Notes on computational-to-statistical gaps: predictions using statistical physics

  • Afonso Bandeira

    Courant Institute, New York University, USA
  • Amelia Perry

    Massachusetts Institute of Technology, Cambridge, USA
  • Alexander S. Wein

    Courant Institute, New York University, USA

Abstract

In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances. The methods we describe here are based on mature, albeit non-rigorous, tools from statistical physics.

Cite this article

Afonso Bandeira, Amelia Perry, Alexander S. Wein, Notes on computational-to-statistical gaps: predictions using statistical physics. Port. Math. 75 (2018), no. 2, pp. 159–186

DOI 10.4171/PM/2014