Solène Thépaut | Searcharxiv

arXiv2022

Construction and Elicitation of a Black Box Model in the Game of Bridge

We address the problem of building a decision model for a specific bidding situation in the game of Bridge. We propose the following multi-step methodology i) Build a set of examples for the decision problem and use simulations to associate a decision to each example ii) Use supervised relational learning to build an accurate and readable model iii) Perform a joint analysis between domain experts and data scientists to improve the learning language, including the production by experts of a handmade model iv) Build a better, more readable and accurate model.

cs.AI↗

arXiv2021

Optimal Estimation of Schatten Norms of a rectangular Matrix

We consider the twin problems of estimating the effective rank and the Schatten norms $\|{\bf A}\|_{s}$ of a rectangular $p\times q$ matrix ${\bf A}$ from noisy observations. When $s$ is an even integer, we introduce a polynomial-time estimator of $\|{\bf A}\|_s$ that achieves the minimax rate $(pq)^{1/4}$. Interestingly, this optimal rate does not depend on the underlying rank of the matrix. When $s$ is not an even integer, the optimal rate is much slower. A simple thresholding estimator of the singular values achieves the rate $(q\wedge p)(pq)^{1/4}$, which turns out to be optimal up to a logarithmic multiplicative term. The tight minimax rate is achieved by a more involved polynomial approximation method. This allows us to build estimators for a class of effective rank indices. As a byproduct, we also characterize the minimax rate for estimating the sequence of singular values of a matrix.

math.ST↗