Estimating the joint probability density function of a dataset is a central task in many machine learning applications. In this work we address the fundamental problem of kernel bandwidth estimation for variable kernel density estimation in high-dimensional feature spaces. We derive a variable kernel bandwidth estimator by minimizing the leave-one-out entropy objective function and show that this estimator is capable of performing estimation in high-dimensional feature spaces with great success. We compare the performance of this estimator to state-of-the art maximum-likelihood estimators on a number of representative high-dimensional machine learning tasks and show that the newly introduced minimum leave-one-out entropy estimator performs optimally on a number of high-dimensional datasets considered.

In this paper, we consider the problem of actively learning a linear classifier through query synthesis where the learner can construct artificial queries in order to estimate the true decision boundaries. This problem has recently gained a lot of interest in automated science and adversarial reverse engineering for which only heuristic algorithms are known. In such applications, queries can be constructed de novo to elicit information (e.g., automated science) or to evade detection with minimal cost (e.g., adversarial reverse engineering). We develop a general framework, called dimension coupling (DC), that 1) reduces a d-dimensional learning problem to d-1 low dimensional sub-problems, 2) solves each sub-problem efficiently, 3) appropriately aggregates the results and outputs a linear classifier, and 4) provides a theoretical guarantee for all possible schemes of aggregation. The proposed method is proved resilient to noise. We show that the DC framework avoids the curse of dimensionality: its computational complexity scales linearly with the dimension. Moreover, we show that the query complexity of DC is near optimal (within a constant factor of the optimum algorithm). To further support our theoretical analysis, we compare the performance of DC with the existing work. We observe that DC consistently outperforms the prior arts in terms of query complexity while often running orders of magnitude faster.

The formalism of multi-objective influence diagrams has recently been developed for modeling and solving sequential decision problems under uncertainty and multiple objectives. Since utility values representing the decision maker's preferences are only partially ordered (e.g., by the Pareto order) we no longer have a unique maximal value of expected utility, but a set of them. Computing the set of maximal values of expected utility and the corresponding policies can be computationally very challenging. In this paper, we consider alternative notions of optimality, one of the most important one being the notion of possibly optimal, namely optimal in at least one scenario compatible with the inter-objective tradeoffs. We develop a variable elimination algorithm for computing the set of possibly optimal expected utility values, prove formally its correctness, and compare variants of the algorithm experimentally.

We present new algorithms for learning Bayesian networks from data with missing values using a data augmentation approach. An exact Bayesian network learning algorithm is obtained by recasting the problem into a standard Bayesian network learning problem without missing data. As expected, the exact algorithm does not scale to large domains. We build on the exact method to create an approximate algorithm using a hill-climbing technique. This algorithm scales to large domains so long as a suitable standard structure learning method for complete data is available. We perform a wide range of experiments to demonstrate the benefits of learning Bayesian networks with such new approach.

Linear Discriminant Analysis (LDA) is a well-known method for dimension reduction and classification with focus on discriminative feature selection. However, how to discover discriminative as well as representative features in LDA model has not been explored. In this paper, we propose a latent Fisher discriminant model with representative feature discovery in an semi-supervised manner. Specifically, our model leverages advantages of both discriminative and generative models by generalizing LDA with data-driven prior over the latent variables. Thus, our method combines multi-class, latent variables and dimension reduction in an unified Bayesian framework. We test our method on MUSK and Corel datasets and yield competitive results compared to baselines. We also demonstrate its capacity on the challenging TRECVID MED11 dataset for semantic keyframe extraction and conduct a human-factors ranking-based experimental evaluation, which clearly demonstrates our proposed method consistently extracts more semantically meaningful keyframes than challenging baselines.

