Related papers: SPM Bulletin 33
The single defining relation of the algebra of $SL_3\times SL_3$-invariants of triples of $3\times 3$ matrices is explicitly computed. Connections to some other prominent algebras of invariants are pointed out.
We consider a model where a subset of candidates must be selected based on voter preferences, subject to general constraints that specify which subsets are feasible. This model generalizes committee elections with diversity constraints,…
When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…
This paper presents a taxonomy for analytical spreadsheet models. It considers both the use case that a spreadsheet is meant to serve, and the engineering resources devoted to its development. We extend a previous three-type taxonomy, to…
For $a \neq 1$ and $p$ prime, we define numbers of the form $pa^2$ to be Square-Prime (SP) Numbers. For example, 75 = 3 $\cdot$ 25; 108 = 3 $\cdot$ 36; 45 = 5 $\cdot$ 9. These numbers are listed in the OEIS as A228056. We study the…
We investigate structured sparsity methods for variable selection in regression problems where the target depends nonlinearly on the inputs. We focus on general nonlinear functions not limiting a priori the function space to additive…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
Mathematics is changing. Computers are verifying proofs, checking calculations, and exploring complex structures that would overwhelm human effort. Yet curiosity-driven research is where tomorrow's breakthroughs are quietly prepared. In…
In the context of machine learning, disparate impact refers to a form of systematic discrimination whereby the output distribution of a model depends on the value of a sensitive attribute (e.g., race or gender). In this paper, we propose an…
Machine Learning techniques have become pervasive across a range of different applications, and are now widely used in areas as disparate as recidivism prediction, consumer credit-risk analysis and insurance pricing. The prevalence of…
We consider Bayesian optimization of expensive-to-evaluate experiments that generate vector-valued outcomes over which a decision-maker (DM) has preferences. These preferences are encoded by a utility function that is not known in closed…
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere…
The majority of machine learning methods and algorithms give high priority to prediction performance which may not always correspond to the priority of the users. In many cases, practitioners and researchers in different fields, going from…
Peer selection, the evaluation and selection of agents by their peers, is an important problem in the field of computational social choice; with applications to grading in massively online courses (MOOCs) and academic peer review. Current…
The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now is growing at a healthy rate. This chapter, for the {\it Highly Structured Stochastic Systems} book (Oxford University Press, 2003)…
Context: Tertiary studies in software engineering (TS@SE) are widely used to synthesise evidence on a research topic systematically. As part of their protocol, TS@SE define inclusion and exclusion criteria (IC/EC) aimed at selecting those…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
We consider a problem concerning tilings of rectangular regions by a finite library of polyominoes. We specifically look at rectangular regions of dimension $n\times m$ and ask whether or not a tiling of this region can be rearranged so…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.