We propose a fast batch learning method for linear-chain Conditional Random Fields (CRFs) based on Newton-CG methods. Newton-CG methods are a variant of Newton method for high-dimensional problems. They only require the Hessian-vector products instead of the full Hessian matrices. To speed up Newton-CG methods for the CRF learning, we derive a novel dynamic programming procedure for the Hessian-vector products of the CRF objective function. The proposed procedure can reuse the byproducts of the time-consuming gradient computation for the Hessian-vector products to drastically reduce the total computation time of the Newton-CG methods. In experiments with tasks in natural language processing, the proposed method outperforms a conventional quasi-Newton method. Remarkably, the proposed method is competitive with online learning algorithms that are fast but unstable.

The Area Under the ROC Curve (AUC) metric has achieved a big success in binary classification problems since they measure the performance of classifiers without making any specific assumptions about the class distribution and misclassification costs. This is desirable because the class distribution and misclassification costs may be unknown during training process or even change in environment. MAUC, the extension of AUC to multi-class problems, has also attracted a lot of attention. However, despite the emergence of approaches for training classifiers with large AUC, little has been done for MAUC. This paper analyzes MAUC in-depth, and reveals that the maximization of MAUC can be achieved by decomposing the multi-class problem into a number of independent sub-problems. These sub-problems are formulated in the form of a “learning to rank” problem, for which well-established methods already exist. Based on the analysis, a method that employs RankBoost algorithm as the sub-problem solver is proposed to achieve classification systems with maximum MAUC. Empirical studies have shown the advantages of the proposed method over other eight relevant methods. Due to the importance of MAUC to multi-class cost-sensitive learning and class imbalanced learning problems, the proposed method is a general technique for both problems. It can also be generalized to accommodate other learning algorithms as the sub-problem solvers.

Advanced e-applications require comprehensive knowledge about their users’ preferences in order to provide accurate personalized services. In this paper, we propose to learn users’ preferences to product brands from their implicit feedbacks such as their searching and browsing behaviors in user Web browsing log data. The user brand preference learning problem is challenge since (1) the users’ implicit feedbacks are extremely sparse in various product domains; and (2) we can only observe positive feedbacks from users’ behaviors. In this paper, we propose a latent factor model to collaboratively mine users’ brand preferences across multiple domains simultaneously. By collective learning, the learning processes in all the domains are mutually enhanced and hence the problem of data scarcity in each single domain can be effectively addressed. On the other hand, we learn our model with an adaption of the Bayesian personalized ranking (BPR) optimization criterion which is a general learning framework for collaborative filtering from implicit feedbacks. Experiments with both synthetic and real world datasets show that our proposed model significantly outperforms the baselines.

Manifold learning is a powerful tool for reducing the dimensionality of a dataset by finding a low-dimensional embedding that retains important geometric and topological features. In many applications it is desirable to add new samples to a previously learnt embedding, this process of adding new samples is known as the out-of-sample extension problem. Since many manifold learning algorithms do not naturally allow for new samples to be added we present an easy to implement generalized solution to the problem that can be used with any existing manifold learning algorithm. Our algorithm is based on simple geometric intuition about the local structure of a manifold and our results show that it can be effectively used to add new samples to a previously learnt embedding. We test our algorithm on both artificial and real world image data and show that our method significantly out performs existing out-of-sample extension strategies.

Planning agents often lack the computational resources needed to build full planning trees for their environments. Agent designers commonly overcome this finite-horizon approximation by applying an evaluation function at the leaf-states of the planning tree. Recent work has proposed an alternative approach for overcoming computational constraints on agent design: modify the reward function. In this work, we compare this reward design approach to the common leaf-evaluation heuristic approach for improving planning agents. We show that in many agents, the reward design approach strictly subsumes the leaf-evaluation approach, i.e., there exists a reward function for every leaf-evaluation heuristic that leads to equivalent behavior, but the converse is not true. We demonstrate that this generality leads to improved performance when an agent makes approximations in addition to the finite-horizon approximation. As part of our contribution, we extend PGRD, an online reward design algorithm, to develop reward design algorithms for Sparse Sampling and UCT, two algorithms capable of planning in large state spaces.

