Matrix factorization with Binary Components

Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared with other matrix factorization schemes, our problem is further complicated by a combinatorial constraint set of size $2^{m \cdot r}$, where $m$ is the dimension of the data points and $r$ the rank of the factorization. Despite apparent intractability, we provide - in the line of recent work on non-negative matrix factorization by Arora et al. (2012) - an algorithm that provably recovers the underlying factorization in the exact case with $O(m r 2^r + mnr + r^2 n)$ operations for $n$ datapoints. To obtain this result, we use theory around the Littlewood-Offord lemma from combinatorics.Comment: appeared in NIPS 201

Regularization-free estimation in trace regression with symmetric positive semidefinite matrices

Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based approaches promoting low-rankedness, notably nuclear norm regularization, have enjoyed great popularity. In the present paper, we argue that such regularization may no longer be necessary if the underlying matrix is symmetric positive semidefinite (\textsf{spd}) and the design satisfies certain conditions. In this situation, simple least squares estimation subject to an \textsf{spd} constraint may perform as well as regularization-based approaches with a proper choice of the regularization parameter, which entails knowledge of the noise level and/or tuning. By contrast, constrained least squares estimation comes without any tuning parameter and may hence be preferred due to its simplicity

Relationships between perceived teachers' controlling behaviour, psychological need thwarting, anger and bullying behaviour in high-school students

© 2015 The Foundation for Professionals in Services for Adolescents. We tested a model of the associations between students' perceptions of their physical education teacher's controlling behaviour, perceptions of basic psychological need thwarting, anger and bullying behaviour. School students (N=602; M age=12.88, SD=1.37) from 10 schools completed measures of perceived teachers' controlling behaviour and perceived thwarting of the psychological needs for autonomy, competence, and relatedness in physical education context and self-reported bullying and anger. A well-fitting structural equation model demonstrated that students' perceptions of the negative conditional regard and intimidation exhibited by the teacher had significant indirect effect on students' feelings of anger and bullying behaviour through the perceived psychological need thwarting in physical education. Findings suggest that physical education teachers who avoid the use of negative conditional regard and intimidation in their classes have students who perceive less need thwarting and report less bullying behaviour

Interlace polynomials

AbstractIn a recent paper Arratia, Bollobás and Sorkin discuss a graph polynomial defined recursively, which they call the interlace polynomial q(G,x). They present several interesting results with applications to the Alexander polynomial and state the conjecture that |q(G,−1)| is always a power of 2. In this paper we use a matrix approach to study q(G,x). We derive evaluations of q(G,x) for various x, which are difficult to obtain (if at all) by the defining recursion. Among other results we prove the conjecture for x=−1. A related interlace polynomial Q(G,x) is introduced. Finally, we show how these polynomials arise as the Martin polynomials of a certain isotropic system as introduced by Bouchet