Learning the kernel matrix with semidefinite programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive semidefinite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space - classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -using the labeled part of the data one can learn an embedding also for the unlabeled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method for learning the 2-norm soft margin parameter in support vector machines, solving an important open problem.

Artful inquiry : an arts-based facilitation approach for individual and organisational learning and development

The research undertaken in these two major doctoral studies investigates the field of artsbased learning, a pedagogical approach to individual and organisational learning and development, my professional creative facilitation practice and development as a researcher. While the studies are stand-alone projects they are intended to build on each other in order to tell the evolving story of my research and professional practice. The first study combines The Role of Arts-based Learning in a Creative Economy; The Need for Artistry in Professional Education the art of knowing what to do when you don’t know what to do and Lines of Inquiry: Making Sense of Research and Professional Practice. The Role of Arts-based Learning in a Creative Economy provides an overview of the field of arts-based learning in business. The study focuses on the relevant literature and interviews with people working in the field. The paper argues that arts-based learning is a valuable addition to organisations for building a culture of creativity and innovation. The Need for Artistry in Professional Education continues that investigation. It explores the way artists approach their work and considers what skills and capabilities from artistic practice can be applied to other professions’ practices. From this research the Sphere of Professional Artistry model is developed and depicts the process of moving toward professional artistry. Lines of Inquiry: making sense of research and professional practice through artful inquiry is a self-reflective study. It explores my method of inquiry as a researcher and as a creative facilitation practitioner using arts-based learning processes to facilitate groups of people for learning, development and change. It discusses how my research and professional practice influence and inspire the other and draws on cased studies. The second major research study Artful Inquiry: Arts-based Learning for Inquiry, Reflection and Action in Professional Practice is a one year practice-led inquiry. It continues the research into arts-based and aesthetic learning experiences and my arts-based facilitation practice. The research is conducted with members of a Women’s Network in a large government service agency. It develops the concept of ‘Artful Inquiry’’ a creative, holistic, and embodied approach for facilitation, inquiry, learning, reflection, and action. Storytelling as Inquiry is used as a methodology for understanding participants’ experiences of being involved in arts-based learning experiences. The study reveals the complex and emergent nature of practice and research. It demonstrates what it can mean to do practice-led research with others, within an organisational context, and to what effect.

Learning and teaching from the edge to centre stage : Critical factors in embedding sustainable university-wide engagement in external awards and grants funding initiatives.

Teaching awards, grants and fellowships are strategies used to recognise outstanding contributions to learning and teaching, encourage innovation, and to shift learning and teaching from the edge to centre stage. Examples range from school, faculty and institutional award and grant schemes to national schemes such as those offered by the Australian Learning and Teaching Council (ALTC), the Carnegie Foundation for the Advancement of Teaching in the United States, and the Fund for the Development of Teaching and Learning in higher education in the United Kingdom. The Queensland University of Technology (QUT) has experienced outstanding success in all areas of the ALTC funding since the inception of the Carrick Institute for Learning and Teaching in 2004. This paper reports on a study of the critical factors that have enabled sustainable and resilient institutional engagement with ALTC programs. As a lens for examining the QUT environment and practices, the study draws upon the five conditions of the framework for effective dissemination of innovation developed by Southwell, Gannaway, Orrell, Chalmers and Abraham (2005, 2010): 1. Effective, multi-level leadership and management 2. Climate of readiness for change 3. Availability of resources 4. Comprehensive systems in institutions and funding bodies 5. Funding design The discussion on the critical factors and practical and strategic lessons learnt for successful university-wide engagement offer insights for university leaders and staff who are responsible for learning and teaching award, grant and associated internal and external funding schemes.

Multitask learning with expert advice

We consider the problem of prediction with expert advice in the setting where a forecaster is presented with several online prediction tasks. Instead of competing against the best expert separately on each task, we assume the tasks are related, and thus we expect that a few experts will perform well on the entire set of tasks. That is, our forecaster would like, on each task, to compete against the best expert chosen from a small set of experts. While we describe the “ideal” algorithm and its performance bound, we show that the computation required for this algorithm is as hard as computation of a matrix permanent. We present an efficient algorithm based on mixing priors, and prove a bound that is nearly as good for the sequential task presentation case. We also consider a harder case where the task may change arbitrarily from round to round, and we develop an efficient approximate randomized algorithm based on Markov chain Monte Carlo techniques.

A learning-based approach to reactive security

Despite the conventional wisdom that proactive security is superior to reactive security, we show that reactive security can be competitive with proactive security as long as the reactive defender learns from past attacks instead of myopically overreacting to the last attack. Our game-theoretic model follows common practice in the security literature by making worst-case assumptions about the attacker: we grant the attacker complete knowledge of the defender’s strategy and do not require the attacker to act rationally. In this model, we bound the competitive ratio between a reactive defense algorithm (which is inspired by online learning theory) and the best fixed proactive defense. Additionally, we show that, unlike proactive defenses, this reactive strategy is robust to a lack of information about the attacker’s incentives and knowledge.