We concern the problem of learning a Mahalanobis distance metric for improving nearest neighbor classification. Our work is built upon the large margin nearest neighbor (LMNN) classification framework. Due to the semidefiniteness constraint in the optimization problem of LMNN, it is not scalable in terms of the dimensionality of the input data. The original LMNN solver partially alleviates this problem by adopting alternating projection methods instead of standard interior-point methods. Still, at each iteration, the computation complexity is at least O(D 3 ) (D is the dimension of input data). In this work, we propose a column generation based algorithm to solve the LMNN optimization problem much more efficiently. Our algorithm is much more scalable in tha tat each iteration, it does not need full eigen-decomposition. Instead, we only need to find the leading eigen value and its corresponding eigen vector, which is of O(D 2 ) complexity. Experiments show the efficiency and efficacy of our algorithms.

Inspired by “GoogleTM Sets” and Bayesian sets, we consider the problem of retrieving complex objects and relations among them, i.e., ground atoms from a logical concept, given a query consisting of a few atoms from that concept. We formulate this as a within-network relational learning problem using few labels only and describe an algorithm that ranks atoms using a score based on random walks with restart (RWR): the probability that a random surfer hits an atom starting from the query atoms. Specifically, we compute an initial ranking using personalized PageRank. Then, we find paths of atoms that are connected via their arguments, variablize the ground atoms in each path, in order to create features for the query. These features are used to re-personalize the original RWR and to finally compute the set completion, based on Label Propagation. Moreover, we exploit that RWR techniques can naturally be lifted and show that lifted inference for label propagation is possible. We evaluate our algorithm on a realworld relational dataset by finding completions of sets of objects describing the Roman city of Pompeii. We compare to Bayesian sets and show that our approach gives very reasonable set completions.

In this paper we propose differential eligibility vectors (DEV) for temporal-difference (TD) learning, a new class of eligibility vectors designed to bring out the contribution of each action in the TD-error at each state. Specifically, we use DEV in TD-Q(lambda) to more accurately learn the relative value of the actions, rather than their absolute value. We identify conditions that ensure convergence w.p.1 of TD-Q(lambda) with DEV and show that this algorithm can also be used to directly approximate the advantage function associated with a given policy, without the need to compute an auxiliary function - something that, to the extent of our knowledge, was not known possible. Finally, we discuss the integration of DEV in LSTDQ and actor-critic algorithms.

Recent Reinforcement Learning (RL) algorithms, such as R-MAX, make (with high probability) only a small number of poor decisions. In practice, these algorithms do not scale well as the number of states grows because the algorithms spend too much effort exploring. We introduce an RL algorithm State TArgeted R-MAX (STAR-MAX) that explores a subset of the state space, called the exploration envelope ξ. When ξ equals the total state space, STAR-MAX behaves identically to R-MAX. When ξ is a subset of the state space, to keep exploration within ξ, a recovery rule β is needed. We compared existing algorithms with our algorithm employing various exploration envelopes. With an appropriate choice of ξ, STAR-MAX scales far better than existing RL algorithms as the number of states increases. A possible drawback of our algorithm is its dependence on a good choice of ξ and β. However, we show that an effective recovery rule β can be learned on-line and ξ can be learned from demonstrations. We also find that even randomly sampled exploration envelopes can improve cumulative rewards compared to R-MAX. We expect these results to lead to more efficient methods for RL in large-scale problems.

Since learning in Boltzmann machines is typically quite slow, there is a need to restrict connections within hidden layers. However, theresulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using l1/l2 regularization upon the activation probabilities of hidden units in restricted Boltzmann machines to capture the local dependencies among hidden units. This regularization not only encourages hidden units of many groups to be inactive given observed data but also makes hidden units within a group compete with each other for modeling observed data. Thus, the l1/l2 regularization on RBMs yields sparsity at both the group and the hidden unit levels. We call RBMs trained with the regularizer sparse group RBMs (SGRBMs). The proposed SGRBMs are appliedto model patches of natural images, handwritten digits and OCR English letters. Then to emphasize that SGRBMs can learn more discriminative features we applied SGRBMs to pretrain deep networks for classification tasks. Furthermore, we illustrate the regularizer can also be applied to deep Boltzmann machines, which lead to sparse group deep Boltzmann machines. When adapted to the MNIST data set, a two-layer sparse group Boltzmann machine achieves an error rate of 0.84%, which is, to our knowledge, the best published result on the permutation-invariant version of the MNIST task.