Real time clustering of time series using triangular potentials

Motivated by the problem of computing investment portfolio weightings we investigate various methods of clustering as alternatives to traditional mean-variance approaches. Such methods can have significant benefits from a practical point of view since they remove the need to invert a sample covariance matrix, which can suffer from estimation error and will almost certainly be non-stationary. The general idea is to find groups of assets which share similar return characteristics over time and treat each group as a single composite asset. We then apply inverse volatility weightings to these new composite assets. In the course of our investigation we devise a method of clustering based on triangular potentials and we present associated theoretical results as well as various examples based on synthetic data.Comment: AIFU1

Regularity properties for quasiminimizers of a (p,q)(p,q)-Dirichlet integral

Using a variational approach we study interior regularity for quasiminimizers of a $(p,q)$-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and supporting a Poincar\'{e} inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally H\"{o}lder continuous and they satisfy Harnack inequality, the strong maximum principle, and Liouville's Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for H\"older continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we consider $(p,q)$-minimizers and we give an estimate for their oscillation at boundary points

Regularity results for quasiminima of a class of double phase problems

We prove boundedness, H\"older continuity, Harnack inequality results for local quasiminima to elliptic double phase problems of $p$-Laplace type in the general context of metric measure spaces. The proofs follow a variational approach and they are based on the De Giorgi method, a careful phase analysis and estimates in the intrinsic geometries.Comment: arXiv admin note: text overlap with arXiv:2304.1485

An Instance-Dependent Analysis for the Cooperative Multi-Player Multi-Armed Bandit

We study the problem of information sharing and cooperation in Multi-Player Multi-Armed bandits. We propose the first algorithm that achieves logarithmic regret for this problem. Our results are based on two innovations. First, we show that a simple modification to a successive elimination strategy can be used to allow the players to estimate their suboptimality gaps, up to constant factors, in the absence of collisions. Second, we leverage the first result to design a communication protocol that successfully uses the small reward of collisions to coordinate among players, while preserving meaningful instance-dependent logarithmic regret guarantees.Comment: 44 page

A Development Evaluation Study of a Professional Development Initiative to Strengthen Organizational Conditions in Early Education Settings

High quality instruction is essential to producing developmental gains for young children and can mitigate risk factors such as family poverty and low parental education. Even in programs with highly qualified teachers, teacher-child interactions often do not provide the level of instructional support that children need to be well-prepared for success in kindergarten. In order to improve instructional quality, an emerging focus on early childhood professional development involves supporting leaders in creating a web of supports for teacher learning and child growth. The purpose of the 3-year evaluation study was to assess the effectiveness of an Early Childhood Education Professional Development Initiative (ECE PDI) in advancing the knowledge, skills, and dispositions of community-based early childhood leaders and teachers in relation to creating the conditions for superior developmental outcomes for low-income students served by these community-based centers. Findings from the implementation and impact studies are reported