Projects per year
Personal profile
Research interests
I work on problems at the boundary of probability theory, statistics and information theory.
I have recently been working on the group testing problem. This is a combinatorial search problem, which acts as a prototype of a wider class of sparse inference problems in estimation and statistics. I have developed the idea of rate and capacity of algorithms, and proved a range of theoretical performance guarantees for them in this sense. I am also interested in the idea of converse bounds: that is to show what performance is optimal. This has included recent work to extend the standard Fano-based bounds in statistical inference problems to a sharper criterion based on Renyi entropy.
I am interested in the relationship between properties of entropy and limit theorems, such as the Central Limit Theorem and Law of Small Numbers (Poisson convergence). This includes trying to understand relationships between information-theoretic properties such as the Entropy Power Inequality and maximum entropy theorems and probabilistic ideas such as log-Sobolev inequalities and transportation of measure. I have a particular interest in developing discrete analogues of these results.
I also work on more applied problems relating to communications. I have a particular interest in characterizing `best possible' performance of algorithms or communication schemes, using information-theoretic ideas. This includes an interest in interference mitigation schemes such as Interference Alignment, and spectrum sensing as an application of group testing.
PhD Projects
All the topics mentioned above can potentially lead into research projects (with almost no pre-requisites), and I would be happy to discuss them by email with any potential applicant.
My more applied work includes links with Electrical Engineering and Computer Science, and I am happy to participate in other interdisciplinary projects.
Fingerprint
- 1 Similar Profiles
Collaborations and top research areas from the last five years
-
-
-
Efficient entropy-based detection of Change-Points in Streaming Data
1/07/10 → 1/01/11
Project: Research
Research output
-
Information theory and the central limit theorem
Johnson, OT., 2004, Imperial College Press. 224 p.Research output: Book/Report › Authored book
-
Discrete versions of the transport equation and the Shepp–Olkin conjecture
Hillion, E. & Johnson, O. T., 2 Feb 2016, In: Annals of Probability. 44, 1, p. 276-306 31 p.Research output: Contribution to journal › Article (Academic Journal) › peer-review
File5 Citations (Scopus)358 Downloads (Pure) -
Group testing: an information theory perspective
Aldridge, M., Johnson, O. & Scarlett, J., 5 Dec 2019, In: Foundations and Trends in Communications and Information Theory. 15, 3-4, p. 196-392 196 p.Research output: Contribution to journal › Review article (Academic Journal) › peer-review
Open AccessFile127 Citations (Scopus)435 Downloads (Pure)
-
Various public talks on the value of mathematics
Oliver T Johnson (Advisor)
30 May 2023 → 31 Dec 2024Activity: Talk or presentation types › Public talk, debate, discussion
-
Six interviews re coronavirus statistics on BBC Radio 4 PM
Oliver T Johnson (Speaker)
18 Jun 2020 → 1 Aug 2022Activity: Other activity types › Media coverage or participation
-
Panellist at Royal Society COVID wrap up event
Oliver T Johnson (Advisor)
13 Jun 2022Activity: Talk or presentation types › Public talk, debate, discussion