We describe the Fourier basis, a linear value function approximation scheme based on the Fourier series. We empirically demonstrate that it performs well compared to radial basis functions and the polynomial basis, the two most popular fixed bases for linear value function approximation, and is competitive with learned proto-value functions.

Multilabel classification is a central problem in many areas of data analysis, including text and multimedia categorization, where individual data objects need to be assigned multiple labels. A key challenge in these tasks is to learn a classifier that can properly exploit label correlations without requiring exponential enumeration of label subsets during training or testing. We investigate novel loss functions for multilabel training within a large margin framework---identifying a simple alternative that yields improved generalization while still allowing efficient training. We furthermore show how covariances between the label models can be learned simultaneously with the classification model itself, in a jointly convex formulation, without compromising scalability. The resulting combination yields state of the art accuracy in multilabel webpage classification.

We consider a learning setting of importance to large scale machine learning: potentially unlimited data arrives sequentially, but only a small fraction of it is labeled. The learner cannot store the data; it should learn from both labeled and unlabeled data, and it may also request labels for some of the unlabeled items. This setting is frequently encountered in real-world applications and has the characteristics of online, semi-supervised, and active learning. Yet previous learning models fail to consider these characteristics jointly. We present OASIS, a Bayesian model for this learning setting. The main contributions of the model include the novel integration of a semi-supervised likelihood function, a sequential Monte Carlo scheme for efficient online Bayesian updating, and a posterior-reduction criterion for active learning. Encouraging results on both synthetic and real-world optical character recognition data demonstrate the synergy of these characteristics in OASIS.

Variable selection problems are typically addressed under apenalized optimization framework. Nonconvex penalties such as the minimax concave plus (MCP) and smoothly clipped absolute deviation(SCAD), have been demonstrated to have the properties of sparsity practically and theoretically. In this paper we propose a new nonconvex penalty that we call exponential-type penalty. The exponential-type penalty is characterized by a positive parameter,which establishes a connection with the ell 0 and ell 1 penalties.We apply this new penalty to sparse supervised learning problems. To solve to resulting optimization problem, we resort to a reweighted ell 1 minimization method. Moreover, we devise an efficient method for the adaptive update of the tuning parameter. Our experimental results are encouraging. They show that the exponential-type penalty is competitive with MCP and SCAD.

The success of transfer learning on a target task is highly dependent on the selected source data. Instance transfer methods reuse data from the source tasks to augment the training data for the target task. If poorly chosen, this source data may inhibit learning, resulting in negative transfer. The current most widely used algorithm for instance transfer, TrAdaBoost, performs poorly when given irrelevant source data. We present a novel task-based boosting technique for instance transfer that selectively chooses the source knowledge to transfer to the target task. Our approach performs boosting at both the instance level and the task level, assigning higher weight to those source tasks that show positive transferability to the target task, and adjusting the weights of individual instances within each source task via AdaBoost. We show that this combination of task- and instance-level boosting significantly improves transfer performance over existing instance transfer algorithms when given a mix of relevant and irrelevant source data, especially for small amounts of data on the target task.

This paper presents a novel symmetric graph regularization framework for pairwise constraint propagation. We first decompose the challenging problem of pairwise constraint propagation into a series of two-class label propagation subproblems and then deal with these subproblems by quadratic optimization with symmetric graph regularization. More importantly, we clearly show that pairwise constraint propagation is actually equivalent to solving a Lyapunov matrix equation, which is widely used in Control Theory as a standard continuous-time equation. Different from most previous constraint propagation methods that suffer from severe limitations, our method can directly be applied to multi-class problem and also can effectively exploit both must-link and cannot-link constraints. The propagated constraints are further used to adjust the similarity between data points so that they can be incorporated into subsequent clustering. The proposed method has been tested in clustering tasks on six real-life data sets and then shown to achieve significant improvements with respect to the state of the arts.

We study the problem of automatically generating features for function approximation in reinforcement learning. We build on the work of Mahadevan and his colleagues, who pioneered the use of spectral clustering methods for basis function construction. Their methods work on top of a graph that captures state adjacency. Instead, we use bisimulation metrics in order to provide state distances for spectral clustering. The advantage of these metrics is that they incorporate reward information in a natural way, in addition to the state transition information. We provide theoretical bounds on the quality of the obtained approximation, which justify the importance of incorporating reward information. We also demonstrate empirically that the approximation quality improves when bisimulation metrics are used instead of the state adjacency graph in the basis function construction process.

Ensemble classification methods that independently construct component models (e.g., bagging) improve accuracy over single models by reducing the error due to variance. Some work has been done to extend ensemble techniques for classification in relational domains by taking relational data characteristics or multiple link types into account during model construction. However, since these approaches follow the conventional approach to ensemble learning, they improve performance by reducing the error due to variance in learning. We note however, that variance in inference can be an additional source of error in relational methods that use collective classification, since inferred values are propagated during inference. We propose a novel ensemble mechanism for collective classification that reduces  both learning and inference variance, by incorporating prediction averaging into the collective inference process itself. We show that our proposed method significantly outperforms a straightforward relational ensemble baseline on both synthetic and real-world datasets.

Behaviour recognition is the process of inferring the behaviour of an individual from a series of observations acquired from sensors such as in a smart home. The majority of existing behaviour recognition systems are based on supervised learning algorithms, which means that training them requires a preprocessed, annotated dataset. Unfortunately, annotating a dataset is a rather tedious process and one that is prone to error. In this paper we suggest a way to identify structure in the data based on text compression and the edit distance between words, without any prior labelling. We demonstrate that by using this method we can automatically identify patterns and segment the data into patterns that correspond to human behaviours. To evaluate the effectiveness of our proposed method, we use a dataset from a smart home and compare the labels produced by our approach with the labels assigned by a human to the activities in the dataset. We find that the results are promising and show significant improvement in the recognition accuracy over Self-Organising Maps (SOMs).

Spectral clustering is one of the most popular clustering approaches. Despite its good performance, it is limited in its applicability to large-scale problems due to its high computational complexity. Recently, many approaches have been proposed to accelerate the spectral clustering. Unfortunately, these methods usually sacrifice quite a lot information of the original data, thus result in a degradation of performance. In this paper, we propose a novel approach, called Landmark-based Spectral Clustering (LSC), for large scale clustering problems. Specifically, we select $p\ (\ll n)$ representative data points as the landmarks and represent the original data points as the linear combinations of these landmarks. The spectral embedding of the data can then be efficiently computed with the landmark-based representation. The proposed algorithm scales linearly with the problem size. Extensive experiments show the effectiveness and efficiency of our approach comparing to the state-of-the-art methods.