We propose a black-box variational inference method to approximate intractable distributions with an increasingly rich approximating class. Our method, termed variational boosting, iteratively refines an existing variational approximation by solving a sequence of optimization problems, allowing the practitioner to trade computation time for accuracy. We show how to expand the variational approximating class by incorporating additional covariance structure and by introducing new components to form a mixture. We apply variational boosting to synthetic and real statistical models, and show that resulting posterior inferences compare favorably to existing posterior approximation algorithms in both accuracy and efficiency.

With the rapid growth of online sharing media, we are facing a huge collection of videos. In the meantime, due to the volume and complexity of video data, it can be tedious and time consuming to index or annotate videos. In this paper, we propose to generate temporal descriptions of videos by exploiting the information of crowdsourced time-sync comments which are receiving increasing popularity on many video sharing websites. In this framework, representative and interesting comments of a video are selected and highlighted along the timeline, which provide an informative description of the video in a time-sync manner. The challenge of the proposed application comes from the extremely informal and noisy nature of the comments, which are usually short sentences and on very different topics. To resolve these issues, we propose a novel temporal summarization model based on the data reconstruction principle, where representative comments are selected in order to best reconstruct the original corpus at the text level as well as the topic level while incorporating the temporal correlations of the comments. Experimental results on real-world data demonstrate the effectiveness of the proposed framework and justify the idea of exploiting crowdsourced time-sync comments as a bridge to describe videos.

In classical planning, cost partitioning is a method for admissibly combining a set of heuristic estimators by distributing operator costs among the heuristics. An optimal cost partitioning is often prohibitively expensive to compute. Saturated cost partitioning is an alternative that is much faster to compute and has been shown to offer high-quality heuristic guidance on Cartesian abstractions. However, its greedy nature makes it highly susceptible to the order in which the heuristics are considered. We show that searching in the space of orders leads to significantly better heuristic estimates than with previously considered orders. Moreover, using multiple orders leads to a heuristic that is significantly better informed than any single-order heuristic. In experiments with Cartesian abstractions, the resulting heuristic approximates the optimal cost partitioning very closely.

Hybrid (mixed discrete and continuous) state and action Markov Decision Processes (HSA-MDPs) provide an expressive formalism for modeling stochastic and concurrent sequential decision-making problems. Existing solvers for HSA-MDPs are either limited to very restricted transition distributions, require knowledge of domain-specific basis functions to achieve good approximations, or do not scale. We explore a domain-independent approach based on the framework of hindsight optimization (HOP) for HSA-MDPs, which uses an upper bound on the finite-horizon action values for action selection. Our main contribution is a linear time reduction to a Mixed Integer Linear Program (MILP) that encodes the HOP objective, when the dynamics are specified as location-scale probability distributions parametrized by Piecewise Linear (PWL) functions of states and actions. In addition, we show how to use the same machinery to select actions based on a lower-bound generated by straight line plans. Our empirical results show that the HSA-HOP approach effectively scales to high-dimensional problems and outperforms baselines that are capable of scaling to such large hybrid MDPs.

Structured knowledge about concepts plays an increasingly important role in areas such as information retrieval. The available ontologies and knowledge graphs that encode such conceptual knowledge, however, are inevitably incomplete. This observation has led to a number of methods that aim to automatically complete existing knowledge bases. Unfortunately, most existing approaches rely on black box models, e.g. formulated as global optimization problems, which makes it difficult to support the underlying reasoning process with intuitive explanations. In this paper, we propose a new method for knowledge base completion, which uses interpretable conceptual space representations and an explicit model for inductive inference that is closer to human forms of commonsense reasoning. Moreover, by separating the task of representation learning from inductive reasoning, our method is easier to apply in a wider variety of contexts. Finally, unlike optimization based approaches, our method can naturally be applied in settings where various logical constraints between the extensions of concepts need to be taken into account.

