We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous variable: Inspired by Occam's razor, we assume that the exogenous variable is simple in the true causal direction. We quantify simplicity using R\'enyi entropy. Our main result is that, under natural assumptions, if the exogenous variable has low $H_0$ entropy (cardinality) in the true direction, it must have high $H_0$ entropy in the wrong direction. We establish several algorithmic hardness results about estimating the minimum entropy exogenous variable. We show that the problem of finding the exogenous variable with minimum entropy is equivalent to the problem of finding minimum joint entropy given $n$ marginal distributions, also known as minimum entropy coupling problem. We propose an efficient greedy algorithm for the minimum entropy coupling problem, that for $n=2$ provably finds a local optimum. This gives a greedy algorithm for finding the exogenous variable with minimum $H_1$ (Shannon Entropy). Our greedy entropy-based causal inference algorithm has similar performance to the state of the art additive noise models in real datasets. One advantage of our approach is that we make no use of the values of random variables but only their distributions. Our method can therefore be used for causal inference for both ordinal and also categorical data, unlike additive noise models.

For over a quarter century, security-relevant detection has been driven by models learned from input features collected from real or simulated environments. An artifact (e.g., network event, potential malware sample, suspicious email) is deemed malicious or non-malicious based on its similarity to the learned model at run-time. However, the training of the models has been historically limited to only those features available at run time. In this paper, we consider an alternate model construction approach that trains models using forensic "privileged" information--features available at training time but not at runtime--to improve the accuracy and resilience of detection systems. In particular, we adapt and extend recent advances in knowledge transfer, model influence, and distillation to enable the use of forensic data in a range of security domains. Our empirical study shows that privileged information increases detection precision and recall over a system with no privileged information: we observe up to 7.7% relative decrease in detection error for fast-flux bot detection, 8.6% for malware traffic detection, 7.3% for malware classification, and 16.9% for face recognition. We explore the limitations and applications of different privileged information techniques in detection systems. Such techniques open the door to systems that can integrate forensic data directly into detection models, and therein provide a means to fully exploit the information available about past security-relevant events.

We consider Bayesian optimization of an expensive-to-evaluate black-box objective function, where we also have access to cheaper approximations of the objective. In general, such approximations arise in applications such as reinforcement learning, engineering, and the natural sciences, and are subject to an inherent, unknown bias. This model discrepancy is caused by an inadequate internal model that deviates from reality and can vary over the domain, making the utilization of these approximations a non-trivial task. We present a novel algorithm that provides a rigorous mathematical treatment of the uncertainties arising from model discrepancies and noisy observations. Its optimization decisions rely on a value of information analysis that extends the Knowledge Gradient factor to the setting of multiple information sources that vary in cost: each sampling decision maximizes the predicted benefit per unit cost. We conduct an experimental evaluation that demonstrates that the method consistently outperforms other state-of-the-art techniques: it finds designs of considerably higher objective value and additionally inflicts less cost in the exploration process.

In this paper, we deal with two challenges for measuring the similarity of the subject identities in practical video-based face recognition - the variation of the head pose in uncontrolled environments and the computational expense of processing videos. Since the frame-wise feature mean is unable to characterize the pose diversity among frames, we define and preserve the overall pose diversity and closeness in a video. Then, identity will be the only source of variation across videos since the pose varies even within a single video. Instead of simply using all the frames, we select those faces whose pose point is closest to the centroid of the K-means cluster containing that pose point. Then, we represent a video as a bag of frame-wise deep face features while the number of features has been reduced from hundreds to K. Since the video representation can well represent the identity, now we measure the subject similarity between two videos as the max correlation among all possible pairs in the two bags of features. On the official 5,000 video-pairs of the YouTube Face dataset for face verification, our algorithm achieves a comparable performance with VGG-face that averages over deep features of all frames. Other vision tasks can also benefit from the generic idea of employing geometric cues to improve the descriptiveness of deep features.