Adverse drug reaction (ADR) is a major burden for patients and healthcare industry. It usually causes preventable hospitalizations and deaths, while associated with a huge amount of cost. Traditional preclinical in vitro safety profiling and clinical safety trials are restricted in terms of small scale, long duration, huge financial costs and limited statistical signifi- cance. The availability of large amounts of drug and ADR data potentially allows ADR predictions during the drugs’ early preclinical stage with data analytics methods to inform more targeted clinical safety tests. Despite their initial success, existing methods have trade-offs among interpretability, predictive power and efficiency. This urges us to explore methods that could have all these strengths and provide practical solutions for real world ADR predictions. We cast the ADR-drug relation structure into a three-layer hierarchical Bayesian model. We interpret each ADR as a symbolic word and apply latent Dirichlet allocation (LDA) to learn topics that may represent certain biochemical mechanism that relates ADRs with drug structures. Based on LDA, we designed an equivalent regularization term to incorporate the hierarchical ADR domain knowledge. Finally, we developed a mixed input model leveraging a fast collapsed Gibbs sampling method that the complexity of each iteration of Gibbs sampling proportional only to the number of positive ADRs. Experiments on real world data show our models achieved higher prediction accuracy and shorter running time than the state-of-the-art alternatives.

Online joint parameter and state estimation is a core problem for temporal models.Most existing methods are either restricted to a particular class of models (e.g., the Storvik filter) or computationally expensive (e.g., particle MCMC). We propose a novel nearly-black-box algorithm, the Assumed Parameter Filter (APF), a hybrid of particle filtering for state variables and assumed density filtering for parameter variables.It has the following advantages:(a) it is online and computationally efficient;(b) it is applicable to both discrete and continuous parameter spaces with arbitrary transition dynamics.On a variety of toy and real models, APF generates more accurate results within a fixed computation budget compared to several standard algorithms from the literature.

Structured regression on graphs aims to predict response variables from multiple nodes by discovering and exploiting the dependency structure among response variables. This problem is challenging since dependencies among response variables are always unknown, and the associated prior knowledge is non-symmetric. In previous studies, various promising solutions were proposed to improve structured regression by utilizing symmetric prior knowledge, learning sparse dependency structure among response variables, or learning representations of attributes of multiple nodes. However, none of them are capable of efficiently learning dependency structure while incorporating non-symmetric prior knowledge. To achieve these objectives, we proposed Continuous Conditional Dependency Network (CCDN) for structured regression. The intuitive idea behind this model is that each response variable is not only dependent on attributes from the same node, but also on response variables from all other nodes. This results in a joint modeling of local conditional probabilities. The parameter learning is formulated as a convex optimization problem and an effective sampling algorithm is proposed for inference. CCDN is flexible in absorbing non-symmetric prior knowledge. The performance of CCDN on multiple datasets provides evidence of its structure recovery ability and superior effectiveness and efficiency as compared to the state-of-the-art alternatives.

Link prediction is a fundamental task in such areas as social network analysis, information retrieval, and bioinformatics. Usually link prediction methods use the link structures or node attributes as the sources of information. Recently, the relational topic model (RTM) and its variants have been proposed as hybrid methods that jointly model both sources of information and achieve very promising accuracy. However, the representations (features) learned by them are still not effective enough to represent the nodes (items). To address this problem, we generalize recent advances in deep learning from solely modeling i.i.d. sequences of attributes to jointly modeling graphs and non-i.i.d. sequences of attributes. Specifically, we follow the Bayesian deep learning framework and devise a hierarchical Bayesian model, called relational deep learning (RDL), to jointly model high-dimensional node attributes and link structures with layers of latent variables. Due to the multiple nonlinear transformations in RDL, standard variational inference is not applicable. We propose to utilize the product of Gaussians (PoG) structure in RDL to relate the inferences on different variables and derive a generalized variational inference algorithm for learning the variables and predicting the links. Experiments on three real-world datasets show that RDL works surprisingly well and significantly outperforms the state of the art.

We address the problem of general function release under differential privacy, by developing a functional mechanism that applies under the weak assumptions of oracle access to target function evaluation and sensitivity. These conditions permit treatment of functions described explicitly or implicitly as algorithmic black boxes. We achieve this result by leveraging the iterated Bernstein operator for polynomial approximation of the target function, and polynomial coefficient perturbation. Under weak regularity conditions, we establish fast rates on utility measured by high-probability uniform approximation. We provide a lower bound on the utility achievable for any functional mechanism that is epsilon-differentially private. The generality of our mechanism is demonstrated by the analysis of a number of example learners, including naive Bayes, non-parametric estimators and regularized empirical risk minimization. Competitive rates are demonstrated for kernel density estimation; and epsilon-differential privacy is achieved for a broader class of support vector machines than known previously.