We introduce the problem Max#SAT, an extension of model counting (#SAT). Given a formula over sets of variables X, Y, and Z, the Max#SAT problem is to maximize over the variables X the number of assignments to Y that can be extended to a solution with some assignment to Z. We demonstrate that Max#SAT has applications in many areas, showing how it can be used to solve problems in probabilistic inference (marginal MAP), planning, program synthesis, and quantitative information flow analysis. We also give an algorithm which by making only polynomially many calls to an NP oracle can approximate the maximum count to within any desired multiplicative error. The NP queries needed are relatively simple, arising from recent practical approximate model counting and sampling algorithms, which allows our technique to be effectively implemented with a SAT solver. Through several experiments we show that our approach can be successfully applied to interesting problems.

Transductive semi-supervised learning can only predict labels for unlabeled data appearing in training data, and can not predict labels for testing data never appearing in training set. To handle this out-of-sample problem, many inductive methods make a constraint such that the predicted label matrix should be exactly equal to a linear model. In practice, this constraint might be too rigid to capture the manifold structure of data. In this paper, we relax this rigid constraint and propose to use an elastic constraint on the predicted label matrix such that the manifold structure can be better explored. Moreover, since unlabeled data are often very abundant in practice and usually there are some outliers, we use a non-squared loss instead of the traditional squared loss to learn a robust model. The derived problem, although is convex, has so many nonsmooth terms, which make it very challenging to solve. In the paper, we propose an efficient optimization algorithm to solve a more general problem, based on which we find the optimal solution to the derived problem.

Multi-instance multi-label learning (MIML) is a learning paradigm where an object is represented by a bag of instances and each bag is associated with multiple labels. Ordinary MIML setting assumes a fixed target label set. In real applications, multiple novel labels may exist outside this set, but hidden in the training data and unknown to the MIML learner. Existing MIML approaches are unable to discover the hidden novel labels, let alone predicting these labels in the previously unseen test data. In this paper, we propose the first approach to discover multiple novel labels in MIML problem using an efficient augmented lagrangian optimization, which has a bag-dependent loss term and a bag-independent clustering regularization term, enabling the known labels and multiple novel labels to be modeled simultaneously. The effectiveness of the proposed approach is validated in experiments.

Bäckström has previously studied a number of optimization problems for partial-order plans, like finding a minimum deordering (MCD) or reordering (MCR), and finding the minimum parallel execution length (PPL), which are all NP-complete. We revisit these problems, but applying parameterized complexity analysis rather than standard complexity analysis. We consider various parameters, including both the original and desired size of the plan order, as well as its width and height. Our findings include that MCD and MCR are W[2]-hard and in W[P] when parameterized with the desired order size, and MCD is fixed-parameter tractable (fpt) when parameterized with the original order size. Problem PPL is fpt if parameterized with the size of the non-concurrency relation, but para-NP-hard in most other cases. We also consider this problem when the number (k) of agents, or processors, is restricted, finding that this number is a crucial parameter; this problem is fixed-parameter tractable with the order size, the parallel execution length and k as parameter, but para-NP-hard without k as parameter.

Personalized ranking is usually considered as an ultimate goal of recommendation systems, but it suffers from efficiency issues when making recommendations. To this end, we propose a learning-based hashing framework called Discrete Personalized Ranking (DPR), to map users and items to a Hamming space, where user-item affinity can be efficiently calculated via Hamming distance. Due to the existence of discrete constraints, it is possible to exploit a two-stage learning procedure for learning binary codes according to most existing methods. This two-stage procedure consists of relaxed optimization by discarding discrete constraints and subsequent binary quantization. However, such a procedure has been shown resulting in a large quantization loss, so that longer binary codes would be required. To this end, DPR directly tackles the discrete optimization problem of personalized ranking. And the balance and un-correlation constraints of binary codes are imposed to derive compact but informatics binary codes. Based on the evaluation on several datasets, the proposed framework shows consistent superiority to the competing baselines even though only using shorter binary code.