feldman (at) math.utah.edu),
Victoria Kala (victoria.kala (at) utah.edu),
or Akil Narayan (akil (at) sci.utah.edu)Monday, September 21 at 4pm. In-person LCB 222
Speaker: Jared Whitehead
Department of Mathematics, Brigham Young University
Title: The Generalized Aliasing Decomposition (GAD): a complete explanation of complicated risk curves in regression
Abstract:
A central problem in data science is to use potentially noisy samples of an unknown function to predict function values for unseen inputs. In classical statistics, the predictive error is understood as a trade-off between the bias and the variance that balances model simplicity with its ability to fit complex functions. However, overparameterized models exhibit counterintuitive behaviors, such as "double descent" in which models of increasing complexity exhibit decreasing generalization error. Other models may exhibit more complicated patterns of predictive error with multiple peaks and valleys. Neither double descent nor multiple descent phenomena are well explained by the bias-variance decomposition. We introduce a decomposition that we call the generalized aliasing decomposition (GAD) to explain the relationship between predictive performance and model complexity. The GAD decomposes the predictive error into three parts: (1) model insufficiency, which dominates when the number of parameters is much smaller than the number of data points, (2) data insufficiency, which dominates when the number of parameters is much greater than the number of data points, and (3) generalized aliasing, which dominates between these two extremes. We demonstrate the applicability of the GAD to diverse applications, including random feature models from machine learning, Fourier transforms from signal processing, solution methods for differential equations, and predictive formation enthalpy in materials discovery. Because key components of the generalized aliasing decomposition can be explicitly calculated from the relationship between model class and samples without seeing any data labels, it can answer questions related to experimental design and model selection before collecting data or performing experiments. We further demonstrate this approach on several examples and discuss implications for predictive modeling and data science.
Monday, November 9 at 4pm. In-person LCB 222
Speaker: Kenneth Beard
Department of Mathematics, University of Utah
Title: TBD
Abstract: TBD
Monday, November 16 at 4pm. In-person LCB 222
Speaker: Bohan Chen
Caltech
Title: TBD
Abstract: TBD
Monday, November 23 at 4pm. In-person LCB 222
Speaker: Zhongjian Wang
Division of Mathematical Sciences, Nanyang Technological University
Title: TBD
Abstract: TBD
Monday, November 30 at 4pm. In-person LCB 222
Speaker: Shivani Prabala
University of Michigan
Title: TBD
Abstract: TBD
feldman (at) math.utah.edu),
Victoria Kala (victoria.kala (at) utah.edu),
and
Akil Narayan (akil (at) sci.utah.edu).
Past lectures: Spring 2026, Fall 2025, Spring 2025, Fall 2024, Spring 2024, Fall 2023, Spring 2023, Fall 2022, Spring 2022, Fall 2021, Spring 2021, Fall 2020, Spring 2020, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017, Spring 2017, Fall 2016, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.