Inverse classification, the process of making meaningful perturbations to a test point such that it is more likely to have a desired classification, has previously been addressed using data from a single static point in time. Such an approach yields inflated probability estimates, stemming from an implicitly made assumption that recommendations are implemented instantaneously. We propose using longitudinal data to alleviate such issues in two ways. First, we use past outcome probabilities as features in the present. Use of such past probabilities ties historical behavior to the present, allowing for more information to be taken into account when making initial probability estimates and subsequently performing inverse classification. Secondly, following inverse classification application, optimized instances' unchangeable features (e.g., age) are updated using values from the next longitudinal time period. Optimized test instance probabilities are then reassessed. Updating the unchangeable features in this manner reflects the notion that improvements in outcome likelihood, which result from following the inverse classification recommendations, do not materialize instantaneously. As our experiments demonstrate, more realistic estimates of probability can be obtained by factoring in such considerations.

In this paper, we propose guaranteed spectral methods for learning a broad range of topic models, which generalize the popular Latent Dirichlet Allocation (LDA). We overcome the limitation of LDA to incorporate arbitrary topic correlations, by assuming that the hidden topic proportions are drawn from a flexible class of Normalized Infinitely Divisible (NID) distributions. NID distributions are generated through the process of normalizing a family of independent Infinitely Divisible (ID) random variables. The Dirichlet distribution is a special case obtained by normalizing a set of Gamma random variables. We prove that this flexible topic model class can be learned via spectral methods using only moments up to the third order, with (low order) polynomial sample and computational complexity. The proof is based on a key new technique derived here that allows us to diagonalize the moments of the NID distribution through an efficient procedure that requires evaluating only univariate integrals, despite the fact that we are handling high dimensional multivariate moments. In order to assess the performance of our proposed Latent NID topic model, we use two real datasets of articles collected from New York Times and Pubmed. Our experiments yield improved perplexity on both datasets compared with the baseline.

How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over the uncertainty in a latent path, like a state space model, we improve the state of the art results on the Blizzard and TIMIT speech modeling data sets by a large margin, while achieving comparable performances to competing methods on polyphonic music modeling.

We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of observed affinity values. Our approach exploits the observation that while preferences are often recorded as numerical scores, the predictive quantity of interest is the underlying rankings. Thus, attempts to closely match the recorded scores may lead to overfitting and impair generalization performance. Instead, we propose an estimator that directly fits the underlying preference order, combined with nuclear norm constraints to encourage low--rank parameters. Besides (approximate) correctness of the ranking order, the proposed estimator makes no generative assumption on the numerical scores of the observations. One consequence is that the proposed estimator can fit any consistent partial ranking over a subset of the items represented as a directed acyclic graph (DAG), generalizing standard techniques that can only fit preference scores. Despite this generality, for supervision representing total or blockwise total orders, the computational complexity of our algorithm is within a $\log$ factor of the standard algorithms for nuclear norm regularization based estimates for matrix completion. We further show promising empirical results for a novel and challenging application of collaboratively ranking of the associations between brain--regions and cognitive neuroscience terms.

Algorithms with fast convergence, small number of data access, and low per-iteration complexity are particularly favorable in the big data era, due to the demand for obtaining \emph{highly accurate solutions} to problems with \emph{a large number of samples} in \emph{ultra-high} dimensional space. Existing algorithms lack at least one of these qualities, and thus are inefficient in handling such big data challenge. In this paper, we propose a method enjoying all these merits with an accelerated convergence rate $O(\frac{1}{k^2})$. Empirical studies on large scale datasets with more than one million features are conducted to show the effectiveness of our methods in practice.

Semi-supervised wrapper methods are concerned with building effective supervised classifiers from partially labeled data. Though previous works have succeeded in some fields, it is still difficult to apply semi-supervised wrapper methods to practice because the assumptions those methods rely on tend to be unrealistic in practice. For practical use, this paper proposes a novel semi-supervised wrapper method, Dual Teaching, whose assumptions are easy to set up. Dual Teaching adopts two external classifiers to estimate the false positives and false negatives of the base learner. Only if the recall of every external classifier is greater than zero and the sum of the precision is greater than one, Dual Teaching will train a base learner from partially labeled data as effectively as the fully-labeled-data-trained classifier. The effectiveness of Dual Teaching is proved in both theory and practice.