Research keywords

Methods

The statistical ideas our lab keeps returning to, drawn the way we sketch them on the whiteboard. Each links to the papers where we develop it.

Penalized regression splines, the thread through most of our work. We start from many candidate knots; the penalty keeps only a few, and the fitted curve bends only where the data asks it to.

Regression splines

Piecewise polynomials joined smoothly at knots. A B-spline basis turns curve estimation into estimating a handful of coefficients, which keeps models interpretable and fast to fit.

Papers [01] [07] [10] [17] [21] [26]

Total variation penalization

Penalizing the total variation of a derivative lets the data decide where the curve bends. Unneeded knots drop out, so the fit stays simple wherever the signal is simple.

Papers [01] [06] [07] [09] [11]

Change point detection

Abrupt shifts in a signal are found as knots with jumps. Adaptive and weighted penalties sharpen where the breaks are placed and cut down false alarms.

Papers [12] [18] [20] [31] [32]

Convex optimization

Non-smooth penalties meet smooth losses. We solve these problems with coordinate descent and ADMM, and study when and how fast the algorithms converge.

Papers [15] [22] [26] [30]

Splines on triangulations

For data on irregular two-dimensional domains, splines are built over a triangulation. A fusion penalty merges neighbouring triangles into a few polygons.

Papers [15]

Smoothing on the sphere

Trajectories on the sphere, such as polar wander paths and cyclone tracks, are smoothed intrinsically with piecewise geodesic curves, without tangent-plane distortion.

Papers [19] [23] [29]

Density estimation

Logspline, wavelet and Legendre polynomial bases estimate densities directly, with penalties that choose the right resolution from the data.

Papers [08] [09] [27]

Graph trend filtering

Signals observed on networks and regions are smoothed along the edges of a graph. Edges between different regimes are cut, revealing spatial boundaries.

Papers [30]