A unifying view of multiple kernel learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion’s dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.

Multiview point cloud kernels for semisupervised learning [Lecture Notes]

In semisupervised learning (SSL), a predictive model is learn from a collection of labeled data and a typically much larger collection of unlabeled data. These paper presented a framework called multi-view point cloud regularization (MVPCR), which unifies and generalizes several semisupervised kernel methods that are based on data-dependent regularization in reproducing kernel Hilbert spaces (RKHSs). Special cases of MVPCR include coregularized least squares (CoRLS), manifold regularization (MR), and graph-based SSL. An accompanying theorem shows how to reduce any MVPCR problem to standard supervised learning with a new multi-view kernel.

Correction to “The Importance of Convexity in Learning With Squared Loss” [Sep 98 1974-1980]

The paper "the importance of convexity in learning with squared loss" gave a lower bound on the sample complexity of learning with quadratic loss using a nonconvex function class. The proof contains an error. We show that the lower bound is true under a stronger condition that holds for many cases of interest.

Open problems in the security of learning

Machine learning has become a valuable tool for detecting and preventing malicious activity. However, as more applications employ machine learning techniques in adversarial decision-making situations, increasingly powerful attacks become possible against machine learning systems. In this paper, we present three broad research directions towards the end of developing truly secure learning. First, we suggest that finding bounds on adversarial influence is important to understand the limits of what an attacker can and cannot do to a learning system. Second, we investigate the value of adversarial capabilities-the success of an attack depends largely on what types of information and influence the attacker has. Finally, we propose directions in technologies for secure learning and suggest lines of investigation into secure techniques for learning in adversarial environments. We intend this paper to foster discussion about the security of machine learning, and we believe that the research directions we propose represent the most important directions to pursue in the quest for secure learning.

Learning to act in uncertain environments : technical perspective

The problem of decision making in an uncertain environment arises in many diverse contexts: deciding whether to keep a hard drive spinning in a net-book; choosing which advertisement to post to a Web site visitor; choosing how many newspapers to order so as to maximize profits; or choosing a route to recommend to a driver given limited and possibly out-of-date information about traffic conditions. All are sequential decision problems, since earlier decisions affect subsequent performance; all require adaptive approaches, since they involve significant uncertainty. The key issue in effectively solving problems like these is known as the exploration/exploitation trade-off: If I am at a cross-roads, when should I go in the most advantageous direction among those that I have already explored, and when should I strike out in a new direction, in the hopes I will discover something better?

Implicit online learning

Online learning algorithms have recently risen to prominence due to their strong theoretical guarantees and an increasing number of practical applications for large-scale data analysis problems. In this paper, we analyze a class of online learning algorithms based on fixed potentials and nonlinearized losses, which yields algorithms with implicit update rules. We show how to efficiently compute these updates, and we prove regret bounds for the algorithms. We apply our formulation to several special cases where our approach has benefits over existing online learning methods. In particular, we provide improved algorithms and bounds for the online metric learning problem, and show improved robustness for online linear prediction problems. Results over a variety of data sets demonstrate the advantages of our framework.

A unifying view of multiple kernel learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion's dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.

Matrix regularization techniques for online multitask learning

In this paper we examine the problem of prediction with expert advice in a setup where the learner is presented with a sequence of examples coming from different tasks. In order for the learner to be able to benefit from performing multiple tasks simultaneously, we make assumptions of task relatedness by constraining the comparator to use a lesser number of best experts than the number of tasks. We show how this corresponds naturally to learning under spectral or structural matrix constraints, and propose regularization techniques to enforce the constraints. The regularization techniques proposed here are interesting in their own right and multitask learning is just one application for the ideas. A theoretical analysis of one such regularizer is performed, and a regret bound that shows benefits of this setup is reported.

Multitask learning with expert advice

We consider the problem of prediction with expert advice in the setting where a forecaster is presented with several online prediction tasks. Instead of competing against the best expert separately on each task, we assume the tasks are related, and thus we expect that a few experts will perform well on the entire set of tasks. That is, our forecaster would like, on each task, to compete against the best expert chosen from a small set of experts. While we describe the "ideal" algorithm and its performance bound, we show that the computation required for this algorithm is as hard as computation of a matrix permanent. We present an efficient algorithm based on mixing priors, and prove a bound that is nearly as good for the sequential task presentation case. We also consider a harder case where the task may change arbitrarily from round to round, and we develop an efficient approximate randomized algorithm based on Markov chain Monte Carlo techniques.

Learning the Kernel Matrix with Semi-Definite Programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.