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.

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.

Optimistic linear programming gives logarithmic regret for irreducible MDPs

We present an algorithm called Optimistic Linear Programming (OLP) for learning to optimize average reward in an irreducible but otherwise unknown Markov decision process (MDP). OLP uses its experience so far to estimate the MDP. It chooses actions by optimistically maximizing estimated future rewards over a set of next-state transition probabilities that are close to the estimates, a computation that corresponds to solving linear programs. We show that the total expected reward obtained by OLP up to time T is within C(P) log T of the reward obtained by the optimal policy, where C(P) is an explicit, MDP-dependent constant. OLP is closely related to an algorithm proposed by Burnetas and Katehakis with four key differences: OLP is simpler, it does not require knowledge of the supports of transition probabilities, the proof of the regret bound is simpler, but our regret bound is a constant factor larger than the regret of their algorithm. OLP is also similar in flavor to an algorithm recently proposed by Auer and Ortner. But OLP is simpler and its regret bound has a better dependence on the size of the MDP.

Pedagogy of introductory computer programming : a people-first approach

Students struggle with learning to program. In recent years, not only has there been a dramatic drop in the number of students enrolling in IT and Computer Science courses, but attrition from these courses continues to be significant. Introductory programming subjects traditionally have high failure rates and as they tend to be core to IT and Computer Science courses can be a road block for many students to their university studies. Is programming really that difficult — or are there other barriers to learning that have a serious and detrimental effect on student progression? In-class experiments were conducted in introductory programming units to confirm our hypothesis that that pair-programming would benefit students' learning to program. We investigated the social and cultural barriers to learning programming by questioning students' perceptions of confidence, difficulty and enjoyment of programming. The results of paired and non-paired students were compared to determine the effect of pair-programming on learning outcomes. Both the empirical and anecdotal results of our experiments strongly supported our hypothesis.

Toward a shared understanding of competency in programming : an invitation to the BABELnot Project

The ICT degrees in most Australian universities have a sequence of up to three programming subjects, or units. BABELnot is an ALTC-funded project that will document the academic standards associated with those three subjects in the six participating universities and, if possible, at other universities. This will necessitate the development of a rich framework for describing the learning goals associated with programming. It will also be necessary to benchmark exam questions that are mapped onto this framework. As part of the project, workshops are planned for ACE 2012, ICER 2012 and ACE 2013, to elicit feedback from the broader Australasian computing education community, and to disseminate the project’s findings. The purpose of this paper is to introduce the project to that broader Australasian computing education community and to invite their active participation.

Street computing : towards an integrated open data Application Programming Interface (API) for cities

This special issue of the Journal of Urban Technology brings together five articles that are based on presentations given at the Street Computing workshop held on 24 November 2009 in Melbourne in conjunction with the Australian Computer-Human Interaction conference (OZCHI 2009). Our own article introduces the Street Computing vision and explores the potential, challenges and foundations of this research vision. In order to do so, we first look at the currently available sources of information and discuss their link to existing research efforts. Section 2 then introduces the notion of Street Computing and our research approach in more detail. Section 3 looks beyond the core concept itself and summarises related work in this field of interest.

Design of a knowledge base to teach programming

Programming is a subject that many beginning students find difficult. This paper describes a knowledge base designed for the purpose of analyzing programs written in the PHP web development language. The aim is to use this knowledge base in an Intelligent Tutoring System that will provide effective feedback to students. The main focus of this research is that a programming exercise can have many correct solutions. This paper presents an overview of how the proposed knowledge base can be utilized to accept different solutions to a given exercise

Programming with time : cyber-physical programming with Impromptu

The act of computer programming is generally considered to be temporally removed from a computer program's execution. In this paper we discuss the idea of programming as an activity that takes place within the temporal bounds of a real-time computational process and its interactions with the physical world. We ground these ideas within the con- text of livecoding -- a live audiovisual performance practice. We then describe how the development of the programming environment "Impromptu" has addressed our ideas of programming with time and the notion of the programmer as an agent in a cyber-physical system.

Programming with time : Cyber-physical programming with impromptu

The act of computer programming is generally considered to be temporally removed from a computer program’s execution. In this paper we discuss the idea of programming as an activity that takes place within the temporal bounds of a real-time computational process and its interactions with the physical world. We ground these ideas within the context of livecoding – a live audiovisual performance practice. We then describe how the development of the programming environment “Impromptu” has addressed our ideas of programming with time and the notion of the programmer as an agent in a cyber-physical system.

Using neo-Piagetian theory, formative in-Class tests and think alouds to better understand student thinking : a preliminary report on computer programming

It is acknowledged around the world that many university students struggle with learning to program (McCracken et al., 2001; McGettrick et al., 2005). In this paper, we describe how we have developed a research programme to systematically study and incrementally improve our teaching. We have adopted a research programme with three elements: (1) a theory that provides an organising framework for defining the type of phenomena and data of interest, (2) data on how the class as a whole performs on formative assessment tasks that are framed from within the organising framework, and (3) data from one-on-one think aloud sessions, to establish why students struggle with some of those in-class formative assessment tasks. We teach introductory computer programming, but this three-element structure of our research is applicable to many areas of engineering education research.

How difficult are exams? A framework for assessing the complexity of introductory programming exams

Student performance on examinations is influenced by the level of difficulty of the questions. It seems reasonable to propose therefore that assessment of the difficulty of exam questions could be used to gauge the level of skills and knowledge expected at the end of a course. This paper reports the results of a study investigating the difficulty of exam questions using a subjective assessment of difficulty and a purpose-built exam question complexity classification scheme. The scheme, devised for exams in introductory programming courses, assesses the complexity of each question using six measures: external domain references, explicitness, linguistic complexity, conceptual complexity, length of code involved in the question and/or answer, and intellectual complexity (Bloom level). We apply the scheme to 20 introductory programming exam papers from five countries, and find substantial variation across the exams for all measures. Most exams include a mix of questions of low, medium, and high difficulty, although seven of the 20 have no questions of high difficulty. All of the complexity measures correlate with assessment of difficulty, indicating that the difficulty of an exam question relates to each of these more specific measures. We discuss the implications of these findings for the development of measures to assess learning standards in programming courses.