This paper investigates algorithms to automatically adapt the learning rate of neural networks (NNs). Starting with stochastic gradient descent, a large variety of learning methods has been proposed for the NN setting. However, these methods are usually sensitive to the initial learning rate which has to be chosen by the experimenter. We investigate several features and show how an adaptive controller can adjust the learning rate without prior knowledge of the learning problem at hand.

We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all alpha-approximate algorithms are robust (i.e., near alpha-approximate) if the utility is Lipschitz continuous in the prior. We further show that robustness may not be achieved if the utility is non-Lipschitz. This suggests we should use a Lipschitz utility for AL if robustness is required. For the minimum cost setting, we can also obtain a robustness result for approximate AL algorithms. Our results imply that many commonly used AL algorithms are robust against perturbed priors. We then propose the use of a mixture prior to alleviate the problem of prior misspecification. We analyze the robustness of the uniform mixture prior and show experimentally that it performs reasonably well in practice.

We propose a novel learning framework for object categorization with interactive semantic feedback. In this framework, a discriminative categorization model improves through human-guided iterative semantic feedbacks. Specifically, the model identifies the most helpful relational semantic queries to discriminatively refine the model. The user feedback on whether the relationship is semantically valid or not is incorporated back into the model, in the form of regularization, and the process iterates. We validate the proposed model in a few-shot multi-class classification scenario, where we measure classification performance on a set of ‘target’ classes, with few training instances, by leveraging and transferring knowledge from ‘anchor’ classes, that contain larger set of labeled instances.

Hierarchical latent tree analysis (HLTA) is recently proposed as a new method for topic detection. It differs fundamentally from the LDA-based methods in terms of topic definition, topic-document relationship, and learning method. It has been shown to discover significantly more coherent topics and better topic hierarchies. However, HLTA relies on the Expectation-Maximization (EM) algorithm for parameter estimation and hence is not efficient enough to deal with large datasets. In this paper, we propose a method to drastically speed up HLTA using a technique inspired by the advances in the method of moments. Empirical experiments show that our method greatly improves the efficiency of HLTA. It is as efficient as the state-of-the-art LDA-based method for hierarchical topic detection and finds substantially better topics and topic hierarchies.

The Dirichlet process mixtures (DPM) can automatically infer the model complexity from data. Hence it has attracted significant attention recently, and is widely used for model selection and clustering. As a generative model, it generally requires prior base distribution to learn component parameters by maximizing posterior probability. In contrast, discriminative classifiers model the conditional probability directly, and have yielded better results than generative classifiers.In this paper, we propose a maximum margin Dirichlet process mixture for clustering, which is different from the traditional DPM for parameter modeling. Our model takes a discriminative clustering approach, by maximizing a conditional likelihood to estimate parameters. In particular, we take a EM-like algorithm by leveraging Gibbs sampling algorithm for inference, which in turn can be perfectly embedded in the online maximum margin learning procedure to update model parameters. We test our model and show comparative results over the traditional DPM and other nonparametric clustering approaches.

In this paper, we present a novel algorithm for the maximum a posteriori decoding (MAPD) of time-homogeneous Hidden Markov Models (HMM), improving the worst-case running time of the classical Viterbi algorithm by a logarithmic factor. In our approach, we interpret the Viterbi algorithm as a repeated computation of matrix-vector (max, +)-multiplications. On time-homogeneous HMMs, this computation is online: a matrix, known in advance, has to be multiplied with several vectors revealed one at a time. Our main contribution is an algorithm solving this version of matrix-vector (max,+)-multiplication in subquadratic time, by performing a polynomial preprocessing of the matrix. Employing this fast multiplication algorithm, we solve the MAPD problem in O(mn 2 /log n) time for any time-homogeneous HMM of size n and observation sequence of length m, with an extra polynomial preprocessing cost negligible for m > n . To the best of our knowledge, this is the first algorithm for the MAPD problem requiring subquadratic time per observation, under the assumption — usually verified in practice — that the transition probability matrix does not change with time.

This paper introduces new optimality-preserving operators on Q-functions. We first describe an operator for tabular representations, the consistent Bellman operator, which incorporates a notion of local policy consistency. We show that this local consistency leads to an increase in the action gap at each state; increasing this gap, we argue, mitigates the undesirable effects of approximation and estimation errors on the induced greedy policies. This operator can also be applied to discretized continuous space and time problems, and we provide empirical results evidencing superior performance in this context. Extending the idea of a locally consistent operator, we then derive sufficient conditions for an operator to preserve optimality, leading to a family of operators which includes our consistent Bellman operator. As corollaries we provide a proof of optimality for Baird's advantage learning algorithm and derive other gap-increasing operators with interesting properties. We conclude with an empirical study on 60 Atari 2600 games illustrating the strong potential of these new operators.

The quality of K-Means clustering is extremely sensitive to proper initialization. The classic remedy is to apply k-means++ to obtain an initial set of centers that is provably competitive with the optimal solution. Unfortunately, k-means++ requires k full passes over the data which limits its applicability to massive datasets. We address this problem by proposing a simple and efficient seeding algorithm for K-Means clustering. The main idea is to replace the exact D2-sampling step in k-means++ with a substantially faster approximation based on Markov Chain Monte Carlo sampling. We prove that, under natural assumptions on the data, the proposed algorithm retains the full theoretical guarantees of k-means++ while its computational complexity is only sublinear in the number of data points. For such datasets, one can thus obtain a provably good clustering in sublinear time. Extensive experiments confirm that the proposed method is competitive with k-means++ on a variety of real-world, large-scale datasets while offering a reduction in runtime of several orders of magnitude.

In many applications, ideas that are described by a set of words often flow between different groups. To facilitate users in analyzing the flow, we present a method to model the flow behaviors that aims at identifying the lead-lag relationships between word clusters of different user groups. In particular, an improved Bayesian conditional cointegration based on dynamic time warping is employed to learn links between words in different groups. A tensor-based technique is developed to cluster these linked words into different clusters (ideas) and track the flow of ideas. The main feature of the tensor representation is that we introduce two additional dimensions to represent both time and lead-lag relationships. Experiments on both synthetic and real datasets show that our method is more effective than methods based on traditional clustering techniques and achieves better accuracy. A case study was conducted to demonstrate the usefulness of our method in helping users understand the flow of ideas between different user groups on social media.

Head pose estimation via embedding model has beendemonstrated its effectiveness from the recent works.However, most of the previous methods only focuson manifold relationship among poses, while overlookthe underlying global structure among subjects and poses.To build a robust and effective head pose estimator,we propose a novel Pose-dependent Low-Rank Embedding(PLRE) method, which is designed to exploita discriminative subspace to keep within-pose samplesclose while between-pose samples far away. Specifically,low-rank embedding is employed under the multitaskframework, where each subject can be naturallyconsidered as one task. Then, two novel terms are incorporatedto align multiple tasks to pursue a better posedependentembedding. One is the cross-task alignmentterm, aiming to constrain each low-rank coefficient toshare the similar structure. The other is pose-dependentgraph regularizer, which is developed to capture manifoldstructure of same pose cross different subjects. Experimentson databases CMU-PIE, MIT-CBCL, and extendedYaleB with different levels of random noise areconducted and six embedding model based baselinesare compared. The consistent superior results demonstratethe effectiveness of our proposed method.