Exploring Discrete Splines and Trend Filtering in Mathematics

Episode 121

I spoke with Professor Ryan Tibshirani about:

* Differences between the ML and statistics communities in scholarship, terminology, and other areas.

* Trend filtering

* Why you can’t just use garbage prediction functions when doing conformal prediction

Ryan is a Professor in the Department of Statistics at UC Berkeley. He is also a Principal Investigator in the Delphi group. From 2011-2022, he was a faculty member in Statistics and Machine Learning at Carnegie Mellon University. From 2007-2011, he did his Ph.D. in Statistics at Stanford University.

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Outline:

* (00:00) Intro

* (01:10) Ryan’s background and path into statistics

* (07:00) Cultivating taste as a researcher

* (11:00) Conversations within the statistics community

* (18:30) Use of terms, disagreements over stability and definitions

* (23:05) Nonparametric Regression

* (23:55) Background on trend filtering

* (33:48) Analysis and synthesis frameworks in problem formulation

* (39:45) Neural networks as a specific take on synthesis

* (40:55) Divided differences, falling factorials, and discrete splines

* (41:55) Motivations and background

* (48:07) Divided differences vs. derivatives, approximation and efficiency

* (51:40) Conformal prediction

* (52:40) Motivations

* (1:10:20) Probabilistic guarantees in conformal prediction, choice of predictors

* (1:14:25) Assumptions: i.i.d. and exchangeability — conformal prediction beyond exchangeability

* (1:25:00) Next directions

* (1:28:12) Epidemic forecasting — COVID-19 impact and trends survey

* (1:29:10) Survey methodology

* (1:38:20) Data defect correlation and its limitations for characterizing datasets

* (1:46:14) Outro

Links:

* Ryan’s homepage

* Works read/mentioned

* Nonparametric Regression

* Adaptive Piecewise Polynomial Estimation via Trend Filtering (2014) 

* Divided Differences, Falling Factorials, and Discrete Splines: Another Look at Trend Filtering and Related Problems (2020)

* Distribution-free Inference

* Distribution-Free Predictive Inference for Regression (2017)

* Conformal Prediction Under Covariate Shift (2019)

* Conformal Prediction Beyond Exchangeability (2023)

* Delphi and COVID-19 research

* Flexible Modeling of Epidemics

* Real-Time Estimation of COVID-19 Infections

* The US COVID-19 Trends and Impact Survey and Big data, big problems: Responding to “Are we there yet?”