (Summer 2017)

EE278 Statistical Signal Processing (Winter 2017)

EE261 The Fourier Transform (Summer 2016)