Spectral Methods from Tensor Networks

A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although they are not presented this way, can be viewed as spectral methods on matrices built from simple tensor networks. In this work we leverage the full power of this abstraction to design new algorithms for certain continuous tensor decomposition problems. An important and challenging family of tensor problems comes from orbit recovery, a class of inference problems involving group actions (inspired by applications such as cryo-electron microscopy). Orbit recovery problems over finite groups can often be solved via standard tensor methods. However, for infinite groups, no general algorithms are known. We give a new spectral algorithm based on tensor networks for one such problem: continuous multi-reference alignment over the infinite group SO(2). Our algorithm extends to the more general heterogeneous case.Comment: 30 pages, 8 figure

Learning Geometric Concepts with Nasty Noise

We study the efficient learnability of geometric concept classes - specifically, low-degree polynomial threshold functions (PTFs) and intersections of halfspaces - when a fraction of the data is adversarially corrupted. We give the first polynomial-time PAC learning algorithms for these concept classes with dimension-independent error guarantees in the presence of nasty noise under the Gaussian distribution. In the nasty noise model, an omniscient adversary can arbitrarily corrupt a small fraction of both the unlabeled data points and their labels. This model generalizes well-studied noise models, including the malicious noise model and the agnostic (adversarial label noise) model. Prior to our work, the only concept class for which efficient malicious learning algorithms were known was the class of origin-centered halfspaces. Specifically, our robust learning algorithm for low-degree PTFs succeeds under a number of tame distributions -- including the Gaussian distribution and, more generally, any log-concave distribution with (approximately) known low-degree moments. For LTFs under the Gaussian distribution, we give a polynomial-time algorithm that achieves error $O(\epsilon)$, where $\epsilon$ is the noise rate. At the core of our PAC learning results is an efficient algorithm to approximate the low-degree Chow-parameters of any bounded function in the presence of nasty noise. To achieve this, we employ an iterative spectral method for outlier detection and removal, inspired by recent work in robust unsupervised learning. Our aforementioned algorithm succeeds for a range of distributions satisfying mild concentration bounds and moment assumptions. The correctness of our robust learning algorithm for intersections of halfspaces makes essential use of a novel robust inverse independence lemma that may be of broader interest

Designing professional learning

The Designing Professional Learning report provides a snapshot of the key elements involved in creating effective and engaging professional learning in a globally dispersed market. AITSL commissioned Learning Forward to undertake this study to give greater guidance around the ‘how’ of professional learning. Learning design involves making careful decisions based on an integration of theories, research and models of human learning in order to contribute to the effectiveness of professional learning. This work is not presented as definitive findings, but seeks to draw attention to observed trends and areas of commonality between learning designs that have demonstrated success. Following an analysis of a broad range of professional learning activities, a Learning Design Anatomy was developed to provide a framework for understanding the elements of effective professional learning. Each learning design element is framed by a detailed series of questions that challenge users to refine and clarify aims, intended learning outcomes and the most effective ways in which to engage—taking into consideration the unique context for learning. Examples of professional learning design are provided to illustrate elements of the Anatomy. The report is designed to be of use to teachers, school leaders, policy makers, system administrators and professional learning providers. It is intended that this report and the Anatomy will serve as provocation for a broader conversation about the composition of professional learning and the elements that establish the strongest correlation between participants, environment, delivery and action

Settling the Sample Complexity of Single-parameter Revenue Maximization

This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by Devanur, Huang, and Psomas (STOC 2016), and an information theoretic argument. This is fundamentally different from the previous approaches that rely on either constructing an $\epsilon$-net of the mechanism space, explicitly or implicitly via statistical learning theory, or learning an approximately accurate version of the virtual values. To our knowledge, it is the first time information theoretical arguments are used to show sample complexity upper bounds, instead of lower bounds. Our lower bounds are also unified under a meta construction of hard instances.Comment: 49 pages, Accepted by STOC1

Red Rock Desert Learning Center & Wild Horse and Burro Facility: Newsletter

The mission of the Red Rock Desert Learning Center is to instill stewardship and respect by increasing knowledge and understanding of the Mojave Desert ecosystemsand cultures through a unique experiential discovery program

Red Rock Desert Learning Center & Wild Horse and Burro Facility: Frequently Asked Questions

The mission of the Red Rock Desert Learning Center is to instill stewardship and respect by increasing knowledge and understanding of the Mojave Desert ecosystems and cultures through a unique experiential discovery program

啟發另類思維 嶺南大學推服務研習課程

原載於2017年3月28日《晴報》。https://commons.ln.edu.hk/osl_press/1025/thumbnail.jp

Service-Learning Times : semester 2, 2018/19

To foster multi-disciplinary learning experience, the three faculties, the Science Unit and Office of Service-Learning offer you plenty of choices and flexibility in S-L projects. Moreover, we also provide trans-border S-L and research opportunities, enabling you to examine challenging issues at both the local and international levels. A number of S-L projects are also available in cluster courses, free elective courses, and major courses. In short, you have a wealth of opportunities to apply your course knowledge while contributing to the local and the international communities. This booklet highlights the courses with S-L elements in this semester. If you want to choose what kind of S-L adventure you want to go on, you should plan and act quickly while places are available.https://commons.ln.edu.hk/sl_times/1003/thumbnail.jp